Regime

Any Reynolds number — viscosity is absent

Every figure drawn under this hypothesis — 1209 of them — with the essay each one belongs to and the generator that drew it.

1209 figure placements state this regime. The strip along the foot of every figure names two things — the model that produced it and the regime it holds in — and this listing is read back out of the finished drawing rather than from what produced it.

A ball that swings without spinning — Γ = -3.4 · ideal-cylinder
A big slow push — any Reynolds number — viscosity is absent from the model entirely · actuator-disc · hero
A big slow push — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
A big slow push — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
A big slow push — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
A big slow push — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
A big slow push — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
A big slow push — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
A big slow push — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
A blade that flies through what it shed — miss distance 0.05 R, circulation 12 m²/s, section speed 200 m/s — inviscid, incompressible · what-a-wake-hands-back · hero
A blade that flies through what it shed — miss distance 0.05 R, circulation 12 m²/s, section speed 200 m/s — inviscid, incompressible · what-a-wake-hands-back
A blade that flies through what it shed — circulation 12 m²/s, section speed 200 m/s — inviscid, incompressible · what-a-wake-hands-back
A blade that flies through what it shed — four blades, 300 rpm, 6 m radius — inviscid, incompressible · what-a-wake-hands-back
A blade that flies through what it shed — 12 m²/s, 200 m/s section speed, four blades at 300 rpm — inviscid, incompressible · what-a-wake-hands-back
A blade that flies through what it shed — 30 upstream blades, 18 per cent deficit, wake width 12 per cent of a pitch — inviscid, incompressible · what-a-wake-hands-back
A body with no lift, and a moment anyway — α = 6°, fineness 6 · ideal flow, viscosity absent · outer-boundary · hero
A body with no lift, and a moment anyway — α = 6°, fineness 6 · ideal flow, viscosity absent · outer-boundary
A body with no lift, and a moment anyway — α = 6°, fineness 6 · ideal flow, viscosity absent · outer-boundary
A body with no lift, and a moment anyway — α = 6°, fineness 6 · ideal flow, viscosity absent · outer-boundary
A body with no lift, and a moment anyway — α = 6°, fineness 12 · ideal flow, viscosity absent · outer-boundary
A body with no lift, and a moment anyway — ideal flow — any Reynolds number, viscosity is absent · outer-boundary
A body with no lift, and a moment anyway — α = 6°, fineness 6 · ideal flow, viscosity absent · outer-boundary
A body with no lift, and a moment anyway — any Reynolds number — inviscid, and vortex breakdown is not modelled at all · delta-wing
A boundary that only exists over a window — any Reynolds number — incompressibility is the only hypothesis used · critical-points
A boundary that only exists over a window — any Reynolds number — this is kinematics, and no equation of motion is solved · stirring
A breeze the boat cannot use — any Reynolds number — a 25 m² rig at 3.6 m, a righting moment of 4.0 kN m, hull drag angle 6° · sailing-polar · hero
A breeze the boat cannot use — any Reynolds number — a 25 m² rig at 3.6 m, a righting moment of 4.0 kN m · sailing-polar
A breeze the boat cannot use — any Reynolds number — a 25 m² rig at 3.6 m, a righting moment of 4.0 kN m · sailing-polar
A breeze the boat cannot use — any Reynolds number — a 25 m² rig at 3.6 m, a righting moment of 4.0 kN m, hull drag angle 6° · sailing-polar
A breeze the boat cannot use — any Reynolds number — a 25 m² rig at 3.6 m, a righting moment of 4.0 kN m, hull drag angle 6° · sailing-polar
A breeze the boat cannot use — any Reynolds number — a 25 m² rig at 3.6 m, a righting moment of 4.0 kN m, hull drag angle 6° · sailing-polar
A breeze the boat cannot use — any Reynolds number — a 25 m² rig at 3.6 m, a righting moment of 4.0 kN m, hull drag angle 6° · sailing-polar
A breeze the boat cannot use — any Reynolds number — a 25 m² rig at 3.6 m, a righting moment of 4.0 kN m, hull drag angle 6° · sailing-polar
A calculation with no memory in it — α = 5° · any Reynolds number — inviscid, thin, small incidence · wagner-lift
A cushion that changes its physics — inviscid, any Reynolds number above the squeeze crossover · ground-effect
A drift made of two things that average to zero — steepness ak = 0.05, deep water — irrotational, inviscid · what-a-parcel-remembers · hero
A drift made of two things that average to zero — steepness ak = 0.05, deep water — irrotational, inviscid · what-a-parcel-remembers
A drift made of two things that average to zero — steepness ak = 0.05, deep water — irrotational, inviscid · what-a-parcel-remembers
A finite force from an infinite speed — incidence 6°, suction collected in full · edge-suction · hero
A finite force from an infinite speed — incidence 6°, suction collected in full · edge-suction
A finite force from an infinite speed — incidence 6°, any Reynolds number · edge-suction
A finite force from an infinite speed — section drag only — no friction, no finite span · edge-suction
A finite force from an infinite speed — incidence 10°, any Reynolds number · edge-suction
A finite force from an infinite speed — any Reynolds number · ideal-cylinder
A keel flies wherever the course puts it — any Reynolds number — a 0.9 m² keel of 1.3 m span, hull resistance 0.012 m² of drag area · sailing-polar · hero
A keel flies wherever the course puts it — any Reynolds number — a 0.9 m² keel of 1.3 m span, hull resistance 0.012 m² of drag area · sailing-polar
A keel flies wherever the course puts it — any Reynolds number — a 0.9 m² keel of 1.3 m span, hull resistance 0.012 m² of drag area · sailing-polar
A keel flies wherever the course puts it — any Reynolds number — a 0.9 m² keel of 1.3 m span, hull resistance 0.012 m² of drag area · sailing-polar
A keel flies wherever the course puts it — any Reynolds number — a 0.9 m² keel of 1.3 m span, hull resistance 0.012 m² of drag area · sailing-polar
A keel flies wherever the course puts it — any Reynolds number — a 25 m² rig at 3.6 m, a righting moment of 4.0 kN m; a 0.9 m² keel of 1.3 m span, hull resistance 0.012 m² of drag area · sailing-polar
A keel flies wherever the course puts it — any Reynolds number — a 25 m² rig at 3.6 m, a righting moment of 4.0 kN m; a 0.9 m² keel of 1.3 m span, hull resistance 0.012 m² of drag area · sailing-polar
A keel flies wherever the course puts it — any Reynolds number — a stall at Cₗ 0.9 is prescribed, not computed · sailing-polar
A layer that is an integral of everything upstream — laminar, and independent of the Reynolds number in this form · bl-profile
A layer with a kink in it — any Reynolds number — viscosity is absent from the criterion · shear-instability · hero
A layer with a kink in it — any Reynolds number — viscosity is absent from the criterion · shear-instability
A layer with a kink in it — any Reynolds number — viscosity is absent from the criterion · shear-instability
A layer with a kink in it — boundary-layer theory — the inflection criterion is inviscid and the profiles are not · shear-instability
A layer with a kink in it — any Reynolds number — viscosity is absent from the criterion · shear-instability
A layer with a kink in it — boundary-layer theory — the inflection criterion is inviscid and the profiles are not · shear-instability
A lighter spar turns a box wing into a biplane — inviscid Trefftz-plane lattice, lift and root moment of the lift about the centreline constrained; mean-zero gauge · closed-wake · hero
A lighter spar turns a box wing into a biplane — inviscid Trefftz-plane lattice, lift and root moment of the lift about the centreline constrained; mean-zero gauge · closed-wake
A lighter spar turns a box wing into a biplane — inviscid Trefftz-plane lattice, lift and root moment of the lift about the centreline constrained; mean-zero gauge · closed-wake
A lighter spar turns a box wing into a biplane — inviscid Trefftz-plane lattice, lift and root moment of the lift about the centreline constrained; mean-zero gauge · closed-wake
A lighter spar turns a box wing into a biplane — inviscid Trefftz-plane lattice, lift and root moment of the lift about the centreline constrained; mean-zero gauge · closed-wake
A lighter spar turns a box wing into a biplane — inviscid; gap 0.2 of span, moment 0.8 of the monoplane's; mean-zero gauge · closed-wake
A lighter spar turns a box wing into a biplane — inviscid Trefftz-plane lattice, lift and root moment of the lift about the centreline constrained; mean-zero gauge · closed-wake
A lighter spar turns a box wing into a biplane — inviscid Trefftz-plane lattice, lift and root moment of the lift about the centreline constrained; mean-zero gauge · closed-wake
A loss with no viscosity in it — any Reynolds number — the loss follows from the geometry, with no viscosity in it · expansion-loss · hero
A loss with no viscosity in it — any Reynolds number — the loss follows from the geometry, with no viscosity in it · expansion-loss
A loss with no viscosity in it — any Reynolds number — the loss follows from the geometry, with no viscosity in it · expansion-loss
A loss with no viscosity in it — any Reynolds number — the loss follows from the geometry, with no viscosity in it · expansion-loss
A loss with no viscosity in it — any Reynolds number — the loss follows from the geometry, with no viscosity in it · expansion-loss
A loss with no viscosity in it — any Reynolds number — the loss follows from the geometry, with no viscosity in it · expansion-loss
A loss with no viscosity in it — any Reynolds number — the loss follows from the geometry, with no viscosity in it · expansion-loss
A loss with no viscosity in it — any Reynolds number — the loss follows from the geometry, with no viscosity in it · expansion-loss
A loss with no viscosity in it — steady, incompressible, inviscid — 3 of 4 rows break one · bernoulli-limits
A loss with no viscosity in it — 8° incidence · control-volume
A pump with no engine — any Reynolds number — every loss set to zero, so this is a bound · ram-cycle · hero
A pump with no engine — any Reynolds number — every loss set to zero, so this is a bound · ram-cycle
A pump with no engine — any Reynolds number — an upper bound rather than a performance · ram-cycle
A pump with no engine — any Reynolds number — no loss model at all, so both are upper bounds · ram-cycle
A pump with no engine — any Reynolds number — the valve shuts at once, so this is the ceiling · ram-cycle
A pump with no engine — any Reynolds number — the audit needs no detail of the valve · ram-cycle
A pump with no engine — any Reynolds number — every loss set to zero, so this is a bound · ram-cycle
A pump with no engine — any Reynolds number — friction is absent from the model by choice · surge
A pump with no engine — any Reynolds number — no loss model at all, so both are upper bounds · ram-cycle
A relation with no turbulence in it — any Reynolds number — the relation carries no dynamics · field-statistics
A ring moves because it is bent — any Reynolds number — inviscid; the cutoff stands in for a core · vortex-ring · hero
A ring moves because it is bent — any Reynolds number — an inviscid filament, and the core is a stated cutoff · vortex-ring
A ring moves because it is bent — any Reynolds number — inviscid; the cutoff stands in for a core · vortex-ring
A ring moves because it is bent — any Reynolds number — inviscid, and the cores neither diffuse nor deform · vortex-ring
A ring moves because it is bent — any Reynolds number — inviscid; the core is a stated model, not a solution · vortex-ring
A ring moves because it is bent — any Reynolds number — inviscid, and the cores are points · point-vortices
A ring moves because it is bent — any Reynolds number — inviscid; the core is a stated model, not a solution · vortex-ring
A ring moves because it is bent — any Reynolds number — inviscid; the cutoff stands in for a core · vortex-ring
A ring moves because it is bent — drawn in the fluid's frame, not the wing's · vortex-pair
A roll that feeds itself — any Reynolds number — the curve past the peak is prescribed, not solved · flight-envelope · hero
A roll that feeds itself — any Reynolds number — the curve past the peak is prescribed, not solved · flight-envelope
A roll that feeds itself — any Reynolds number — the post-stall curve is prescribed, not solved · flight-envelope
A roll that feeds itself — any Reynolds number — the curve past the peak is prescribed, not solved · flight-envelope
A roll that feeds itself — any Reynolds number — the post-stall curve is prescribed, not solved · flight-envelope
A roll that feeds itself — any Reynolds number — the maximum is assumed, not solved · flight-envelope
A row is not a set of aerofoils — solidity 0.02 to 3 at 30° stagger — an inviscid blade row · circulation-ledger · hero
A row is not a set of aerofoils — any Reynolds number — an inviscid row, at any spacing · circulation-ledger
A row is not a set of aerofoils — solidity 1, stagger 30° — an inviscid blade row · circulation-ledger
A row is not a set of aerofoils — solidity 0.02 to 2 at 30° stagger — an inviscid blade row · circulation-ledger
A row is not a set of aerofoils — solidity 0.02 to 3 at 30° stagger — an inviscid blade row · circulation-ledger
A row is not a set of aerofoils — solidity 0.1 to 2 at 30° stagger, inlet at 45° — an inviscid blade row · circulation-ledger
A row is not a set of aerofoils — solidity 0.02 to 2 at 30° stagger — an inviscid blade row · circulation-ledger
A row is not a set of aerofoils — solidity 0.1 to 2 at 30° stagger, inlet at 45° — an inviscid blade row · circulation-ledger
A row is not a set of aerofoils — an inviscid blade row at 30° stagger, inlet at 45° · circulation-ledger
A row that meets the row before it — 30 upstream blades, 18 per cent deficit, wake width 12 per cent of a pitch — inviscid, incompressible · what-a-wake-hands-back · hero
A row that meets the row before it — 30 upstream blades, 18 per cent deficit, wake width 12 per cent of a pitch — inviscid, incompressible · what-a-wake-hands-back
A row that meets the row before it — 30 upstream blades, 18 per cent deficit — inviscid, incompressible · what-a-wake-hands-back
A row that meets the row before it — 30 upstream blades, wake width 12 per cent of a pitch — inviscid, incompressible · what-a-wake-hands-back
A row that meets the row before it — 30 upstream blades, 18 per cent deficit — inviscid, incompressible · what-a-wake-hands-back
A row that meets the row before it — 30 upstream blades — the ratio is dimensionless, inviscid · what-a-wake-hands-back
A row that meets the row before it — 30 upstream blades, 18 per cent deficit — inviscid, incompressible · what-a-wake-hands-back
A row that meets the row before it — solidity 1, stagger 30° — an inviscid blade row · circulation-ledger
A row that meets the row before it — miss distance 0.05 R, circulation 12 m²/s, section speed 200 m/s — inviscid, incompressible · what-a-wake-hands-back
A scalar is a record of where its fluid was — any Reynolds number — molecular diffusion is absent, so nothing ever blurs · stirring
A scalar is a record of where its fluid was — steady, so a photograph would show no change at all · velocity-field
A slot is not a nozzle — any Reynolds number — inviscid, at 4° with a 2.5% gap · two-element · hero
A slot is not a nozzle — any Reynolds number — inviscid, at 4° with a 2.5% gap · two-element
A slot is not a nozzle — any Reynolds number — inviscid, 30° of flap at 4° · two-element
A slot is not a nozzle — any Reynolds number — inviscid, at 4° with the rigging held · two-element
A slot is not a nozzle — any Reynolds number — inviscid, 20° of flap at 4° · two-element
A slot is not a nozzle — any Reynolds number — inviscid, 30° of flap at 4° · two-element
A slot is not a nozzle — any Reynolds number — inviscid, so nothing here can separate · two-element
A slot is not a nozzle — any Reynolds number — inviscid, at 6° with a 2.0% gap · two-element
A slot is not a nozzle — any Reynolds number — inviscid, at 2° with the rigging held · two-element
