Incompressible — Ma → 0, and nothing else assumed

• A blade that flies through what it shed — miss distance 0.05 R — incompressible, two-dimensional section · what-a-wake-hands-back
• A blade that flies through what it shed — circulation 12 m²/s — incompressible section · what-a-wake-hands-back
• A force forgets the datum, a stress cannot — incompressible — the same dynamic pressure at every altitude, so the same C_p · absolute-pressure · hero
• A force forgets the datum, a stress cannot — incompressible — the same dynamic pressure at every altitude, so the same C_p · absolute-pressure
• A force forgets the datum, a stress cannot — incompressible, sea level, and the section is a Joukowski solution · absolute-pressure
• A force forgets the datum, a stress cannot — incompressible, sea level, and the section is a Joukowski solution · absolute-pressure
• A force forgets the datum, a stress cannot — incompressible, sea level, and the section is a Joukowski solution · absolute-pressure
• A force forgets the datum, a stress cannot — incompressible — the same dynamic pressure at every altitude, so the same C_p · absolute-pressure
• A layer that is an integral of everything upstream — one metre of surface in air — laminar, incompressible · how-long-viscosity-remembers · hero
• A layer that is an integral of everything upstream — one metre of surface in air — laminar, incompressible · how-long-viscosity-remembers
• A layer that is an integral of everything upstream — laminar, incompressible, air · how-long-viscosity-remembers
• A layer that is an integral of everything upstream — laminar, incompressible — separation at lambda = −0.09 · how-long-viscosity-remembers
• A layer that is an integral of everything upstream — laminar, incompressible, air · how-long-viscosity-remembers
• A layer that is an integral of everything upstream — laminar, incompressible, air at 1.5·10⁻⁵ m²/s · how-long-viscosity-remembers
• A rate of change that will not hold still — an incompressible flow — det of the flow map is one · carried-region
• A right total from a wrong picture — a NACA 2412 from zero to thirteen degrees — incompressible, attached, thin · wrong-picture · hero
• A right total from a wrong picture — geometry only — incompressible thin-aerofoil theory throughout this subject · wrong-picture
• A right total from a wrong picture — a NACA 2412 at five degrees — incompressible, attached, thin · wrong-picture
• A right total from a wrong picture — a NACA 2412 at five degrees — incompressible, attached, thin · wrong-picture
• A right total from a wrong picture — a NACA 2412 from zero to thirteen degrees — incompressible, attached, thin · wrong-picture
• A right total from a wrong picture — zero to twelve degrees — incompressible, attached, thin · wrong-picture
• A right total from a wrong picture — a NACA 2412 — incompressible, attached, thin · wrong-picture
• A right total from a wrong picture — minus six to eight degrees — incompressible, attached, thin · wrong-picture
• A right total from a wrong picture — a NACA 2412 — incompressible, attached, thin · wrong-picture
• A right total from a wrong picture — a comparison of models rather than of flows — incompressible, attached, thin · wrong-picture
• A spiral is a legible record — one period, smoothing 0.15 — ideal, incompressible, two-dimensional · what-an-ideal-flow-keeps · hero
• A spiral is a legible record — one period, smoothing 0.15 — ideal, incompressible, two-dimensional · what-an-ideal-flow-keeps
• A spiral is a legible record — one period, smoothing 0.15 — ideal, incompressible · what-an-ideal-flow-keeps
• A spiral is a legible record — one period, smoothing 0.15 — ideal, incompressible · what-an-ideal-flow-keeps
• A spiral is a legible record — smoothings 0.10, 0.15 and 0.25 — ideal, incompressible · what-an-ideal-flow-keeps
• A spiral is a legible record — smoothings 0.10, 0.15 and 0.25 — ideal, incompressible · what-an-ideal-flow-keeps
• A spiral is a legible record — one period, one unit of time — ideal, incompressible, two-dimensional · what-an-ideal-flow-keeps
• A spiral is a legible record — four time units each way — ideal, incompressible · what-an-ideal-flow-keeps
• A swimmer that cannot go backwards — steady, incompressible, no inertia anywhere — the kinetic-energy flux is zero · energy-budget
• A tank that turns a hammer into a swing — incompressible tunnel water — 2 km of 3 m tunnel, a 10 m tank, full load rejection · surge · hero
• A tank that turns a hammer into a swing — incompressible tunnel water — 2 km of 3 m tunnel, a 10 m tank, full load rejection · surge
• A tank that turns a hammer into a swing — incompressible tunnel water — 2 km of 3 m tunnel at 2 m/s, 5 m of friction · surge
• A tank that turns a hammer into a swing — incompressible tunnel water — a 10 m tank, 5 m of friction at full flow · surge
• A tank that turns a hammer into a swing — incompressible in the rigid run, wave speed 1000 m/s in the characteristics · surge
• A viscosity that depends on the question — steady, incompressible, no inertia anywhere — the kinetic-energy flux is zero · energy-budget
• Equal on average, and nothing else — one synthetic incompressible field, wavenumbers 1 to 8 · turbulent-exact · hero
• Equal on average, and nothing else — one synthetic incompressible field, wavenumbers 1 to 8 · turbulent-exact
• Equal on average, and nothing else — one synthetic incompressible field · turbulent-exact
• Equal on average, and nothing else — one synthetic incompressible field · turbulent-exact
• Equal on average, and nothing else — six synthetic incompressible fields, wavenumbers 1 to 8 · turbulent-exact
• Everything about the start, except one vector — a cylinder in an unbounded ideal fluid — incompressible, irrotational · what-an-ideal-flow-keeps · hero
• Everything about the start, except one vector — a cylinder in an unbounded ideal fluid — incompressible, irrotational · what-an-ideal-flow-keeps
• Everything about the start, except one vector — a cylinder in an unbounded ideal fluid — incompressible, irrotational · what-an-ideal-flow-keeps
• Everything about the start, except one vector — a cylinder in an unbounded ideal fluid — incompressible, irrotational · what-an-ideal-flow-keeps
• Everything about the start, except one vector — a cylinder in an unbounded ideal fluid — incompressible, irrotational · what-an-ideal-flow-keeps
• Everything about the start, except one vector — a cylinder in an unbounded ideal fluid — incompressible, irrotational · what-an-ideal-flow-keeps
• Everything about the start, except one vector — a cylinder in an unbounded ideal fluid — incompressible, irrotational · what-an-ideal-flow-keeps
• Four Bernoullis and one name — an editorial figure — incompressible, attached, thin · wrong-picture
• Four Bernoullis and one name — the same shear layer — incompressible · wrong-picture
• Four Bernoullis and one name — irrotational, steady, incompressible · wrong-picture
• Four Bernoullis and one name — the same shear layer — incompressible · wrong-picture
• Four Bernoullis and one name — an area ratio of two, with the flow rate rising at 2 per unit time — incompressible · wrong-picture
• Four Bernoullis and one name — an area ratio of two, dQ/dt = 2 — incompressible · wrong-picture
• Four Bernoullis and one name — gamma = 1.4 — incompressible · wrong-picture
• Four Bernoullis and one name — the flows on this page — incompressible · wrong-picture
• Four profiles, one drag — a flat plate at zero pressure gradient — incompressible, a laminar layer · profile-and-total · hero
• Four profiles, one drag — a flat plate at zero pressure gradient — incompressible, a laminar layer · profile-and-total
• Four profiles, one drag — a flat plate — incompressible, a laminar layer · profile-and-total
• Four profiles, one drag — a flat plate; both profiles rise from zero to one — incompressible, a laminar layer · profile-and-total
• Four profiles, one drag — a flat plate — incompressible, a laminar layer · profile-and-total
• Four profiles, one drag — a flat plate — incompressible, a laminar layer · profile-and-total
• Four profiles, one drag — a flat plate — incompressible, a laminar layer · profile-and-total
• Four profiles, one drag — the parameter from −12 to +12 — incompressible, a laminar layer · profile-and-total
• Four profiles, one drag — U = U0(1 − x/L) — incompressible, a laminar layer · profile-and-total
• How far a parcel gets — incompressible · velocity-field
• How long the fluid has been in there — area ratio four — steady, incompressible · what-a-parcel-remembers
• How long the fluid has been in there — area ratio four — steady, incompressible · what-a-parcel-remembers
• How long the fluid has been in there — area ratio four — steady, incompressible · what-a-parcel-remembers
• How long the fluid has been in there — steady, incompressible, one dimensional · what-a-parcel-remembers
• How long the fluid has been in there — area ratio four — steady, incompressible · what-a-parcel-remembers
• Incompressible is not a property of the fluid — M∞ = 0.3 — correct to O(M²) · field-anatomy
• Incompressible is not a property of the fluid — correct to O(M²) — which is the order of the quantity being computed · field-anatomy