A stall that is a place — any Reynolds number — the wake's effect on the tail is modelled, not solved · flight-envelope · hero
A stall that is a place — any Reynolds number — the wake's effect on the tail is modelled, not solved · flight-envelope
A stall that is a place — any Reynolds number — the wake's effect on the tail is modelled, not solved · flight-envelope
A stall that is a place — any Reynolds number — the wake's effect on the tail is modelled, not solved · flight-envelope
A stall that is a place — any Reynolds number — the wake's effect on the tail is modelled, not solved · flight-envelope
A stall that is a place — any Reynolds number — the curve past the peak is prescribed, not solved · flight-envelope
A surface that remembers the diaphragm — p₄/p₁ = 10 · inviscid, one-dimensional, γ = 1.4 throughout · shock-tube
A transition that needs a second number — Rayleigh's inviscid criterion — no Reynolds number and no Taylor number in it · regime-collapse
A transition that needs a second number — Rayleigh's inviscid criterion — the boundary contains no Taylor number · regime-collapse
A transition that needs a second number — Rayleigh's inviscid criterion — the boundary contains no Taylor number · regime-collapse
A wake that closes on itself — ideal flow — any Reynolds number, viscosity is absent · closed-wake · hero
A wake that closes on itself — ideal flow — any Reynolds number, viscosity is absent · closed-wake
A wake that closes on itself — ideal flow — any Reynolds number, viscosity is absent · closed-wake
A wake that closes on itself — ideal flow — any Reynolds number, viscosity is absent · closed-wake
A wake that closes on itself — ideal flow — any Reynolds number, viscosity is absent · closed-wake
A wake that closes on itself — ideal flow — any Reynolds number, viscosity is absent · closed-wake
A wake that closes on itself — any Reynolds number — inviscid, one lift constraint · wake-plane
A wake that says what made it — a 220-tonne aircraft at 75 m/s at sea level — inviscid, a rolled-up vortex pair · what-a-wake-hands-back · hero
A wake that says what made it — a 220-tonne aircraft at 75 m/s at sea level — inviscid, a rolled-up vortex pair · what-a-wake-hands-back
A wake that says what made it — a 220-tonne aircraft at 75 m/s at sea level — inviscid, a rolled-up vortex pair · what-a-wake-hands-back
A wake that says what made it — the same aircraft — algebraic, no model uncertainty included — inviscid · what-a-wake-hands-back
A wake that says what made it — quiescent atmosphere; a turbulent one is far faster — inviscid, with a stated decay rate · what-a-wake-hands-back
A wake that says what made it — elliptic loading, 75 m/s, sea level — inviscid · what-a-wake-hands-back
A wake that says what made it — a 220-tonne aircraft at 75 m/s at sea level — inviscid, a rolled-up vortex pair · what-a-wake-hands-back
A wake that says what made it — any Reynolds number — inviscid, and the core size is assumed · wake-rollup
A wake that says what made it — circulation 12 m²/s, section speed 200 m/s — inviscid, incompressible · what-a-wake-hands-back
A wall made by reflection — any Re — inviscid · flow-net · hero
A wall made by reflection — exact · flow-net
A wall made by reflection — exact · flow-net
A wall made by reflection — there is no wall here · flow-net
A wall made by reflection — drawn in the fluid's frame, not the wing's · vortex-pair
A wall made by reflection — any Re — inviscid · flow-net
A wall made by reflection — any Re — inviscid · flow-net
A wall made by reflection — Γ = -3.4 · ideal-cylinder
A wall puts in exactly its own speed — any Reynolds number, laminar swirl — outer boundary at 300 radii; balanced to 6.9×10⁻⁶ · oscillating-wall · hero
A wall puts in exactly its own speed — any Reynolds number, a wall in its own plane — ν = 1.0×10⁻⁶ m²/s, 0.1 m/s · oscillating-wall
A wall puts in exactly its own speed — any Reynolds number — ν = 1.0×10⁻⁶ m²/s, a smooth start to 0.1 m/s over 1 s · oscillating-wall
A wall puts in exactly its own speed — any Reynolds number — ν = 1.0×10⁻⁶ m²/s, smooth starts to 0.1 m/s · oscillating-wall
A wall puts in exactly its own speed — any Reynolds number — wall speed 0.1 m/s, three fluids · oscillating-wall
A wall puts in exactly its own speed — any Reynolds number — ν = 1.0×10⁻⁶ m²/s, 0.1 m/s for 1 s · oscillating-wall
A wall puts in exactly its own speed — any Reynolds number, laminar swirl — outer boundary at 300 radii; balanced to 6.9×10⁻⁶ · oscillating-wall
A wall puts in exactly its own speed — any Reynolds number, laminar swirl — outer boundary at 949 radii · oscillating-wall
A wall puts in exactly its own speed — any Reynolds number, laminar swirl — outer boundary at 949 radii · oscillating-wall
A wall that is not quite there — any Reynolds number — this is a property of the equations, not of a flow · extra-condition
A wing that leaves the plane — any Reynolds number — inviscid, far downstream of everything · wake-plane · hero
A wing that leaves the plane — any Reynolds number — inviscid, far downstream of everything · wake-plane
A wing that leaves the plane — any Reynolds number — inviscid, one lift constraint and nothing else · wake-plane
A wing that leaves the plane — any Reynolds number — inviscid, one lift constraint · wake-plane
A wing that leaves the plane — any Reynolds number — inviscid, far downstream of everything · wake-plane
A wing that leaves the plane — any Reynolds number — inviscid, no profile drag anywhere · wake-plane
A wing that leaves the plane — any Reynolds number — inviscid, no profile drag anywhere · wake-plane
A wing that leaves the plane — any Reynolds number — inviscid, one lift constraint · wake-plane
A wing that leaves the plane — any Reynolds number — inviscid, no profile drag anywhere · wake-plane
Air must be pushed down, and the usual sum is wrong — 8° incidence · control-volume · hero
Air must be pushed down, and the usual sum is wrong — 8° incidence · control-volume
Air must be pushed down, and the usual sum is wrong — 8° incidence · aerofoil
Air must be pushed down, and the usual sum is wrong — 8° incidence · control-volume
Air must be pushed down, and the usual sum is wrong — 8° incidence · control-volume
Air must be pushed down, and the usual sum is wrong — 4° incidence · control-volume
Air must be pushed down, and the usual sum is wrong — 8° incidence · control-volume
Air must be pushed down, and the usual sum is wrong — 6° incidence · any Re — inviscid · equal-transit
An angle, not a speed — any Reynolds number — C_Lmax = 1.45, at 12000 N and sea level · flight-envelope · hero
An angle, not a speed — any Reynolds number — the maximum is assumed, not solved · flight-envelope
An angle, not a speed — any Reynolds number — C_Lmax = 1.45 held fixed throughout · flight-envelope
An angle, not a speed — any Reynolds number — C_Lmax = 1.45, at sea level · flight-envelope
An angle, not a speed — any Reynolds number — C_Lmax = 1.45, at 12000 N and sea level · flight-envelope
An angle, not a speed — any Reynolds number — C_Lmax = 1.45, at sea level · flight-envelope
An angle, not a speed — any Reynolds number — C_Lmax = 1.45, at 16000 N and sea level · flight-envelope
An angle, not a speed — any Reynolds number — C_Lmax = 1.45 held fixed throughout · flight-envelope
An angle, not a speed — any Reynolds number — the maximum is assumed, not solved · flight-envelope
Ask for the pressure, and see what shape that is — ideal flow at α = 4° — any Reynolds number, viscosity is absent · shape-from-pressure · hero
Ask for the pressure, and see what shape that is — ideal flow at α = 4° — any Reynolds number, viscosity is absent · shape-from-pressure
Ask for the pressure, and see what shape that is — 4° incidence, thickness 0.1, camber 0.02 · any Re — inviscid · conformal-map
Ask for the pressure, and see what shape that is — ideal flow — any Reynolds number, viscosity is absent · shape-from-pressure
Ask for the pressure, and see what shape that is — ideal flow — any Reynolds number, viscosity is absent · shape-from-pressure
Ask for the pressure, and see what shape that is — ideal flow at α = 4° — any Reynolds number, viscosity is absent · shape-from-pressure
Ask for the pressure, and see what shape that is — ideal flow at α = 4° — any Reynolds number, viscosity is absent · shape-from-pressure
Ask for the pressure, and see what shape that is — ideal flow — any Reynolds number, viscosity is absent · shape-from-pressure
Between hover and twice the hover inflow — any Reynolds number — viscosity absent; uniform inflow, axial flight · actuator-disc · hero
Between hover and twice the hover inflow — any Reynolds number — viscosity absent; uniform inflow, axial flight · actuator-disc
Between hover and twice the hover inflow — any Reynolds number — viscosity absent; uniform inflow, axial flight · actuator-disc
Between hover and twice the hover inflow — any Reynolds number — viscosity absent; uniform inflow, axial flight · actuator-disc
Between hover and twice the hover inflow — any Reynolds number — viscosity absent; uniform inflow, axial flight · actuator-disc
Between hover and twice the hover inflow — any Reynolds number — viscosity absent; uniform inflow, axial flight · actuator-disc
Between hover and twice the hover inflow — any Reynolds number — viscosity absent; uniform inflow, axial flight · actuator-disc
Between hover and twice the hover inflow — any Reynolds number — viscosity absent; uniform inflow, axial flight · actuator-disc
Bodies made out of nothing — any Re — inviscid · flow-net · hero
Bodies made out of nothing — closed: everything the source emits, the sink takes · flow-net
Bodies made out of nothing — 3 exact solutions added · any Re — inviscid · ideal-cylinder
Bodies made out of nothing — open downstream: this body has no back · flow-net
Bodies made out of nothing — the dashed circle is the equivalent doublet · flow-net
Bodies made out of nothing — no circulation · ideal-cylinder
Bodies made out of nothing — any Re — inviscid · flow-net
Bodies made out of nothing — any Re — inviscid · flow-net
Circulation is vorticity, added up — Γ = 2 · any Re — inviscid · stokes-loop
Circulation is vorticity, added up — 3 exact fields · any Re — inviscid · velocity-field
Drag in the theory that forbids it — the whole flow, at every point, as one quarter disc · cavity-flow
Drag in the theory that forbids it — any Reynolds number — viscosity is absent · cavity-flow
Drag in the theory that forbids it — no circulation · ideal-cylinder
Every compression becomes a shock in the end — an inviscid gas — the spectrum spreads with no loss at all · nonlinear-wave
Every compression becomes a shock in the end — an inviscid gas — the slope is a property of the quadratic nonlinearity · nonlinear-wave
Every flow is two flows — any Reynolds number — the comparison is kinematic · field-anatomy
Every mode decays and it grows anyway — any Reynolds number — viscosity is absent from the criterion · shear-instability
Every unstable wave is inside one circle — inviscid parallel flow, six profiles, wavenumbers from 0.05 to 0.99 · turbulent-exact · hero
Every unstable wave is inside one circle — inviscid parallel flow — Rayleigh's equation, with no Reynolds number in it · turbulent-exact
Every unstable wave is inside one circle — inviscid parallel flow, six profiles, wavenumbers from 0.05 to 0.99 · turbulent-exact
Every unstable wave is inside one circle — six inviscid profiles · turbulent-exact
Every unstable wave is inside one circle — six inviscid profiles at their own fastest wavenumber · turbulent-exact
Every unstable wave is inside one circle — six inviscid parallel profiles · turbulent-exact
Every wavelength at once — any Reynolds number — viscosity is absent from the criterion · shear-instability · hero
Every wavelength at once — any Reynolds number — viscosity is absent from the criterion · shear-instability
Every wavelength at once — any Reynolds number — viscosity is absent from the criterion · shear-instability
Every wavelength at once — any Reynolds number — viscosity is absent from the criterion · shear-instability
Every wavelength at once — any Reynolds number — viscosity is absent from the criterion · shear-instability
Every wavelength at once — any Reynolds number — viscosity is absent from the criterion · shear-instability
Everything about the start, except one vector — inviscid, the tube full, 2 m long under a 1 m head · added-mass
Everything happens in a layer you cannot see — no circulation · ideal-cylinder
Exact in the total, free in the profile — a small deficit against the free stream, where the balance is linear — any Reynolds number, the far-wake momentum balance · constraint-and-freedom · hero
Exact in the total, free in the profile — a small deficit against the free stream, where the balance is linear — any Reynolds number, the far-wake momentum balance · constraint-and-freedom
Exact in the total, free in the profile — profiles normalised to a deficit integral of exactly 0.1 free streams — any Reynolds number, the far-wake momentum balance · constraint-and-freedom
Exact in the total, free in the profile — the same four profiles, at one deficit integral — any Reynolds number, the far-wake momentum balance · constraint-and-freedom
Fast means low pressure — no circulation · ideal-cylinder · hero
Fast means low pressure — no circulation · ideal-cylinder
Fast means low pressure — no circulation · ideal-cylinder
Fast means low pressure — any Reynolds number · ideal-cylinder
Fast means low pressure — U = 1, 4, 16 · any Re — inviscid · ideal-cylinder
Fast means low pressure — 6° incidence · aerofoil
Fast means low pressure — 10° incidence · aerofoil
Fast means low pressure — U = 1 · any Re — inviscid · ideal-cylinder
Faster than the wind that drives it — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar · hero
Faster than the wind that drives it — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
Faster than the wind that drives it — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
Faster than the wind that drives it — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
Faster than the wind that drives it — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
Faster than the wind that drives it — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
Faster than the wind that drives it — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
Faster than the wind that drives it — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
Five numbers, one name — any Reynolds number — viscosity is absent from the criterion · shear-instability
Flows add up — no circulation · ideal-cylinder · hero
Flows add up — 3 exact solutions added · any Re — inviscid · ideal-cylinder
Flows add up — no circulation · ideal-cylinder
Flows add up — Γ = -3.4 · ideal-cylinder
Flows add up — Γ = -3.4 · any Re — inviscid · ideal-cylinder
Flows add up — 3 exact solutions added · any Re — inviscid · ideal-cylinder
Flows add up — fastest 1.91U · velocity-field
Four Bernoullis and one name — steady, inviscid, incompressible, rotational · wrong-picture · hero
Four Bernoullis and one name — steady, inviscid, incompressible, rotational · wrong-picture
Four Bernoullis and one name — steady, inviscid, rotational · wrong-picture
From a circle to a wing — 0° incidence, thickness 0.1, camber 0.08 · any Re — inviscid · conformal-map · hero
From a circle to a wing — 0° incidence, thickness 0.1, camber 0.08 · any Re — inviscid · conformal-map
From a circle to a wing — 0° incidence, thickness 0.02, camber 0 · any Re — inviscid · conformal-map
From a circle to a wing — 3×3 of the family · any Re — inviscid · conformal-map
From a circle to a wing — 0° incidence, thickness 0.1, camber 0.08 · any Re — inviscid · conformal-map
From a circle to a wing — 6° incidence, thickness 0.1, camber 0.08 · any Re — inviscid · conformal-map
From a circle to a wing — 6° incidence · aerofoil
From a circle to a wing — attached flow only · aerofoil
Half the jet speed takes everything — any Reynolds number — a frictionless bucket in a free jet · wheel · hero
Half the jet speed takes everything — any Reynolds number — a frictionless bucket in a free jet · wheel
Half the jet speed takes everything — any Reynolds number — no friction on the bucket, no windage · wheel
Half the jet speed takes everything — any Reynolds number — a frictionless bucket in a free jet · wheel