• Incompressible is not a property of the fluid — M∞ = 0.5 — correct to O(M²) · field-anatomy
• Incompressible is not a property of the fluid — M∞ = 0.5 — correct to O(M²) · field-anatomy
• Incompressible is not a property of the fluid — M∞ = 0.6 — correct to O(M²) · field-anatomy
• Nothing in the present picks the flow — ideal, incompressible, irrotational · what-an-ideal-flow-keeps
• Nothing in the present picks the flow — ideal, incompressible, irrotational — the six circulations above · what-an-ideal-flow-keeps
• Nothing in the present picks the flow — ideal, incompressible, irrotational · what-an-ideal-flow-keeps
• Nothing in the present picks the flow — ideal, incompressible, irrotational — up to the critical circulation · what-an-ideal-flow-keeps
• Nothing sucks — α = 6° · incompressible, so this is honest below about 100 m/s · absolute-pressure · hero
• Nothing sucks — α = 6° · incompressible, so this is honest below about 100 m/s · absolute-pressure
• Nothing sucks — α = 6° · incompressible — which is why the air curve is fiction past M 0.3 · absolute-pressure
• Nothing sucks — α = 6° · incompressible, so this is honest below about 100 m/s · absolute-pressure
• Nothing sucks — α = 10° · incompressible — which is why the air curve is fiction past M 0.3 · absolute-pressure
• Reversible, and unusable — four point vortices, four time units — ideal, incompressible · what-an-ideal-flow-keeps · hero
• Reversible, and unusable — four point vortices, four time units — ideal, incompressible · what-an-ideal-flow-keeps
• Reversible, and unusable — four time units each way — ideal, incompressible · what-an-ideal-flow-keeps
• Reversible, and unusable — twelve time units each way — ideal, incompressible · what-an-ideal-flow-keeps
• Reversible, and unusable — windows of 4 to 16 time units — ideal, incompressible · what-an-ideal-flow-keeps
• Reversible, and unusable — twelve time units — ideal, incompressible · what-an-ideal-flow-keeps
• Reversible, and unusable — four and twelve time units — ideal, incompressible, two-dimensional · what-an-ideal-flow-keeps
• Steady does not mean nothing is happening — incompressible · velocity-field
• Steady, three-dimensional, and mixing anyway — steady, incompressible flow — the same hypotheses in both dimensions · carried-region
• Streamlines are not the paths particles take — incompressible · velocity-field · hero
• Streamlines are not the paths particles take — incompressible · velocity-field
• Streamlines are not the paths particles take — incompressible · velocity-field
• Streamlines are not the paths particles take — incompressible · velocity-field
• The better tunnel needs the bigger tank — incompressible tunnel water — 2 m/s, 5 m of friction, gross head 100 m · surge · hero
• The better tunnel needs the bigger tank — incompressible tunnel water — 2 m/s, 5 m of friction, gross head 100 m · surge
• The better tunnel needs the bigger tank — any incompressible scheme — the governor taken as instantaneous, with no dynamics of its own · surge
• The better tunnel needs the bigger tank — incompressible tunnel water — 2 km of 3 m tunnel at 2 m/s, 5 m of friction · surge
• The better tunnel needs the bigger tank — incompressible tunnel water — 2 km of 3 m tunnel at 2 m/s, gross head 100 m · surge
• The better tunnel needs the bigger tank — incompressible tunnel water — 2 m/s, 5 m of friction, gross head 100 m · surge
• The better tunnel needs the bigger tank — any incompressible tunnel — its length, bore and velocity cancel from the comparison · surge
• The cheapest shape the walls allow — steady, incompressible, no inertia anywhere — the kinetic-energy flux is zero · energy-budget
• The drift was the instrument — ideal, incompressible, two-dimensional — no viscosity anywhere · what-an-ideal-flow-keeps · hero
• The drift was the instrument — ideal, incompressible, two-dimensional — no viscosity anywhere · what-an-ideal-flow-keeps
• The drift was the instrument — ideal, incompressible, two-dimensional — the loop material throughout · what-an-ideal-flow-keeps
• The drift was the instrument — ideal, incompressible, two-dimensional · what-an-ideal-flow-keeps
• The drift was the instrument — ideal, incompressible, two-dimensional · what-an-ideal-flow-keeps
• The drift was the instrument — ideal, incompressible, two-dimensional · what-an-ideal-flow-keeps
• The effect that is real, and where it stops — a circular cylinder in a uniform stream — potential flow, incompressible · wrong-picture · hero
• The effect that is real, and where it stops — any steady flow, viscous or not — potential flow, incompressible · wrong-picture