Half the jet speed takes everything — any Reynolds number — the relative speed is unchanged by the bucket · wheel
Half the jet speed takes everything — any Reynolds number — no friction in the bucket, no windage · wheel
Half the jet speed takes everything — any Reynolds number — a frictionless bucket in a free jet · wheel
Half the jet speed takes everything — any Reynolds number — no friction on the bucket, no windage · wheel
Half the jet speed takes everything — any Reynolds number — the relative speed is unchanged by the bucket · wheel
How far before a duct forgets what was fed into it — any Reynolds number — the loss follows from the geometry, with no viscosity in it · expansion-loss
How long the fluid has been in there — steady, incompressible, one dimensional — any Reynolds number · what-a-parcel-remembers · hero
How long the fluid has been in there — steady, incompressible, one dimensional — any Reynolds number · what-a-parcel-remembers
How long the fluid has been in there — steady: ∂u/∂t = 0 · velocity-field
How many things a flow must be told — any Reynolds number — this is a property of the equations, not of a flow · extra-condition
How many things a flow must be told — Laplace's equation — any Reynolds number, viscosity is absent · extra-condition
How many things a flow must be told — incompressible flow — any Reynolds number, this is kinematics · extra-condition
How many things a flow must be told — laminar boundary layer — the identity holds at any Reynolds number · extra-condition
How many things a flow must be told — ideal surface pressure — the cancellation holds at any Reynolds number · extra-condition
How much circulation is too much — Γ = -9 · any Re — inviscid · ideal-cylinder · hero
How much circulation is too much — Γ = -3 · any Re — inviscid · ideal-cylinder
How much circulation is too much — Γ = -12 · any Re — inviscid · ideal-cylinder
How much circulation is too much — Γ = -14 · any Re — inviscid · ideal-cylinder
How much circulation is too much — circulation -9 · ideal-cylinder
How much circulation is too much — Γ = -6 · ideal-cylinder
How much circulation is too much — 6° incidence · aerofoil
How much more than the least — any Reynolds number — viscosity is absent, a = 1 and R = 4 · ideal-exact
How much more than the least — any Reynolds number — the comparison is between admissible fields, not between flows · ideal-exact
How much uphill a layer can take — no circulation · ideal-cylinder
How much uphill a layer can take — laminar, zero pressure gradient — any Reynolds number below transition · bl-profile
How thick is thin — laminar, zero pressure gradient — any Reynolds number below transition · bl-profile
Incompressible is not a property of the fluid — any Reynolds number — the density is advected and nothing else · field-anatomy · hero
Incompressible is not a property of the fluid — any Reynolds number — the density is advected and nothing else · field-anatomy
Incompressible is not a property of the fluid — any Reynolds number — v is identically zero, so Dρ/Dt is too · field-anatomy
Inviscid does not mean irrotational — uniform vorticity −0.4, no circulation · rotational-flow · hero
Inviscid does not mean irrotational — uniform vorticity −0.4, no circulation · rotational-flow
Inviscid does not mean irrotational — no circulation, no vorticity · rotational-flow
Inviscid does not mean irrotational — uniform vorticity −0.4, measured six radii upstream · rotational-flow
Inviscid does not mean irrotational — any Reynolds number while the stretching lasts; viscosity enters only at the core · vortex-stretch
Inviscid does not mean irrotational — uniform vorticity, no circulation, unit radius · rotational-flow
Inviscid does not mean irrotational — 2 exact fields · any Re — inviscid · velocity-field
Inviscid does not mean irrotational — an exact solution — vorticity proportional to distance from the axis · rotational-flow
Inviscid does not mean irrotational — uniform vorticity −0.8, no circulation · rotational-flow
Lift out of a failure — any Reynolds number — inviscid, and vortex breakdown is not modelled at all · delta-wing · hero
Lift out of a failure — any Reynolds number — inviscid, and vortex breakdown is not modelled at all · delta-wing
Lift out of a failure — any Reynolds number — an inviscid model, with the separation imposed by the edge · delta-wing
Lift out of a failure — any Reynolds number — the separation is imposed by the geometry, not computed · delta-wing
Lift out of a failure — any Reynolds number — inviscid, and the slender theory frays above AR ≈ 1.5 · delta-wing
Lift out of a failure — any Reynolds number — inviscid, and no profile drag is included in either · delta-wing
Lift out of a failure — any Reynolds number — inviscid, and vortex breakdown is not modelled at all · delta-wing
Lift out of a failure — any Reynolds number — an inviscid model, with the separation imposed by the edge · delta-wing
Lift with no wing at all — circulation -3.4 · ideal-cylinder · hero
Lift with no wing at all — Γ = -3.4 · ideal-cylinder
Lift with no wing at all — circulation -1.5 · ideal-cylinder
Lift with no wing at all — 6° incidence · aerofoil
Lift with no wing at all — circulation -3 · ideal-cylinder
Lift with no wing at all — Γ = -3.4 · any Re — inviscid · ideal-cylinder
Lift with no wing at all — Γ = -13 · any Re — inviscid · ideal-cylinder
Lift with no wing at all — 8° incidence · aerofoil
Mass has nowhere to go — fastest 1.91U · velocity-field
Mass has nowhere to go — unscaled · velocity-field
Mixing is a pump — any Reynolds number — mixing supplies the loss, not viscosity · ejector-map · hero
Mixing is a pump — any Reynolds number — mixing supplies the loss, not viscosity · ejector-map
Mixing is a pump — any Reynolds number — uniform inlets and a uniform outlet by assumption · ejector-map
Mixing is a pump — any Reynolds number — no viscosity is used anywhere in either · ejector-map
Mixing is a pump — any Reynolds number — the loss is mixing rather than viscosity · ejector-map
Mixing is a pump — any Reynolds number — an inviscid mixing model with no diffuser · ejector-map
Mixing is a pump — any Reynolds number — mixing supplies the loss, not viscosity · ejector-map
Mixing is a pump — any Reynolds number — the loss is mixing rather than viscosity · ejector-map
Mixing is a pump — any Reynolds number — uniform inlets and a uniform outlet by assumption · ejector-map
No randomness, and it mixes anyway — any Reynolds number — no diffusion, and the particle count is conserved · stirring · hero
No randomness, and it mixes anyway — any Reynolds number — no diffusion, and the particle count is conserved · stirring
No randomness, and it mixes anyway — any Reynolds number — this is kinematics, and no equation of motion is solved · stirring
No randomness, and it mixes anyway — any Reynolds number — a kinematic measurement on a prescribed field · stirring
No randomness, and it mixes anyway — any Reynolds number — the arithmetic is the experiment here · stirring
No randomness, and it mixes anyway — any Reynolds number — molecular diffusion is absent, so nothing ever blurs · stirring
No randomness, and it mixes anyway — any Reynolds number — no diffusion, and the particle count is conserved · stirring
No randomness, and it mixes anyway — any Reynolds number — molecular diffusion is absent, so nothing ever blurs · stirring
No randomness, and it mixes anyway — any Reynolds number — this is kinematics, and no equation of motion is solved · stirring
Not half a venturi — ideal flow — inviscid, with the Kutta condition applied at 5° · venturi-claim · hero
Not half a venturi — ideal flow — inviscid, with the Kutta condition applied at 5° · venturi-claim
Not half a venturi — ideal flow — inviscid, 12% section at 5° · venturi-claim
Not half a venturi — ideal flow — inviscid, 12% section at 5° · venturi-claim
Not half a venturi — ideal flow — inviscid, symmetric section at zero incidence · venturi-claim
Not half a venturi — ideal flow — inviscid, with the Kutta condition applied at 5° · venturi-claim
Not half a venturi — ideal flow — inviscid, with the Kutta condition applied at 10° · venturi-claim
Not half a venturi — ideal flow — inviscid, 8% section at 8° · venturi-claim
Not half a venturi — 8° incidence · aerofoil
Nothing but the edge — any Reynolds number — inviscid, at 5° incidence throughout · panel-solve · hero
Nothing but the edge — any Reynolds number — a discretisation, with no flow in it yet · panel-solve
Nothing but the edge — no circulation · ideal-cylinder
Nothing but the edge — any Reynolds number — inviscid, at 5° incidence throughout · panel-solve
Nothing but the edge — any Reynolds number — inviscid, 100 cosine panels at 5° · panel-solve
Nothing but the edge — 6° incidence · aerofoil
Nothing but the edge — any Reynolds number — both inviscid, at 5° incidence · panel-solve
Nothing but the edge — any Reynolds number — both flows inviscid, at 5° incidence · panel-solve
Nothing but the edge — any Reynolds number — both inviscid, at 5° incidence · panel-solve
Nothing but the edge — any Reynolds number — a discretisation, with no flow in it yet · panel-solve
Nothing in the present picks the flow — ideal, incompressible, irrotational — any Reynolds number · what-an-ideal-flow-keeps · hero
Nothing in the present picks the flow — ideal, incompressible, irrotational — any Reynolds number · what-an-ideal-flow-keeps
Nothing in the present picks the flow — ideal after the spin-up — irrotational except for what the spin put in — inviscid · what-an-ideal-flow-keeps
Nothing in the present picks the flow — unit cylinder, unit stream · ideal-limit
Nothing in the present picks the flow — no circulation · ideal-cylinder
Nothing sucks — α = 6° · any Reynolds number — inviscid, incompressible · absolute-pressure
Nothing sucks — α = 6° · any Reynolds number — the identity is geometry, not flow · absolute-pressure
Nothing sucks — α = 10° · any Reynolds number — inviscid, incompressible · absolute-pressure
One diaphragm, every wave — p₄/p₁ = 10 · inviscid, one-dimensional, γ = 1.4 · shock-tube · hero
One diaphragm, every wave — p₄/p₁ = 10 · inviscid, one-dimensional, γ = 1.4 · shock-tube
One diaphragm, every wave — p₄/p₁ = 10 · inviscid, one-dimensional, γ = 1.4 throughout · shock-tube
One diaphragm, every wave — γ = 1.4 on both sides · inviscid and one-dimensional · shock-tube
One diaphragm, every wave — p₄/p₁ = 40 · inviscid, one-dimensional, γ = 1.4 · shock-tube
One formula, and it does not ask what the shape is — circulation 2 in a unit stream — inviscid · lift-exact · hero
One formula, and it does not ask what the shape is — circulation 2 in a unit stream — inviscid · lift-exact
One formula, and it does not ask what the shape is — circulation 2 in a unit stream — inviscid, steady, and any Reynolds number · lift-exact
One function instead of two — any Re — inviscid · flow-net · hero
One function instead of two — any Re — inviscid · flow-net
One function instead of two — any Re — inviscid · flow-net
One function instead of two — any Re — inviscid · flow-net
One function instead of two — any Re — inviscid · flow-net
One function instead of two — 3 exact solutions added · any Re — inviscid · ideal-cylinder
One function instead of two — any Re — inviscid · flow-net
One function instead of two — any Reynolds number · ideal-cylinder
One group, three exponents — ε = h/w — a slenderness expansion, at any Reynolds number below transition · regime-collapse
One group, three exponents — ε = kh — long-wave theory, inviscid and irrotational · regime-collapse
One group, three exponents — ε = b/a — a slenderness expansion, inviscid and irrotational · regime-collapse
Past three, an ellipse is a shear layer — area drift 2.1e-3 to t = 42; uniform vorticity ω, semi-axes λ and 1; inviscid, two-dimensional · ideal-limit · hero
Past three, an ellipse is a shear layer — uniform vorticity ω, semi-axes λ and 1; inviscid, two-dimensional · ideal-limit
Past three, an ellipse is a shear layer — uniform vorticity ω, semi-axes λ and 1; inviscid, two-dimensional · ideal-limit
Past three, an ellipse is a shear layer — ε = 10⁻⁴; area drift 6.1e-4; uniform vorticity ω, semi-axes λ and 1; inviscid, two-dimensional · ideal-limit
Past three, an ellipse is a shear layer — area drift 2.1e-3 to t = 42; uniform vorticity ω, semi-axes λ and 1; inviscid, two-dimensional · ideal-limit
Past three, an ellipse is a shear layer — uniform vorticity ω, semi-axes λ and 1; inviscid, two-dimensional · ideal-limit
Past three, an ellipse is a shear layer — uniform vorticity ω, semi-axes λ and 1; inviscid, two-dimensional · ideal-limit
Pressure has no speed — any Reynolds number — incompressible and inviscid, so the pressure is elliptic · pressure-poisson · hero
Pressure has no speed — any Reynolds number — incompressible and inviscid, so the pressure is elliptic · pressure-poisson
Pressure has no speed — any Reynolds number — incompressible and inviscid, so the pressure is elliptic · pressure-poisson
Pressure has no speed — any Reynolds number — incompressible and inviscid · pressure-poisson
Pressure has no speed — any Reynolds number — incompressible, so the equation is elliptic · pressure-poisson
Pressure has no speed — any Reynolds number — incompressible, so the equation is elliptic · pressure-poisson
Reversible, and unusable — any Reynolds number — the arithmetic is the experiment here · stirring
Slow enough to be steady — α = 5° · any Reynolds number — inviscid, thin, small incidence · wagner-lift
Spin is not the same as going round — fastest 1.91U · velocity-field · hero
Spin is not the same as going round — 3 exact fields · any Re — inviscid · velocity-field
Spin is not the same as going round — 1 exact field · any Re — inviscid · velocity-field
Spin is not the same as going round — fastest 1.91U · velocity-field
Spin is not the same as going round — 1 exact field · any Re — inviscid · velocity-field
Spin is not the same as going round — 1 exact field · any Re — inviscid · velocity-field
Steady does not mean nothing is happening — steady: ∂u/∂t = 0 · velocity-field · hero
Steady does not mean nothing is happening — steady: ∂u/∂t = 0 · velocity-field
Steady does not mean nothing is happening — fastest 1.91U · velocity-field
Steady does not mean nothing is happening — steady, so a photograph would show no change at all · velocity-field
Steady does not mean nothing is happening — no circulation · ideal-cylinder
Stopping water costs more than moving it — any Reynolds number — friction is absent from the model by choice · surge · hero
Stopping water costs more than moving it — any Reynolds number — friction is absent from the model by choice · surge
Stopping water costs more than moving it — any Reynolds number — a thin-walled elastic pipe, no soil restraint · surge
Stopping water costs more than moving it — any Reynolds number — friction is absent, which is why nothing decays · surge
Stopping water costs more than moving it — any Reynolds number — frictionless, so the peak is the first crest · surge
Stopping water costs more than moving it — any Reynolds number — no column separation is computed anywhere here · surge
Stopping water costs more than moving it — any Reynolds number — friction is absent from the model by choice · surge
Stopping water costs more than moving it — any Reynolds number — friction is absent, which is why nothing decays · surge
Stopping water costs more than moving it — any Reynolds number — no column separation is computed anywhere here · surge
Streamlines are not the paths particles take — no circulation · ideal-cylinder
Streamlines are not the paths particles take — fastest 1.91U · velocity-field
Sufficient, and not necessary — inviscid parallel flow, six profiles, wavenumbers from 0.05 to 0.99 · turbulent-exact
Sufficient, and not necessary — inviscid and non-diffusive throughout · turbulent-exact
The air a wing does not carry — laminar, zero pressure gradient — any Reynolds number below transition · bl-profile
The air that breaks a siphon nothing else can — water at 20 °C, vertical tube — optimistic just above the cut-off · siphon-profile
The balance that is its own error — a circular system of 500 km radius at 45°N; inviscid, steady, curvature stated · rotating-frame
The bed that weighs itself — any Reynolds number — the balance holds however the grains resist · bed-flow
The bed that weighs itself — any Reynolds number — the balance holds however the grains resist · bed-flow
The bee that cannot fly — any Reynolds number — a property of the shape, with no flow in it · flapping-wing
The bee that cannot fly — any Reynolds number — a property of the shape, with no flow in it · flapping-wing
The body the outer flow actually sees — laminar, zero pressure gradient, any Reynolds number · bl-profile
The body the outer flow actually sees — laminar, and independent of the Reynolds number in this form · bl-profile
The body the outer flow actually sees — laminar, zero pressure gradient — any Reynolds number below transition · bl-profile
The borrowed mass the boundary decides — inviscid, impulsive — a free surface at high frequency, gravity absent · ground-effect · hero
The borrowed mass the boundary decides — inviscid, impulsive — a free surface at high frequency, gravity absent · ground-effect
The borrowed mass the boundary decides — inviscid, plane flow, impulsive — gravity absent · ground-effect
The borrowed mass the boundary decides — inviscid, plane flow — a check the image method has to pass · ground-effect
The borrowed mass the boundary decides — inviscid, plane flow, impulsive — gravity absent · ground-effect
The borrowed mass the boundary decides — inviscid, plane flow, impulsive — the open jet's edge at constant pressure · ground-effect
The cascade that runs backwards — any Reynolds number — the argument is inviscid and contains no cascade model · inverse-cascade · hero
The cascade that runs backwards — any Reynolds number — the argument is inviscid and contains no cascade model · inverse-cascade
The cascade that runs backwards — any Reynolds number — an identity of the kinematics rather than a regime · inverse-cascade
The cascade that runs backwards — any Reynolds number — the constraint is conservation, not a cascade model · inverse-cascade
The cascade that runs backwards — any Reynolds number — two conservation laws and no model of turbulence at all · inverse-cascade
The cascade that runs backwards — any Reynolds number — the argument is inviscid and contains no cascade model · inverse-cascade
The cascade that runs backwards — any Reynolds number — the argument is inviscid and contains no cascade model · inverse-cascade
The cascade that runs backwards — any Reynolds number — the argument is inviscid and contains no cascade model · inverse-cascade
The cheapest shape the walls allow — steady, laminar, fully developed — any Reynolds number below transition · energy-budget
The cheapest way to stay up — elliptic loading, span efficiency 1 · lifting-line
The condition that can be bought — 6° incidence — inviscid, with the circulation as a free parameter · circulation-ledger · hero
The condition that can be bought — c/a = 0.9 at 6° — inviscid, with no Kutta condition applied · circulation-ledger
The condition that can be bought — 6° incidence — inviscid, with the circulation as a free parameter · circulation-ledger
The condition that can be bought — 6° incidence — inviscid, the circulation as a control · circulation-ledger
The condition that can be bought — inviscid — the ceiling is set by the geometry, not by a Reynolds number · circulation-ledger
The condition that can be bought — inviscid for the bound — the measurements are at Re of a few million · circulation-ledger
The condition that can be bought — inviscid — the ceiling is set by the geometry, not by a Reynolds number · circulation-ledger
The condition that can be bought — inviscid for the bound — the measurements are at Re of a few million · circulation-ledger
The condition that can be bought — 6° incidence, inviscid — no Kutta condition applied anywhere · circulation-ledger
The constant a hole leaves behind — unit cylinder, unit stream · ideal-limit · hero
The constant a hole leaves behind — unit cylinder, unit stream · ideal-limit
The constant a hole leaves behind — unit cylinder, unit stream · ideal-limit
The constant a hole leaves behind — a unit cylinder inside a boundary at forty radii · ideal-limit
The constant a hole leaves behind — unit cylinder, boundary at eight radii, unit circulation · ideal-limit
The constant a hole leaves behind — two cylinders of radius 0.5, outer boundary at sixty · ideal-limit
The constant a hole leaves behind — unit cylinder, boundary at eight radii, unit circulation · ideal-limit
The constant a hole leaves behind — unit circulation, outer boundary at forty · ideal-limit
The constant a hole leaves behind — two cylinders of radius 0.5, outer boundary at sixty · ideal-limit
The constant a hole leaves behind — two-dimensional ideal flow outside one and two cylinders · ideal-limit
The control that works backwards — any Reynolds number — inviscid, incompressible, a plain flap · circulation-ledger
The control that works backwards — any Reynolds number — inviscid, incompressible, a plain flap · circulation-ledger
The count a pattern cannot break — any Reynolds number — the arrangement is topological and carries no viscosity · critical-points · hero
The count a pattern cannot break — any Reynolds number — the arrangement is topological and carries no viscosity · critical-points
The count a pattern cannot break — any Reynolds number — incompressibility is the only hypothesis used · critical-points
The count a pattern cannot break — any Reynolds number — the theorem knows nothing about the equations · critical-points
The count a pattern cannot break — any Reynolds number — a prescribed field, checked as a pattern · critical-points
The count a pattern cannot break — any Reynolds number — an ideal flow, and the merge is a property of its algebra · critical-points
The count a pattern cannot break — any Reynolds number — an ideal flow, and the merge is a property of its algebra · critical-points
The count a pattern cannot break — any Reynolds number — the arrangement is topological and carries no viscosity · critical-points
The count a pattern cannot break — any Reynolds number — incompressibility is the only hypothesis used · critical-points
The count computed on a body — any Reynolds number — Poincaré–Hopf uses no equation of motion at all · critical-points · hero
The count computed on a body — any Reynolds number — Poincaré–Hopf uses no equation of motion at all · critical-points
The count computed on a body — any Reynolds number — the pattern is a direction field and carries no speed · critical-points
The count computed on a body — any Reynolds number — the count is a property of the surface, not of the flow · critical-points
The count computed on a body — any Reynolds number — Poincaré–Hopf uses no equation of motion at all · critical-points
The count computed on a body — any Reynolds number — Poincaré–Hopf uses no equation of motion at all · critical-points
The count computed on a body — any Reynolds number — Poincaré–Hopf uses no equation of motion at all · critical-points
The count computed on a body — any Reynolds number — an existence statement, with no equation of motion in it · critical-points
The curve that measures a gradient — laminar, any Reynolds number — the profile is prescribed and no layer was solved · velocity-field · hero
The curve that measures a gradient — laminar, any Reynolds number — the profile is prescribed and no layer was solved · velocity-field
The curve that measures a gradient — laminar, any Reynolds number — the profile is prescribed and no layer was solved · velocity-field
The curve that measures a gradient — laminar, any Reynolds number — the profile is prescribed and no layer was solved · velocity-field
The curve that measures a gradient — laminar, any Reynolds number — the profile is prescribed and no layer was solved · velocity-field
The curve that measures a gradient — laminar, any Reynolds number — the profile is prescribed and no layer was solved · velocity-field
The curve that measures a gradient — laminar, any Reynolds number — the profile is prescribed and no layer was solved · velocity-field
The cushion that is not there — ideal flow — any Reynolds number, viscosity is absent · closed-wake · hero
The cushion that is not there — 5° incidence, 60 panels · any Re — inviscid · ground-effect
The cushion that is not there — h/c = 0.4, 5° incidence · any Re — inviscid · ground-effect
The cushion that is not there — ideal flow — any Reynolds number, viscosity is absent · closed-wake
The cushion that is not there — h/c = 0.1, 5° incidence · any Re — inviscid · ground-effect
The cushion that is not there — h/c = 0.8, 5° incidence · any Re — inviscid · ground-effect
The cushion that is not there — h/c = 0.15, 5° incidence · any Re — inviscid · ground-effect
The cushion that is not there — h/c = 0.4, 5° incidence · any Re — inviscid · ground-effect
The cushion that is not there — ideal flow — any Reynolds number, viscosity is absent · closed-wake
The cushion that is there after all — incompressible, inviscid, and the added mass is a blend rather than a solution · ground-effect
The cushion that is there after all — any Reynolds number, in the hover — a borrowed correlation with no forward speed · ground-effect
The cushion that is there after all — incompressible, inviscid, and the added mass is a blend rather than a solution · ground-effect
The cushion that is there after all — 5° incidence, 60 panels · any Re — inviscid · ground-effect
The drag a wake keeps however it rolls up — any Reynolds number — the roll-up is inviscid and two-dimensional · control-volume · hero
The drag a wake keeps however it rolls up — any Reynolds number — the roll-up is inviscid and two-dimensional · control-volume
The drag a wake keeps however it rolls up — any Reynolds number — the roll-up is inviscid and two-dimensional · control-volume
The drag a wake keeps however it rolls up — any Reynolds number — the roll-up is inviscid and two-dimensional · control-volume
The drag a wake keeps however it rolls up — any Reynolds number — the roll-up is inviscid and two-dimensional · control-volume
The drag a wake keeps however it rolls up — any Reynolds number — the roll-up is inviscid and two-dimensional · control-volume
The drag a wake keeps however it rolls up — any Reynolds number — the roll-up is inviscid and two-dimensional · control-volume
The drag that integrates a whole history — an impulsive start from rest · any Re — inviscid · added-mass
The drag that is made of waves — an inviscid, irrotational, steady, incompressible flow with a free surface · ideal-limit
The drift was the instrument — three time units, sixty material points — ideal, two-dimensional, inviscid · what-an-ideal-flow-keeps
The drift was the instrument — Γ = 2 · any Re — inviscid · stokes-loop
The drop that is not a tear — steady, which is why the first two agree · ideal-cylinder
The duty that had no machine — any Reynolds number — dimensional analysis, with the bands borrowed · machine-map · hero
The duty that had no machine — any Reynolds number — dimensional analysis, with the bands borrowed · machine-map
The duty that had no machine — any Reynolds number — dimensional analysis, with the bands borrowed · machine-map
The duty that had no machine — any Reynolds number — dimensional analysis, with the bands borrowed · machine-map
The duty that had no machine — any Reynolds number — dimensional analysis, with the bands borrowed · machine-map
The duty that had no machine — any Reynolds number — dimensional analysis, with the bands borrowed · machine-map
The effect that explains nothing — any Reynolds number — potential flow, so no boundary layer and no separation · wall-jet · hero
The effect that explains nothing — any Reynolds number — potential flow, so no boundary layer and no separation · wall-jet
The effect that explains nothing — any Reynolds number — inviscid, so the balance is exact · wall-jet
The effect that explains nothing — any Reynolds number — inviscid, and no entrainment is modelled · wall-jet
The effect that explains nothing — any Reynolds number — both are inviscid, so the gap is the first neglected term · wall-jet
The effect that explains nothing — any Reynolds number — the free-vortex solution is exact and inviscid · wall-jet
The effect that explains nothing — any Reynolds number — inviscid, and no entrainment is modelled · wall-jet
The effect that explains nothing — any Reynolds number — inviscid, and no entrainment is modelled · wall-jet
The effect that explains nothing — any Reynolds number — inviscid, so the balance is exact · wall-jet
The energy a vortex cannot have — any Reynolds number — the nonlinear term vanishes identically for this flow · vortex-decay
The energy a vortex cannot have — incompressible Newtonian, any Reynolds number — no flow is being solved · energy-budget
The energy a vortex cannot have — any Reynolds number — every slope here is a property of the diffusion equation · vortex-decay
The exact theory says nothing has any drag — any Reynolds number · ideal-cylinder · hero
The exact theory says nothing has any drag — any Reynolds number · ideal-cylinder
The exact theory says nothing has any drag — no circulation · ideal-cylinder
The exact theory says nothing has any drag — no circulation · ideal-cylinder
The exact theory says nothing has any drag — Γ = -3.4 · ideal-cylinder
The exact theory says nothing has any drag — U = 1, 4, 16 · any Re — inviscid · ideal-cylinder
The exact theory, drawn by viscosity — no circulation · ideal-cylinder
The exact theory, drawn by viscosity — no circulation · ideal-cylinder
The exact theory, drawn by viscosity — 3 exact solutions added · any Re — inviscid · ideal-cylinder
The fastest way is not the straight one — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar · hero
The fastest way is not the straight one — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
The fastest way is not the straight one — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
The fastest way is not the straight one — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
The fastest way is not the straight one — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
The fastest way is not the straight one — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
The fastest way is not the straight one — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
The fastest way is not the straight one — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
The fastest way is not the straight one — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
The fastest way is not the straight one — any Reynolds number — the rig and foil enter as drag angles only · sailing-polar
The flow with the least energy in it — between a unit cylinder and a circle of six radii · least-energy
The flow with the least energy in it — a cylinder in a stream, plus a vortex of strength −3 · least-energy
The flow with the least energy in it — a unit cylinder with circulation −3, sampled outside it · least-energy
The flow with the least energy in it — truncated at 60 radii · any Re — inviscid · added-mass
The flow with the least energy in it — 6 Rankine ovals, integrated to 200 radii · any Re — inviscid · added-mass
The force of getting going — cylinder moving at U = 1 · any Re — inviscid · added-mass · hero
The force of getting going — cylinder moving at U = 1 · any Re — inviscid · added-mass
The force of getting going — truncated at 60 radii · any Re — inviscid · added-mass
The force of getting going — 6 Rankine ovals, integrated to 200 radii · any Re — inviscid · added-mass
The force of getting going — no circulation · ideal-cylinder
The force of getting going — an impulsive start from rest · any Re — inviscid · added-mass
The force of getting going — a cylinder translating through fluid at rest · any Re — inviscid · added-mass
The force of getting going — drawn in the fluid's frame, not the wing's · vortex-pair
The gradient that does both — any Reynolds number — viscosity is absent from the criterion · shear-instability · hero
The gradient that does both — boundary-layer theory — the inflection criterion is inviscid and the profiles are not · shear-instability
The gradient that does both — any Reynolds number — viscosity is absent from the criterion · shear-instability
The gradient that does both — any Reynolds number — viscosity is absent from the criterion · shear-instability