• The effect that is real, and where it stops — potential flow past a circular cylinder — potential flow, incompressible · wrong-picture
• The effect that is real, and where it stops — potential flow past a circular cylinder — potential flow, incompressible · wrong-picture
• The effect that is real, and where it stops — a circular cylinder in a uniform stream — potential flow, incompressible · wrong-picture
• The effect that is real, and where it stops — a 1 mm jet on a 50 mm radius — potential flow, incompressible · wrong-picture
• The effect that is real, and where it stops — a jet of 1 mm on a 50 mm radius — potential flow, incompressible · wrong-picture
• The effect that is real, and where it stops — a cylinder in a stream, and a jet two per cent of the radius thick — potential flow, incompressible · wrong-picture
• The effect that is real, and where it stops — distance in radii for the body, in jet thicknesses for the jet — potential flow, incompressible · wrong-picture
• The effect that is real, and where it stops — an editorial figure, whose numbers are the ones computed above — potential flow, incompressible · wrong-picture
• The effect that is real, and where it stops — air on a 50 mm radius with a 1 mm jet — potential flow, incompressible · wrong-picture
• The equation that changes type inside its own answer — C_p₀ = −0.6, γ = 1.4 — both are approximations of the same order · hot-gas
• The fraction that is really four thirds — three dimensions; homogeneity, isotropy, incompressibility · field-statistics
• The fraction that is really four thirds — three dimensions; an inertial or inertial-convective range · field-statistics
• The inflow that takes time to arrive — flat plate, incompressible, attached — reduced frequencies 0.01 to 10 · what-a-wake-hands-back
• The inside a flow does not decide — potential flow, zero incidence — potential flow, incompressible and irrotational · constraint-and-freedom · hero
• The inside a flow does not decide — potential flow, zero incidence — potential flow, incompressible and irrotational · constraint-and-freedom
• The inside a flow does not decide — a ring at 0.4, a uniform disc of the same radius — potential flow, incompressible and irrotational · constraint-and-freedom
• The inside a flow does not decide — rings of 6, 8 and 12 doublets at a radius of 0.4 — potential flow, incompressible and irrotational · constraint-and-freedom
• The inside a flow does not decide — 36 sources, 288 collocation points, a 4:5 ellipse — potential flow, incompressible and irrotational · constraint-and-freedom
• The inside a flow does not decide — the same sweep of source depths — potential flow, incompressible and irrotational · constraint-and-freedom
• The inside a flow does not decide — a 4:5 ellipse at zero incidence — potential flow, incompressible and irrotational · constraint-and-freedom
• The inside a flow does not decide — 36 sources on a 4:5 ellipse — potential flow, incompressible and irrotational · constraint-and-freedom
• The inside a flow does not decide — the same depth sweep — potential flow, incompressible and irrotational · constraint-and-freedom
• The inside a flow does not decide — depths of 0.05, 0.1, 0.2 and 0.4 of the body — potential flow, incompressible and irrotational · constraint-and-freedom
• The lag that makes flutter possible — flat plate, incompressible, attached — reduced frequencies 0.01 to 10 · what-a-wake-hands-back · hero
• The lag that makes flutter possible — flat plate, incompressible, attached — reduced frequencies 0.01 to 10 · what-a-wake-hands-back
• The lag that makes flutter possible — flat plate, incompressible, attached · what-a-wake-hands-back
• The lag that makes flutter possible — the same section throughout — incompressible, attached · what-a-wake-hands-back
• The last of the oil — steady, incompressible, no inertia anywhere — the kinetic-energy flux is zero · energy-budget
• The number on a streamline is a flow rate — incompressible · velocity-field
• The one number that runs out at three dimensions — incompressible flow throughout — a divergence removes even the first row · field-anatomy
• The pocket on top of the wing — Ma below 1 — first order, and it fails where it says it does · transonic
• The price of a gradient — steady, incompressible, no inertia anywhere — the kinetic-energy flux is zero · energy-budget · hero
• The price of a gradient — steady, incompressible, no inertia anywhere — the kinetic-energy flux is zero · energy-budget