The gradient that does both — 10° incidence · laminar layer only, no transition model · separation-onset
The gradient that does both — any Reynolds number — viscosity is absent from the criterion · shear-instability
The gradient that does both — boundary-layer theory — the inflection criterion is inviscid and the profiles are not · shear-instability
The gradient the heat never hears — any Reynolds number within the laminar self-similar layer — Pr = 1, constant properties · thermal-layer
The gradient the heat never hears — any Reynolds number within the laminar self-similar layer — Pr = 1, constant properties · thermal-layer
The gradient the heat never hears — any Reynolds number within the laminar self-similar layer — Pr = 1, constant properties · thermal-layer
The gradient the heat never hears — any Reynolds number within the laminar self-similar layer — Pr = 1, constant properties · thermal-layer
The group with no head in it — any Reynolds number — the limits are practice and are drawn as borrowed · machine-map · hero
The group with no head in it — any Reynolds number — the limits are practice and are drawn as borrowed · machine-map
The group with no head in it — any Reynolds number — the limit is practice and is drawn as borrowed · machine-map
The group with no head in it — any Reynolds number — the limits are practice and are drawn as borrowed · machine-map
The group with no head in it — any Reynolds number — the limits are practice and are drawn as borrowed · machine-map
The group with no head in it — any Reynolds number — the limit is practice and is drawn as borrowed · machine-map
The group with no head in it — any Reynolds number — the limit is practice and is drawn as borrowed · machine-map
The half that carries nothing — inviscid for both computed curves — the measured trend is at Re of a few million · circulation-ledger · hero
The half that carries nothing — inviscid, incompressible — the sections themselves, at zero incidence · circulation-ledger
The half that carries nothing — inviscid, incompressible, zero incidence · circulation-ledger
The half that carries nothing — inviscid for both computed curves — the measured trend is at Re of a few million · circulation-ledger
The half that carries nothing — inviscid, incompressible, zero incidence — no lift anywhere in the figure · circulation-ledger
The half that carries nothing — inviscid, incompressible, zero incidence · circulation-ledger
The half that carries nothing — inviscid, incompressible, zero incidence — no lift anywhere in the figure · circulation-ledger
The half that carries nothing — inviscid, incompressible, zero incidence · circulation-ledger
The half that carries nothing — inviscid, incompressible — thickness ratios up to 17 per cent · circulation-ledger
The hole that halves the flow — any Reynolds number — an inviscid jet at constant pressure · free-jet · hero
The hole that halves the flow — any Reynolds number — viscosity is absent from all three · free-jet
The hole that halves the flow — any Reynolds number — the balance holds whatever the fluid · free-jet
The hole that halves the flow — any Reynolds number — an inviscid jet at constant pressure · free-jet
The hole that halves the flow — any Reynolds number — the free surface is a constant-pressure boundary · free-jet
The hole that halves the flow — any Reynolds number — an inviscid free-streamline flow · free-jet
The hole that halves the flow — any Reynolds number — no viscosity, so no boundary layer on the wall · free-jet
The hole that halves the flow — any Reynolds number — an inviscid jet at constant pressure · free-jet
The hole that halves the flow — any Reynolds number — inviscid, so the coefficient is geometry alone · meter
The inside a flow does not decide — a 4:5 ellipse; the foci are at plus and minus 0.6 · constraint-and-freedom
The instrument in the answer — any Reynolds number — potential flow, so no wake and no separation · tunnel-blockage · hero
The instrument in the answer — any Reynolds number — potential flow, so no wake and no separation · tunnel-blockage
The instrument in the answer — any Reynolds number — an inviscid, incompressible correction · tunnel-blockage
The instrument in the answer — any Reynolds number — a potential-flow correction · tunnel-blockage
The instrument in the answer — any Reynolds number — solid blockage only, with no wake in it · tunnel-blockage
The instrument in the answer — any Reynolds number — potential flow between two plane walls · tunnel-blockage
The instrument in the answer — any Reynolds number — potential flow, so no wake and no separation · tunnel-blockage
The instrument in the answer — any Reynolds number — potential flow, so no wake and no separation · tunnel-blockage
The instrument in the answer — any Reynolds number — solid blockage only, with no wake in it · tunnel-blockage
The last of the oil — incompressible Newtonian, any Reynolds number — no flow is being solved · energy-budget
The lift at the mean angle — attached flow only · aerofoil
The lift beside a wing — any Reynolds number — inviscid, both wings carrying the same lift · two-wings · hero
The lift beside a wing — any Reynolds number — inviscid, both wings carrying the same lift · two-wings
The lift beside a wing — any Reynolds number — inviscid, equal lift on each surface · two-wings
The lift beside a wing — any Reynolds number — inviscid, both wings carrying the same lift · two-wings
The lift beside a wing — any Reynolds number — inviscid, and the core size is assumed · wake-rollup
The lift beside a wing — any Reynolds number — inviscid, elliptic loadings of equal lift · two-wings
The lift beside a wing — any Reynolds number — inviscid, both wings carrying the same lift · two-wings
The lift beside a wing — any Reynolds number — inviscid, both wings carrying the same lift · two-wings
The lift beside a wing — any Reynolds number — inviscid, equal lifts and a fixed gap · two-wings
The lift curve, and why it is a straight line — 6° incidence · aerofoil · hero
The lift curve, and why it is a straight line — attached flow only · aerofoil
The lift curve, and why it is a straight line — 4° incidence · aerofoil
The lift curve, and why it is a straight line — 12° incidence · aerofoil
The lift curve, and why it is a straight line — attached flow only · aerofoil
The lift curve, and why it is a straight line — attached flow only · aerofoil
The lift that arrives late — α = 5° · any Reynolds number — inviscid, thin, small incidence · wagner-lift · hero
The lift that arrives late — α = 5° · any Reynolds number — inviscid, thin, small incidence · wagner-lift
The lift that arrives late — α = 5° · any Reynolds number — inviscid, thin, and at small incidence · wagner-lift
The lift that arrives late — α = 5° · any Reynolds number — inviscid · wagner-lift
The lift that arrives late — α = 5° · any Reynolds number — inviscid, and the wake is a row of points · wagner-lift
The lift that arrives late — α = 10° · any Reynolds number — inviscid, thin, small incidence · wagner-lift
The lift that arrives late — 6° incidence · aerofoil
The lift that arrives late — α = 5° · any Reynolds number — inviscid, and the wake is discrete · wagner-lift
The lift that arrives late — 6° incidence · aerofoil
The line the dye actually draws — any Reynolds number — a kinematic field, with no equation of motion in it · velocity-field · hero
The line the dye actually draws — any Reynolds number — a kinematic field, with no equation of motion in it · velocity-field
The line the dye actually draws — any Reynolds number — a kinematic field, with no equation of motion in it · velocity-field
The line the dye actually draws — any Reynolds number — a kinematic field, with no equation of motion in it · velocity-field
The line the dye actually draws — any Reynolds number — a kinematic field, with no equation of motion in it · velocity-field
The line the dye actually draws — any Reynolds number — a kinematic field, with no equation of motion in it · velocity-field
The line the dye actually draws — any Reynolds number — a kinematic field, with no equation of motion in it · velocity-field
The loading nobody used — any Reynolds number — inviscid, at fixed lift throughout · span-load · hero
The loading nobody used — any Reynolds number — inviscid, one lift constraint and nothing else · wake-plane
The loading nobody used — any Reynolds number — inviscid, in the Trefftz plane · span-load
The loading nobody used — any Reynolds number — inviscid, at fixed lift throughout · span-load
The loading nobody used — any Reynolds number — inviscid, at fixed lift throughout · span-load
The loading nobody used — any Reynolds number — inviscid, on a wake five quarters as wide · span-load
The loading nobody used — any Reynolds number — inviscid, the same lift on the same span · span-load
The loading nobody used — any Reynolds number — inviscid, the same lift on the same span · span-load
The loading nobody used — any Reynolds number — inviscid, in the Trefftz plane · span-load
The loading nobody used — aspect ratio 10, 4° incidence · lifting-line
The lowest pressure is on the body — any Reynolds number — viscosity is absent from all four · ideal-exact · hero
The lowest pressure is on the body — any Reynolds number — viscosity is absent · ideal-exact
The lowest pressure is on the body — any Reynolds number — viscosity is absent from all four · ideal-exact
The lowest pressure is on the body — any Reynolds number — viscosity is absent · ideal-exact
The lowest pressure is on the body — inviscid except the vortex, which has vorticity and no Reynolds number either · ideal-exact
The mass a body has to borrow — any Reynolds number — the fluid is inviscid and the motion is impulsive · ideal-exact
The mass a body has to borrow — ellipses from 1:1.25 to 1:4, translating in an unbounded ideal fluid · ideal-exact
The mass a body has to borrow — an ellipse of 5:2, and a circle for comparison — inviscid throughout · ideal-exact
The mass a body has to borrow — fineness ratios from 1.2 to 12, inviscid throughout · ideal-exact
The mass a body has to borrow — gaps from 1.05 to 50 radii — inviscid, and the motion is normal to the wall · ideal-exact
The mass a body has to borrow — an unbounded inviscid fluid except where a wall is named · ideal-exact
The mean is not the flow — any Reynolds number — viscosity is absent, and the frequency cancels out of the mean · mean-field · hero
The mean is not the flow — any Reynolds number — viscosity is absent, and the frequency cancels out of the mean · mean-field
The mean is not the flow — any Reynolds number — viscosity is absent, and the average is over one cycle · mean-field
The mirror that is a circle — any Re — inviscid · flow-net · hero
The mirror that is a circle — zero circulation round the cylinder · any Re — inviscid · flow-net
The mirror that is a circle — no circulation · ideal-cylinder
The mirror that is a circle — exact · flow-net
The mirror that is a circle — a vortex two radii out · any Re — inviscid · flow-net
The mirror that is a circle — any Reynolds number — inviscid, and the vortices are points with no core · point-vortices
The mirror that is a circle — exact · flow-net
The mirror that is a circle — a vortex half a gap from the surface · any Re — inviscid · flow-net
The mirror that is a circle — zero circulation round the cylinder · any Re — inviscid · flow-net
The moment a spectrum cannot hold — any Reynolds number — molecular diffusion is absent, so nothing ever blurs · stirring
The momentum with no value — a cylinder translating through fluid at rest · any Re — inviscid · added-mass · hero
The momentum with no value — a cylinder translating through fluid at rest · any Re — inviscid · added-mass
The momentum with no value — an impulsive start from rest · any Re — inviscid · added-mass
The momentum with no value — truncated at 60 radii · any Re — inviscid · added-mass
The momentum with no value — 6 Rankine ovals, integrated to 200 radii · any Re — inviscid · added-mass
The momentum with no value — inviscid, the tube full, 2 m long under a 1 m head · added-mass
The momentum with no value — inviscid, 1 m of liquid, released at 10 cm off balance · added-mass
The momentum with no value — any Reynolds number — the comparison is of geometry, not of regimes · sphere-flow
The most a disc can take — any Reynolds number — viscosity is absent from the model entirely · actuator-disc · hero
The most a disc can take — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
The most a disc can take — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
The most a disc can take — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
The most a disc can take — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
The most a disc can take — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
The most a disc can take — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
The most a disc can take — any Reynolds number — the loss here is rotation, not friction · actuator-disc
The number on a streamline is a flow rate — closed: everything the source emits, the sink takes · flow-net
The number on a streamline is a flow rate — any Re — inviscid · flow-net
The number on a streamline is a flow rate — unscaled · velocity-field
The number on a streamline is a flow rate — fastest 1.91U · velocity-field
The number that does not depend on the tunnel — U = 1 · any Re — inviscid · ideal-cylinder · hero
The number that does not depend on the tunnel — U = 1 · any Re — inviscid · ideal-cylinder
The number that does not depend on the tunnel — no circulation · ideal-cylinder
The number that does not depend on the tunnel — U = 1, 4, 16 · any Re — inviscid · ideal-cylinder
The number that does not depend on the tunnel — 6° incidence · aerofoil
The number that does not depend on the tunnel — U = 4 · any Re — inviscid · ideal-cylinder
The number that does not depend on the tunnel — 12° incidence · aerofoil
The number that does not depend on the tunnel — any Reynolds number · ideal-cylinder
The number that is an answer — a laminar flat plate — Pr from 0.02 to 100, at any Reynolds number · regime-collapse
The number that is not a number — any Reynolds number — viscosity is absent from the criterion · shear-instability
The number that really is one — hydrostatic, one-dimensional, frictionless; any Reynolds number at all · specific-energy · hero
The number that really is one — hydrostatic, one-dimensional, frictionless; any Reynolds number at all · specific-energy
The one number that runs out at three dimensions — any Reynolds number — no viscosity appears · field-anatomy · hero
The one number that runs out at three dimensions — any Reynolds number — the statement is Green's theorem · field-anatomy
The one number that runs out at three dimensions — a loop of radius 1.4 — the answer does not depend on the radius · field-anatomy
The one number that runs out at three dimensions — any Reynolds number — no viscosity appears · field-anatomy
The one number that runs out at three dimensions — any Reynolds number — the factor is geometric · field-anatomy
The one number that runs out at three dimensions — Γ = 12 — the azimuthal component is invisible to ψ at every Γ · field-anatomy
The one number that runs out at three dimensions — a loop of radius 1.4 — the answer does not depend on the radius · field-anatomy
The one number that runs out at three dimensions — any Reynolds number — no viscosity appears · field-anatomy
The one rotational solution anybody can write down — an exact solution — vorticity proportional to distance from the axis · rotational-flow · hero
The one rotational solution anybody can write down — an exact solution — vorticity proportional to distance from the axis · rotational-flow
The one rotational solution anybody can write down — the same cell, the same walls, two different F(ψ) · rotational-flow
The one rotational solution anybody can write down — no circulation, no vorticity · rotational-flow
The one rotational solution anybody can write down — truncated at 60 radii · any Re — inviscid · added-mass
The one rotational solution anybody can write down — uniform vorticity −0.4, no circulation · rotational-flow
The one rotational solution anybody can write down — uniform vorticity −0.4, measured six radii upstream · rotational-flow
The one thing that does not add up — a unit cylinder with circulation −3, sampled outside it · least-energy · hero
The one thing that does not add up — a unit cylinder with circulation −3, sampled outside it · least-energy
The one thing that does not add up — unit cylinder, unit stream, circulation −3 · least-energy
The one thing that does not add up — a cylinder in a stream, plus a vortex of strength −3 · least-energy
The one thing that does not add up — circulation -3 · ideal-cylinder
The one thing that does not add up — between a unit cylinder and a circle of six radii · least-energy
The one thing that does not add up — 3 exact solutions added · any Re — inviscid · ideal-cylinder
The optimum that does not matter — aspect ratio 8, five degrees, any Reynolds number — the theory has no viscosity · lift-exact
The other layer, and the one number that separates them — laminar flat plate, zero pressure gradient — any Reynolds number in similarity form · thermal-layer · hero
The other layer, and the one number that separates them — laminar flat plate, zero pressure gradient — any Reynolds number in similarity form · thermal-layer
The other layer, and the one number that separates them — laminar flat plate — the similarity form holds at any Reynolds number · thermal-layer
The other layer, and the one number that separates them — laminar flat plate, zero pressure gradient — any Reynolds number in similarity form · thermal-layer
The other layer, and the one number that separates them — laminar flat plate — any Reynolds number in similarity form · thermal-layer
The other layer, and the one number that separates them — laminar flat plate at Pr = 0.71 — any Reynolds number in similarity form · thermal-layer
The part of the closure a pipe cannot see — any Reynolds number — friction is absent, which is why nothing decays · surge
The part of the flow inside the body — symmetric sections, thickness 1.3 to 20 per cent · ideal-limit · hero
The part of the flow inside the body — symmetric sections, thickness 1.3 to 20 per cent · ideal-limit
The part of the flow inside the body — a unit cylinder, unit circulation, no free stream · ideal-limit
The part of the flow inside the body — source and sink at ∓1 · ideal-limit
The part of the flow inside the body — fineness 1.17 and 6.69 · ideal-limit
The part of the flow inside the body — a unit cylinder, unit circulation, no free stream · ideal-limit
The part of the flow inside the body — a unit cylinder, unit circulation · ideal-limit
The part of the flow inside the body — a unit cylinder, unit circulation, no free stream · ideal-limit
The picture belongs to whoever is watching — any Reynolds number — the boost is exact and viscosity is absent · observer-and-strain · hero
The picture belongs to whoever is watching — any Reynolds number — the boost is exact and viscosity is absent · observer-and-strain
The picture belongs to whoever is watching — one point, seven observers — no Reynolds number enters · observer-and-strain
The picture belongs to whoever is watching — the moving frame's field is unsteady — steadiness belongs to the observer too · observer-and-strain
The picture belongs to whoever is watching — any Reynolds number — neither field solves anything dynamical · observer-and-strain
The picture belongs to whoever is watching — one point, seven observers — no Reynolds number enters · observer-and-strain
The picture belongs to whoever is watching — any Reynolds number — the boost is exact and viscosity is absent · observer-and-strain
The pressure that depends on the past — inviscid, the tube full, 2 m long under a 1 m head · added-mass · hero
The pressure that depends on the past — inviscid, the tube full, 2 m long under a 1 m head · added-mass
The pressure that depends on the past — an impulsive start from rest · any Re — inviscid · added-mass
The pressure that depends on the past — α = 5° · any Reynolds number — inviscid, thin, small incidence · wagner-lift
The pressure that depends on the past — inviscid, 1 m of liquid, released at 10 cm off balance · added-mass
The pressure that depends on the past — truncated at 60 radii · any Re — inviscid · added-mass
The pressure that depends on the past — cylinder moving at U = 1 · any Re — inviscid · added-mass
The pressure that depends on the past — any Reynolds number — incompressible, so the equation is elliptic · pressure-poisson
The pressure that depends on the past — a cylinder translating through fluid at rest · any Re — inviscid · added-mass
The price of a gradient — incompressible Newtonian, any Reynolds number — no flow is being solved · energy-budget
The price of a gradient — steady, laminar, fully developed — any Reynolds number below transition · energy-budget
The price of having ends — aspect ratio 7, 5° incidence · lifting-line · hero
The price of having ends — aspect ratio 7, 5° incidence · lifting-line
The price of having ends — drawn in the fluid's frame, not the wing's · vortex-pair
The price of having ends — aspect ratio 7, 5° incidence · lifting-line
The price of having ends — aspect ratio 12, 3° incidence · lifting-line
The price of having ends — elliptic loading, span efficiency 1 · lifting-line
The price of having ends — elliptic loading, C_L = 0.4 throughout · any Re — inviscid · lifting-line
The price of having ends — 6° incidence · aerofoil
The price of knowing the flow rate — any Reynolds number — the loss downstream contains no viscosity · meter · hero
The price of knowing the flow rate — any Reynolds number — the loss downstream contains no viscosity · meter
The price of knowing the flow rate — any Reynolds number — inviscid, so the coefficient is geometry alone · meter
The price of knowing the flow rate — any Reynolds number — the gap between them is the loss · meter
The price of knowing the flow rate — any Reynolds number — the loss contains no viscosity · meter
The price of knowing the flow rate — any Reynolds number — the loss downstream contains no viscosity · meter
The price of knowing the flow rate — any Reynolds number — inviscid, so the coefficient is geometry alone · meter
The price of knowing the flow rate — any Reynolds number — the loss downstream contains no viscosity · meter
The price of knowing the flow rate — any Reynolds number — the loss contains no viscosity · meter
The radius that costs least — any Reynolds number — the laminar solution holds at all of them · pipe-transition
The randomness that is not in the equations — any Reynolds number — this is kinematics, and no equation of motion is solved · stirring
The shape a vortex keeps — equal co-rotating patches of unit radius · ideal-limit
The sharp edge decides — 8° incidence · aerofoil · hero
The sharp edge decides — 8° incidence · aerofoil
The sharp edge decides — 6° incidence · aerofoil
The sharp edge decides — attached flow only · aerofoil
The sharp edge decides — 10° incidence · aerofoil
The sharp edge decides — attached flow only · aerofoil
The sharp edge decides — 2° incidence · aerofoil
The sign a stagnation point carries in space — any Reynolds number — the count is topological and the flow is inviscid · critical-points · hero
The sign a stagnation point carries in space — any Reynolds number — the count is topological and the flow is inviscid · critical-points
The sign a stagnation point carries in space — any Reynolds number — the count is topological and the flow is inviscid · critical-points
The sign a stagnation point carries in space — any Reynolds number — the count is topological and the flow is inviscid · critical-points
The sign a stagnation point carries in space — any Reynolds number — the count is topological and the flow is inviscid · critical-points
The sign a stagnation point carries in space — any Reynolds number — the count is topological and the flow is inviscid · critical-points
The sign a stagnation point carries in space — any Reynolds number — the count is topological and the flow is inviscid · critical-points
The sign a stagnation point carries in space — any Reynolds number — the count is topological and the flow is inviscid · critical-points
The signature that forgets the shape — the sharing is exact by construction, which is what makes the far fields identical · nonlinear-wave
The siphon that does not break — any Reynolds number — frictionless, so the rate is an upper bound · siphon-profile · hero
The siphon that does not break — any Reynolds number — frictionless, so the rate is an upper bound · siphon-profile
The siphon that does not break — any Reynolds number — frictionless, so the emptying time is a lower bound · siphon-profile
The siphon that does not break — any Reynolds number — frictionless, so the emptying time is a lower bound · siphon-profile
The siphon that does not break — any Reynolds number — frictionless, so the rate is an upper bound · siphon-profile
The solution that keeps its nonlinear term — any Reynolds number — the similarity variable is the whole solution; the far field found at eta = 16 · oscillating-wall · hero
The solution that keeps its nonlinear term — any Reynolds number — the similarity variable is the whole solution; the far field found at eta = 16 · oscillating-wall
The solution that keeps its nonlinear term — any Reynolds number — von Karman's problem, with the terms scaled by Omega²r · oscillating-wall
The solution that keeps its nonlinear term — any Reynolds number — von Karman's problem; the reference is the solution at eta = 18 · oscillating-wall
The solution that keeps its nonlinear term — any Reynolds number — the inflow holds no radius and no height; water, nu = 10⁻⁶ m²/s · oscillating-wall
The solution that keeps its nonlinear term — any Reynolds number in the similarity; radial blue, azimuthal dark, axial pale · oscillating-wall
The solution that keeps its nonlinear term — any Reynolds number — von Karman's and Bodewadt's problems · oscillating-wall
The solution that keeps its nonlinear term — any Reynolds number in the similarity; a disc of radius 0.1 m at 100 rad/s in water for the last four rows · oscillating-wall
The solutions stop being chosen — any Reynolds number — the laminar solution holds at all of them · pipe-transition
The sound is what does not cancel — ideal flow — any Reynolds number, viscosity is absent · outer-boundary
The span is the whole story — elliptic loading, C_L = 0.6 throughout · any Re — inviscid · lifting-line · hero
The span is the whole story — elliptic loading, C_L = 0.6 throughout · any Re — inviscid · lifting-line
The span is the whole story — aspect ratio 8, 5° incidence · lifting-line
The span is the whole story — elliptic loading, span efficiency 1 · lifting-line
The span is the whole story — aspect ratio 8, 5° incidence · lifting-line
The span is the whole story — elliptic loading, C_L = 0.4 throughout · any Re — inviscid · lifting-line
The span is the whole story — the cross-flow plane behind the wing, not the plane of flight · vortex-pair
The specific speed a pump spends its life at — fully turbulent flow — any Reynolds number large enough that the coefficients do not move · machine-map · hero
The specific speed a pump spends its life at — fully turbulent flow — any Reynolds number large enough that the coefficients do not move · machine-map
The specific speed a pump spends its life at — fully turbulent flow — any Reynolds number large enough that the coefficients do not move · machine-map
The specific speed a pump spends its life at — fully turbulent flow — any Reynolds number large enough that the coefficients do not move · machine-map
The specific speed a pump spends its life at — fully turbulent flow — any Reynolds number large enough that the coefficients do not move · machine-map
The specific speed a pump spends its life at — fully turbulent flow — any Reynolds number large enough that the coefficients do not move · machine-map
The specific speed a pump spends its life at — fully turbulent flow — any Reynolds number large enough that the coefficients do not move · machine-map
The specific speed a pump spends its life at — fully turbulent flow — any Reynolds number large enough that the coefficients do not move · machine-map
The spin that feeds itself — any Reynolds number while the stretching lasts; viscosity enters only at the core · vortex-stretch
The spin that feeds itself — any Reynolds number while the stretching lasts; viscosity enters only at the core · vortex-stretch
The spin that feeds itself — any Reynolds number while the stretching lasts; viscosity enters only at the core · vortex-stretch
The spin that feeds itself — any Reynolds number — inviscid and irrotational outside the body · parcel-split
The spin that feeds itself — Γ = 2 · any Re — inviscid · stokes-loop
The story about air meeting up again — 6° incidence · any Re — inviscid · equal-transit · hero
The story about air meeting up again — 6° incidence · any Re — inviscid · equal-transit
The story about air meeting up again — 8° incidence · aerofoil
The story about air meeting up again — 2° incidence · aerofoil
The story about air meeting up again — 10° incidence · aerofoil
The story about air meeting up again — Γ = -3.4 · ideal-cylinder
The story about air meeting up again — 6° incidence · aerofoil
The story about air meeting up again — 2° incidence · aerofoil
The stress that picks the aerodynamics — any Reynolds number — a solid-mechanics result about an aerodynamic variable · velocity-triangle · hero
The stress that picks the aerodynamics — any Reynolds number — a solid-mechanics result about an aerodynamic variable · velocity-triangle
The stress that picks the aerodynamics — any Reynolds number — a solid-mechanics constraint on an aerodynamic variable · velocity-triangle
The stress that picks the aerodynamics — any Reynolds number — a solid-mechanics result about an aerodynamic variable · velocity-triangle
The stress that picks the aerodynamics — any Reynolds number — a solid-mechanics constraint on an aerodynamic variable · velocity-triangle
The stress that picks the aerodynamics — any Reynolds number — a solid-mechanics result about an aerodynamic variable · velocity-triangle
The surface in the wake — any Reynolds number — inviscid, elliptic loading and a flat rigid wake · tail-balance · hero
The surface in the wake — any Reynolds number — inviscid, and both surfaces are below their stalling angle · tail-balance
The surface in the wake — any Reynolds number — inviscid, elliptic loading and a flat rigid wake · tail-balance
The surface in the wake — any Reynolds number — inviscid, elliptic loading and a flat rigid wake · tail-balance
The surface in the wake — any Reynolds number — inviscid, elliptic loading and a flat rigid wake · tail-balance
The surface in the wake — any Reynolds number — inviscid, rigid wake, lift slopes held fixed · tail-balance
The surface in the wake — any Reynolds number — inviscid, and both surfaces are below their stalling angle · tail-balance
The surface in the wake — any Reynolds number — a diagram of where the wake goes, not a solve · tail-balance
The surface in the wake — any Reynolds number — inviscid, rigid wake, lift slopes held fixed · tail-balance
The surface that moves with the flow — any Reynolds number — this is a property of the equations, not of a flow · extra-condition
The sweep a root does not have — any Reynolds number — inviscid, incompressible, flat wings at 4° · circulation-ledger · hero
The sweep a root does not have — any Reynolds number — inviscid, incompressible, a flat swept wing at 4° · circulation-ledger
The sweep a root does not have — any Reynolds number — inviscid, incompressible, flat wings at 4° · circulation-ledger
The sweep a root does not have — any Reynolds number — inviscid, incompressible, flat wings at 4° · circulation-ledger
The sweep a root does not have — any Reynolds number — inviscid, incompressible, flat wings at 4° · circulation-ledger
The sweep a root does not have — any Reynolds number — inviscid, incompressible, flat wings at 4° · circulation-ledger
The sweep a root does not have — any Reynolds number — inviscid, incompressible, flat wings at 4° · circulation-ledger
The sweep a root does not have — any Reynolds number — inviscid, incompressible · circulation-ledger
The swirl that holds a wave still — Rankine vortices of varying core radius in a uniform axial flow · ideal-limit
The swirl that holds a wave still — Rankine vortices of varying core radius in a uniform axial flow · ideal-limit
The teapot effect is a tension, not a pressure — water at 20 °C — inviscid, no gravity, the lip perfectly wetted · wall-jet · hero
The teapot effect is a tension, not a pressure — water at 20 °C — inviscid, no gravity, the lip perfectly wetted · wall-jet
The teapot effect is a tension, not a pressure — 20 °C — inviscid; the air jet's real limit is a viscous separation · wall-jet
The teapot effect is a tension, not a pressure — water at 20 °C — inviscid, the lip perfectly wetted · wall-jet
The teapot effect is a tension, not a pressure — 20 °C — inviscid, no gravity, lips perfectly wetted · wall-jet
The teapot effect is a tension, not a pressure — 20 °C — inviscid, the sheet's thickness taken as given · wall-jet
The theory that forbade flight — 6° incidence · any Re — inviscid · equal-transit
The theory that solves everything — no circulation · ideal-cylinder · hero
The theory that solves everything — no circulation · ideal-cylinder
The theory that solves everything — any Reynolds number · ideal-cylinder
The theory that solves everything — no circulation · ideal-cylinder
The theory that solves everything — 6° incidence · aerofoil
The theory that solves everything — 3 exact solutions added · any Re — inviscid · ideal-cylinder
The theory with no memory in it — six crossing times — shapes rather than magnitudes — inviscid · what-an-ideal-flow-keeps
The theory with no memory in it — one body, three models — shapes rather than magnitudes — inviscid · what-an-ideal-flow-keeps
The theory with no memory in it — six crossing times — shapes rather than magnitudes — inviscid · what-an-ideal-flow-keeps
The theory with no memory in it — a statement about the model rather than a computation · what-an-ideal-flow-keeps
The theory with no memory in it — shapes rather than magnitudes — the three are not to a common scale — inviscid · what-an-ideal-flow-keeps
The theory with no memory in it — no circulation · ideal-cylinder
The third thickness — laminar, zero pressure gradient — any Reynolds number below transition · bl-profile
The third thickness — laminar, and independent of the Reynolds number in this form · bl-profile
The two drags a wing pays — aspect ratio 7, 5° incidence · lifting-line
The two theories, side by side — no circulation · ideal-cylinder
The two theories, side by side — 6° incidence · aerofoil
The viscosity nobody uses — incompressible Newtonian, any Reynolds number — no flow is being solved · energy-budget
The vortex a wing leaves behind — drawn in the fluid's frame, not the wing's · vortex-pair · hero
The vortex a wing leaves behind — drawn in the fluid's frame, not the wing's · vortex-pair
The vortex a wing leaves behind — drawn in the fluid's frame, not the wing's · vortex-pair
The vortex a wing leaves behind — 8° incidence · aerofoil
The vortex a wing leaves behind — 8° incidence · aerofoil
The vortex a wing leaves behind — 8° incidence · aerofoil
The vortex a wing leaves behind — attached flow only · aerofoil
The vortex a wing leaves behind — 8° incidence · aerofoil
The vorticity a clean surface cannot refuse — any size and speed — the stress is in units of μU/a · extra-condition
The vorticity a clean surface cannot refuse — Levich's drag is this divided by U · extra-condition
The vorticity nothing decides — the same cell, the same walls, two different F(ψ) · rotational-flow · hero
The vorticity nothing decides — the same cell, the same walls, two different F(ψ) · rotational-flow
The vorticity nothing decides — an exact solution — vorticity proportional to distance from the axis · rotational-flow
The vorticity nothing decides — the same cell, the same walls, two different F(ψ) · rotational-flow
The vorticity nothing decides — uniform vorticity, no circulation, unit radius · rotational-flow
The vorticity nothing decides — uniform vorticity −0.4, no circulation · rotational-flow
The wake that has to spin — any Reynolds number — the loss here is rotation, not friction · actuator-disc · hero
The wake that has to spin — any Reynolds number — the loss here is rotation, not friction · actuator-disc
The wake that has to spin — any Reynolds number — the loss here is rotation, not friction · actuator-disc
The wake that has to spin — any Reynolds number — the loss here is rotation, not friction · actuator-disc
The wake that has to spin — any Reynolds number — the loss here is rotation, not friction · actuator-disc
The wake that has to spin — any Reynolds number — the loss here is rotation, not friction · actuator-disc
The wake that has to spin — any Reynolds number — viscosity is absent from the model entirely · actuator-disc
The wake that has to spin — any Reynolds number — the torque follows from what crosses the two faces · velocity-triangle
The wake that has to spin — any Reynolds number — the loss here is rotation, not friction · actuator-disc
The wall that heats itself — laminar flat plate at Pr = 0.71 — any Reynolds number in similarity form · thermal-layer
The wall that heats itself — laminar flat plate — any Reynolds number in similarity form; the turbulent factor is not drawn · thermal-layer
The wall that heats itself — laminar flat plate, zero pressure gradient — any Reynolds number in similarity form · thermal-layer
The wall that heats itself — laminar flat plate — any Reynolds number in similarity form · thermal-layer
The wall that heats itself — any Reynolds number — every loss set to zero, so this is a bound · ram-cycle
The wall that pushes back — h/c = 0.4, 5° incidence · any Re — inviscid · ground-effect · hero
The wall that pushes back — h/c = 0.4, 5° incidence · any Re — inviscid · ground-effect
The wall that pushes back — 5° incidence, 60 panels · any Re — inviscid · ground-effect
The wall that pushes back — h/c = 0.3, 5° incidence · any Re — inviscid · ground-effect
The wall that pushes back — h/c = 0.6, 5° incidence · any Re — inviscid · ground-effect
The wall that pushes back — h/c = 0.25, 8° incidence · any Re — inviscid · ground-effect
The wall that pushes back — 10° incidence, 60 panels · any Re — inviscid · ground-effect
The walls are in the answer — span 0.5 of the tunnel's diameter · ideal flow, viscosity absent · closed-wake · hero
The walls are in the answer — span 0.5 of the tunnel's diameter · ideal flow, viscosity absent · closed-wake
The walls are in the answer — span 0.8 of the tunnel's diameter · ideal flow, viscosity absent · closed-wake
The walls are in the answer — ideal flow — any Reynolds number, viscosity is absent · closed-wake
The walls are in the answer — span 0.5 of the tunnel's diameter · ideal flow, viscosity absent · closed-wake
The walls are in the answer — AR 6, model 6% of the section · ideal flow, viscosity absent · closed-wake
The walls are in the answer — ideal flow — any Reynolds number, viscosity is absent · closed-wake
The walls are in the answer — any Reynolds number — potential flow, so no wake and no separation · tunnel-blockage
The wind a swept wing feels — any Reynolds number — inviscid, and the wing is infinite in both directions · swept-wing
The wind a swept wing feels — ideal flow — inviscid, on a wing yawed at 35° at 4° incidence · swept-wing
The window every vector is averaged over — any Reynolds number — a window model, with the vortex prescribed · optical-response · hero
The window every vector is averaged over — any Reynolds number — a window model, with the vortex prescribed · optical-response
The window every vector is averaged over — any Reynolds number — linear in the field, for any flow the window is small against · optical-response
The window every vector is averaged over — any Reynolds number — linear in the field, any structure shorter than the window · optical-response
The window every vector is averaged over — any Reynolds number — first-order correlation, no noise, no particle lag · optical-response
The window every vector is averaged over — any Reynolds number — first-order correlation, the layer prescribed · optical-response
The window every vector is averaged over — any Reynolds number — first-order correlation, no noise · optical-response
Three dimensions are kinder — any Reynolds number — viscosity is absent from both bodies · sphere-flow
Three dimensions are kinder — any Reynolds number — the comparison is of geometry, not of regimes · sphere-flow
Three dimensions are kinder — any Reynolds number — an ideal flow, and the body is made of streamlines · sphere-flow
Three dimensions are kinder — any Reynolds number — the body exists because two strengths match exactly · sphere-flow
Three dimensions are kinder — any Reynolds number — the body exists because two strengths match exactly · sphere-flow
Three dimensions are kinder — any Reynolds number — an ideal flow, and the body is made of streamlines · sphere-flow
Three is the most that can be predicted — any Reynolds number — inviscid points with no core · point-vortices · hero
Three is the most that can be predicted — any Reynolds number — inviscid, and the vortices are points with no core · point-vortices
Three is the most that can be predicted — any Reynolds number — inviscid, and the vortices are points with no core · point-vortices
Three is the most that can be predicted — any Reynolds number — inviscid points with no core · point-vortices
Three is the most that can be predicted — any Reynolds number — inviscid point vortices, no cores · point-vortices
Three is the most that can be predicted — any Reynolds number — inviscid points, RK4 at dt = 0.001 · point-vortices
Three is the most that can be predicted — any Reynolds number — inviscid, and the cores are points · point-vortices
Three is the most that can be predicted — any Reynolds number — inviscid, and the vortices are points with no core · point-vortices
Twice the margin, on top of the hammer — any Reynolds number — friction absent; H₀ = 25 m, a = 1200 m/s · surge
Twice the margin, on top of the hammer — any Reynolds number — friction absent; H₀ = 25 m, a = 1200 m/s · surge
Twice the margin, on top of the hammer — any Reynolds number — friction absent; V₀ = 0.5 m/s, a = 1200 m/s · surge
Two answers to one question — any Reynolds number — inviscid, incompressible, Kelvin imposed exactly · circulation-ledger · hero
Two answers to one question — any Reynolds number — inviscid, incompressible, Kelvin imposed exactly · circulation-ledger
Two answers to one question — any Reynolds number — inviscid, incompressible, the first four semichords · circulation-ledger
Two answers to one question — any Reynolds number — inviscid, incompressible · circulation-ledger
Two answers to one question — any Reynolds number — inviscid, incompressible · circulation-ledger
Two kinds is a plane flow's privilege — any Reynolds number — the classification uses no equation of motion · critical-points · hero
Two kinds is a plane flow's privilege — any Reynolds number — the classification uses no equation of motion · critical-points
Two kinds is a plane flow's privilege — any Reynolds number — a local model, valid within one gradient length · critical-points
Two kinds is a plane flow's privilege — any Reynolds number — incompressibility is the only hypothesis used · critical-points
Two kinds is a plane flow's privilege — any Reynolds number — a local model, with no diffusion in it · critical-points
Two kinds is a plane flow's privilege — any Reynolds number — a local model, with no diffusion in it · critical-points
Two kinds is a plane flow's privilege — any Reynolds number — a sampling of a model, with no turbulence in it · critical-points
Two lifts at one incidence — any Reynolds number — inviscid, and vortex breakdown is not modelled at all · delta-wing
Two rings leapfrog only if they start alike — total impulse 1.115 πΓ, core 0.06, core volume conserved; coaxial thin-cored filaments, Γ equal, exact mutual field; inviscid · vortex-ring · hero
Two rings leapfrog only if they start alike — core 0.06 of the larger radius, core volume conserved; coaxial thin-cored filaments, Γ equal, exact mutual field; inviscid · vortex-ring
Two rings leapfrog only if they start alike — core 0.06, core volume conserved; coaxial thin-cored filaments, Γ equal, exact mutual field; inviscid · vortex-ring
Two rings leapfrog only if they start alike — total impulse 1.115 πΓ, core 0.06, core volume conserved; coaxial thin-cored filaments, Γ equal, exact mutual field; inviscid · vortex-ring
Two rings leapfrog only if they start alike — core 0.06, core volume conserved; time in units of R²/Γ; coaxial thin-cored filaments, Γ equal, exact mutual field; inviscid · vortex-ring
Two rings leapfrog only if they start alike — coaxial thin-cored filaments, Γ equal, exact mutual field; inviscid · vortex-ring
Two rings leapfrog only if they start alike — coaxial thin-cored filaments, Γ equal, exact mutual field; inviscid · vortex-ring
Two strainings, and the order they came in — two unit-time pieces at equal strain rate — incompressible, any Reynolds number · what-a-parcel-remembers · hero
Two strainings, and the order they came in — two unit-time pieces at equal strain rate — incompressible, any Reynolds number · what-a-parcel-remembers
Two strainings, and the order they came in — two unit-time pieces — incompressible, any Reynolds number · what-a-parcel-remembers
Two strainings, and the order they came in — after two unit-time pieces — incompressible, any Reynolds number · what-a-parcel-remembers
Two strainings, and the order they came in — the two pieces of the history — incompressible, any Reynolds number · what-a-parcel-remembers
Two strainings, and the order they came in — one unit of each piece, subdivided — incompressible, any Reynolds number · what-a-parcel-remembers
Two strainings, and the order they came in — two unit-time pieces — incompressible, any Reynolds number · what-a-parcel-remembers
Two wings and it does not matter where — any Reynolds number — inviscid, equal lifts and a fixed gap · two-wings · hero
Two wings and it does not matter where — any Reynolds number — inviscid, equal lifts and a fixed gap · two-wings
Two wings and it does not matter where — any Reynolds number — inviscid, equal lift on each surface · two-wings
Two wings and it does not matter where — any Reynolds number — inviscid, one lift constraint and nothing else · wake-plane
Two wings and it does not matter where — any Reynolds number — inviscid, elliptic loadings of equal lift · two-wings
Two wings and it does not matter where — any Reynolds number — inviscid, equal lift on each surface · two-wings
Two wings and it does not matter where — any Reynolds number — inviscid, equal lift on each surface · two-wings
Two wings and it does not matter where — any Reynolds number — inviscid, elliptic loadings of equal lift · two-wings
Two wings and it does not matter where — any Reynolds number — inviscid, both wings carrying the same lift · two-wings
Universal, and one of five — any Reynolds number — neither exponent contains a viscosity · turbulent-limit
Vortices move each other — any Reynolds number — inviscid, and the vortices are points with no core · point-vortices · hero
Vortices move each other — any Reynolds number — inviscid, and the vortices are points with no core · point-vortices
Vortices move each other — any Reynolds number — inviscid, and the vortices are points with no core · point-vortices
Vortices move each other — 3 exact solutions added · any Re — inviscid · ideal-cylinder
Vortices move each other — any Reynolds number — inviscid point vortices, no cores · point-vortices
Vortices move each other — any Reynolds number — inviscid, and the vortices are points with no core · point-vortices
Vortices move each other — any Reynolds number — inviscid, and the cores are points · point-vortices
Vortices move each other — any Reynolds number — inviscid points with no core · point-vortices
What a code says to a wall — laminar, zero pressure gradient — any Reynolds number below transition · bl-profile
What a flap does, and what it does not — hinge at 0.75 chord, 120 panels · any Re — inviscid · flap · hero
What a flap does, and what it does not — hinge at 0.75 chord, 120 panels · any Re — inviscid · flap
What a flap does, and what it does not — hinge at 0.75 chord · any Re — inviscid · flap
What a flap does, and what it does not — 4° incidence, 120 panels · any Re — inviscid · flap
What a flap does, and what it does not — hinge at 0.6 chord, 120 panels · any Re — inviscid · flap
What a flap does, and what it does not — 4° incidence, 120 panels · any Re — inviscid · flap
What a flap does, and what it does not — attached flow only · aerofoil
What a flow is — fastest 1.91U · velocity-field · hero
What a flow is — fastest 1.91U · velocity-field
What a flow is — no circulation · ideal-cylinder
What a flow is — steady: ∂u/∂t = 0 · velocity-field
What a flow is — unscaled · velocity-field
What a fluid takes out of a swing — cylinder moving at U = 1 · any Re — inviscid · added-mass
What a jet cannot push sideways — any Reynolds number — inviscid, so no force along the surface · jet-force · hero
What a jet cannot push sideways — any Reynolds number — inviscid, so no force along the surface · jet-force
What a jet cannot push sideways — any Reynolds number — an inviscid jet, so no tangential force · jet-force
What a jet cannot push sideways — any Reynolds number — inviscid by assumption, which is what the zero states · jet-force
What a jet cannot push sideways — any Reynolds number — the sheet leaves at the speed it arrived · jet-force
What a jet cannot push sideways — any Reynolds number — inviscid, so no force along the surface · jet-force
What a jet cannot push sideways — any Reynolds number — inviscid, so no force along the surface · jet-force
What a jet cannot push sideways — any Reynolds number — an inviscid jet, so no tangential force · jet-force
What a jet cannot push sideways — any Reynolds number — no friction in the bucket, no windage · wheel
What a mean profile cannot tell anybody — any Reynolds number — viscosity is absent, and the frequency cancels out of the mean · mean-field
What a parcel does in the first instant — any Reynolds number — the split is kinematics, with no fluid property in it · parcel-split · hero
What a parcel does in the first instant — any Reynolds number — the split is kinematics, with no fluid property in it · parcel-split
What a parcel does in the first instant — any Reynolds number — the split is kinematics, with no fluid property in it · parcel-split
What a parcel does in the first instant — 3 exact fields · any Re — inviscid · velocity-field
What a parcel does in the first instant — any Reynolds number — no fluid property appears in the split · parcel-split
What a parcel does in the first instant — any Reynolds number — the split is kinematics, with no fluid property in it · parcel-split
What a parcel does in the first instant — any Reynolds number — inviscid and irrotational outside the body · parcel-split
What a parcel does in the first instant — any Reynolds number — the split is kinematics, with no fluid property in it · parcel-split
What a parcel does in the first instant — steady: ∂u/∂t = 0 · velocity-field
What a photograph of a flow shows — steady, which is why the first two agree · ideal-cylinder · hero
What a photograph of a flow shows — steady, which is why the first two agree · ideal-cylinder
What a photograph of a flow shows — fastest 1.91U · velocity-field
What a photograph of a flow shows — 3 exact fields · any Re — inviscid · velocity-field
What a photograph of a flow shows — unscaled · velocity-field
What a plate takes with it — incompressible Newtonian, any Reynolds number — no flow is being solved · energy-budget
What a point vortex is not — equal co-rotating patches of unit radius · ideal-limit
What a point vortex is not — equal co-rotating patches of unit radius · ideal-limit
What actually holds a wing up — 6° incidence · aerofoil · hero
What actually holds a wing up — 6° incidence · aerofoil
What actually holds a wing up — Γ = -3.4 · ideal-cylinder
What actually holds a wing up — 6° incidence · aerofoil
What actually holds a wing up — 6° incidence · aerofoil
What actually holds a wing up — 8° incidence · aerofoil
What actually holds a wing up — 10° incidence · aerofoil
What averaging costs — 8° incidence · control-volume
What survives being wound up — any Reynolds number — ideal and barotropic, forces conservative · material-loop · hero
What survives being wound up — any Reynolds number — ideal and barotropic, forces conservative · material-loop
What survives being wound up — any Reynolds number — an ideal, barotropic flow under no body force · material-loop
What survives being wound up — any Reynolds number — the fluid is ideal, which is the theorem's first hypothesis · material-loop
What survives being wound up — any Reynolds number — the mechanism is inviscid, and viscosity would only damp it · material-loop
What survives being wound up — any Reynolds number for two of them, and a stated viscosity for the first · material-loop
What survives being wound up — any Reynolds number — ideal and barotropic, forces conservative · material-loop
What the far field remembers — any Reynolds number — viscosity is absent, and both bodies are exact · outer-boundary · hero
What the far field remembers — any Reynolds number — viscosity is absent, and both bodies are exact · outer-boundary
What the far field remembers — ideal flow — any Reynolds number, viscosity is absent · outer-boundary
What the far field remembers — any Reynolds number — viscosity is absent, and the comparison is of two exact solutions · outer-boundary
What the far field remembers — ideal flow — any Reynolds number, viscosity is absent · outer-boundary
What the far field remembers — any Reynolds number — potential flow, so no wake and no separation · tunnel-blockage
What the far field remembers — α = 6°, fineness 6 · ideal flow, viscosity absent · outer-boundary
What the far field remembers — closed: everything the source emits, the sink takes · flow-net
What the far field remembers — ideal flow — any Reynolds number, viscosity is absent · outer-boundary
What viscosity cannot take away — any Reynolds number — the nonlinear term vanishes identically for this flow · vortex-decay
What viscosity cannot take away — any Reynolds number — the similarity variable is the whole solution · vortex-decay
What viscosity cannot take away — any Reynolds number — every slope here is a property of the diffusion equation · vortex-decay
What viscosity cannot take away — any Reynolds number — the estimate contains no velocity at all · vortex-decay
What viscosity cannot take away — any Reynolds number — the test is of the equation, not of a regime · vortex-decay
What viscosity cannot take away — any Reynolds number — every slope here is a property of the diffusion equation · vortex-decay
When a body tears the water — 4° incidence, thickness 0.12, camber 0.02 · any Re — inviscid · conformal-map
When air stops being incompressible — no circulation · ideal-cylinder
Where a fluid stops being one — any Reynolds number — this is a property of the equations, not of a flow · extra-condition
Where a vortex stops — any Reynolds number — the criteria are kinematic · observer-and-strain · hero
Where a vortex stops — any Reynolds number — the layer's own thickness is the only length · observer-and-strain
Where a vortex stops — any Reynolds number — the criteria are kinematic · observer-and-strain
Where a vortex stops — any Reynolds number — the criteria are kinematic · observer-and-strain
Where Bernoulli's equation applies — steady, incompressible, inviscid — 4 of 5 rows break one · bernoulli-limits · hero
Where Bernoulli's equation applies — steady, incompressible, inviscid — 4 of 5 rows break one · bernoulli-limits
Where Bernoulli's equation applies — steady, incompressible, inviscid — 1 of 1 rows break one · bernoulli-limits
Where Bernoulli's equation applies — steady, incompressible, inviscid — 0 of 1 rows break one · bernoulli-limits
Where Bernoulli's equation applies — steady, incompressible, inviscid — 1 of 1 rows break one · bernoulli-limits
Where Bernoulli's equation applies — steady, incompressible, inviscid — 2 of 2 rows break one · bernoulli-limits
Where lift starts — any Reynolds number — a statement about shape, with no flow in it · thin-aerofoil · hero
Where lift starts — any Reynolds number — a statement about shape, with no flow in it · thin-aerofoil
Where lift starts — 0° incidence, thickness 0.12, camber 0.06 · any Re — inviscid · conformal-map
Where lift starts — any Reynolds number — inviscid, and the thickness is discarded · thin-aerofoil
Where lift starts — attached flow only · aerofoil
Where lift starts — any Reynolds number — a property of the shape, with no flow in it · thin-aerofoil
Where lift starts — any Reynolds number — a statement about shape, with no flow in it · thin-aerofoil
Where lift starts — any Reynolds number — inviscid, and small incidences throughout · thin-aerofoil
Where lift starts — any Reynolds number — thin-aerofoil theory, inviscid · thin-aerofoil
Where lift starts — any Reynolds number — both flows inviscid, at 4° incidence · thin-aerofoil
Where the heat of a drag is made — steady, laminar, fully developed — any Reynolds number below transition · energy-budget
Where the lift acts — the crossing is interpolated, not assumed · moment-about · hero
Where the lift acts — the crossing is interpolated, not assumed · moment-about
Where the lift acts — 6° incidence · aerofoil
Where the lift acts — 12° incidence · aerofoil
Where the lift acts — 4° incidence · aerofoil
Where the lift acts — the crossing is interpolated, not assumed · moment-about
Where the lift acts — 8° incidence · aerofoil
Where the lift acts — attached flow only · aerofoil
Where the line stops being a line — any Reynolds number — inviscid, incompressible, elliptic loading · circulation-ledger · hero
Where the line stops being a line — any Reynolds number — inviscid, incompressible, elliptic loading · circulation-ledger
Where the line stops being a line — any Reynolds number — inviscid, incompressible · circulation-ledger
Where the line stops being a line — any Reynolds number — inviscid, incompressible · circulation-ledger
Where the line stops being a line — any Reynolds number — inviscid, incompressible, elliptic loading · circulation-ledger
Where the line stops being a line — any Reynolds number — inviscid, incompressible · circulation-ledger
Where the line stops being a line — any Reynolds number — inviscid, incompressible, elliptic loading · circulation-ledger
Where the line stops being a line — any Reynolds number — inviscid, incompressible · circulation-ledger
Where the line stops being a line — any Reynolds number — inviscid, incompressible · circulation-ledger
Where the reaction to a wing's lift is — ideal flow — any Reynolds number, viscosity is absent · outer-boundary · hero
Where the reaction to a wing's lift is — ideal flow — any Reynolds number, viscosity is absent · outer-boundary
Where the reaction to a wing's lift is — 8° incidence · control-volume
Where the reaction to a wing's lift is — ideal flow — any Reynolds number, viscosity is absent · outer-boundary
Where the reaction to a wing's lift is — ideal flow — any Reynolds number, viscosity is absent · outer-boundary
Where the reaction to a wing's lift is — Γ = -3.4 · ideal-cylinder
Where the reaction to a wing's lift is — any Reynolds number — viscosity is absent, and both bodies are exact · outer-boundary
Where the reaction to a wing's lift is — any Reynolds number — viscosity is absent, and the comparison is of two exact solutions · outer-boundary
Where the straight line stops — 6° incidence · laminar layer only, no transition model · separation-onset · hero
Where the straight line stops — 6° incidence · laminar layer only, no transition model · separation-onset
Where the straight line stops — 0.02 camber, 0.1 thickness · laminar layer only, no transition model · separation-onset
Where the straight line stops — 10° incidence · laminar layer only, no transition model · separation-onset
Where the straight line stops — 6° incidence · laminar layer only, no transition model · separation-onset
Where the straight line stops — 0.06 camber, 0.1 thickness · laminar layer only, no transition model · separation-onset
Where the straight line stops — attached flow only · aerofoil
Where the unknown boundary is the known one — the whole flow, at every point, as one quarter disc · cavity-flow · hero
Where the unknown boundary is the known one — the whole flow, at every point, as one quarter disc · cavity-flow
Where the unknown boundary is the known one — any Reynolds number — viscosity is absent · cavity-flow
Where the unknown boundary is the known one — any Re — inviscid · flow-net
Where the wake ends up — any Reynolds number — inviscid, and nothing here rolls anything up · wake-rollup · hero
Where the wake ends up — any Reynolds number — inviscid, and nothing here rolls anything up · wake-rollup
Where the wake ends up — any Reynolds number — inviscid, and the roll-up itself is not computed · wake-rollup
Where the wake ends up — any Reynolds number — the strength is a borrowed shape, not a result · wake-rollup
Where the wake ends up — any Reynolds number — ideal and barotropic, forces conservative · material-loop
Where the wake ends up — any Reynolds number — inviscid, and the core size is assumed · wake-rollup
Where the wake ends up — any Reynolds number — inviscid, and nothing here rolls anything up · wake-rollup
Where the wake ends up — any Reynolds number — inviscid, and the roll-up itself is not computed · wake-rollup
Where the wake ends up — the cross-flow plane behind the wing, not the plane of flight · vortex-pair
Where the wake ends up — any Reynolds number — inviscid, and the core size is assumed · wake-rollup
Where vorticity comes from — laminar boundary layer — the identity holds at any Reynolds number · extra-condition · hero
Where vorticity comes from — laminar boundary layer — the identity holds at any Reynolds number · extra-condition
Where vorticity comes from — any Reynolds number — this is a property of the equations, not of a flow · extra-condition
Where vorticity comes from — boundary-layer theory — the inflection criterion is inviscid and the profiles are not · shear-instability
Where vorticity comes from — ideal surface pressure — the cancellation holds at any Reynolds number · extra-condition
Where vorticity comes from — laminar boundary layer — the identity holds at any Reynolds number · extra-condition
Which part of a wing stalls first — any Reynolds number — inviscid, aspect ratio 8, no twist · span-load · hero
Which part of a wing stalls first — any Reynolds number — inviscid, aspect ratio 8 at 8° · span-load
Which part of a wing stalls first — any Reynolds number — inviscid, aspect ratio 8 at 8° · span-load
Which part of a wing stalls first — any Reynolds number — inviscid, aspect ratio 8, no twist · span-load
Which part of a wing stalls first — aspect ratio 8, 5° incidence · lifting-line
Which part of a wing stalls first — any Reynolds number — inviscid, aspect ratio 8 at 8° · span-load
Which part of a wing stalls first — any Reynolds number — inviscid, aspect ratio 8 · span-load
Which part of a wing stalls first — any Reynolds number — inviscid, aspect ratio 12 at 6° · span-load
Which part of a wing stalls first — any Reynolds number — inviscid, aspect ratio 12, no twist · span-load
Work out of a change of swirl — any Reynolds number — the work follows from what crosses the two faces · velocity-triangle · hero
Work out of a change of swirl — any Reynolds number — the work follows from what crosses the two faces · velocity-triangle
Work out of a change of swirl — any Reynolds number — the work follows from what crosses the two faces · velocity-triangle
Work out of a change of swirl — any Reynolds number — the work follows from what crosses the two faces · velocity-triangle
Work out of a change of swirl — any Reynolds number — the work follows from what crosses the two faces · velocity-triangle
Work out of a change of swirl — any Reynolds number — the work follows from what crosses the two faces · velocity-triangle
Work out of a change of swirl — any Reynolds number — the work follows from what crosses the two faces · velocity-triangle
Work out of a change of swirl — any Reynolds number — the torque follows from what crosses the two faces · velocity-triangle
Work out of a change of swirl — any Reynolds number — the work follows from what crosses the two faces · velocity-triangle
Work out of a change of swirl — 8° incidence · control-volume

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