• The spin a shock leaves behind — K = 0.4 — incompressible, so ∇h₀ becomes ∇H and T∇s vanishes · reactive-shock
• The stress a pipe knows — an editorial figure, whose arithmetic is above — incompressible, attached, thin · profile-and-total
• The theory that forbade flight — incompressible for the linear curve; the impact model claims no regime at all · newtonian-lift · hero
• The theory that forbade flight — incompressible for the linear curve; the impact model claims no regime at all · newtonian-lift
• The theory that forbade flight — incompressible for the linear curve; the impact model claims no regime at all · newtonian-lift
• The third thickness — steady, incompressible, no inertia anywhere — the kinetic-energy flux is zero · energy-budget
• The wind a swept wing feels — laminar boundary layer — incompressible, 35° of sweep · swept-wing
• The wind a swept wing feels — laminar boundary layer — incompressible, on an infinite yawed wing · swept-wing
• The wing that is flat, and flies — geometry only — incompressible, attached, thin · wrong-picture · hero
• The wing that is flat, and flies — geometry only — incompressible, attached, thin · wrong-picture
• The wing that is flat, and flies — sections of 0, 12 and 21 per cent thickness — incompressible, attached, thin · wrong-picture
• The wing that is flat, and flies — a four per cent cambered section, twelve per cent thick — incompressible, attached, thin · wrong-picture
• The wing that is flat, and flies — at six degrees of incidence — incompressible, attached, thin · wrong-picture
• The wing that is flat, and flies — at six degrees of incidence — incompressible, attached, thin · wrong-picture
• The wing that is flat, and flies — twelve and six per cent thick — incompressible, attached, thin · wrong-picture
• The wing that is flat, and flies — at six degrees of incidence — incompressible, attached, thin · wrong-picture
• The wing that is flat, and flies — the story's own assumptions — incompressible, attached, thin · wrong-picture
• The wing that is flat, and flies — an editorial figure — incompressible, attached, thin · wrong-picture
• Three numbers out of a camber line — thin-aerofoil theory, incompressible, attached · profile-and-total · hero
• Three numbers out of a camber line — the two camber lines above — incompressible, attached, thin · profile-and-total
• Three numbers out of a camber line — thin-aerofoil theory, incompressible, attached · profile-and-total
• Three numbers out of a camber line — minus four to twelve degrees — incompressible, attached, thin · profile-and-total
• Three numbers out of a camber line — six degrees of incidence — incompressible, attached, thin · profile-and-total
• Three numbers out of a camber line — six degrees of incidence — incompressible, attached, thin · profile-and-total
• Three numbers out of a camber line — six degrees of incidence — incompressible, attached, thin · profile-and-total
• Three numbers out of a camber line — an editorial figure, whose arithmetic is above — incompressible, attached, thin · profile-and-total
• Three numbers out of a camber line — arcs of two, four and six per cent camber — incompressible, attached, thin · profile-and-total
• Three numbers out of a camber line — zero to twelve degrees — incompressible, attached, thin · profile-and-total
• Three numbers out of a camber line — geometry, with the coefficients computed — incompressible, attached, thin · profile-and-total
• Two lifts at one incidence — mean 12°, amplitude 8° — incompressible · what-a-wake-hands-back
• Two lifts at one incidence — mean 12°, amplitude 8° — incompressible · what-a-wake-hands-back
• Two lifts at one incidence — mean 12°, amplitude 8° — incompressible, attached until it is not · what-a-wake-hands-back
• Weighing what is missing — incompressible, two-dimensional, with the static pressure recovered · control-volume · hero
• Weighing what is missing — incompressible, two-dimensional, with the static pressure recovered · control-volume
• Weighing what is missing — incompressible, two-dimensional, with the static pressure recovered · control-volume
• Weighing what is missing — incompressible, two-dimensional, and the total pressure conserved downstream · control-volume
• Weighing what is missing — incompressible, two-dimensional, with the static pressure recovered · control-volume
• Weighing what is missing — incompressible, two-dimensional, with the static pressure recovered · control-volume
• What a flow is — incompressible · velocity-field
• What a photograph of a flow shows — incompressible · velocity-field
• What a turning frame keeps — incompressible — the pressure rise is exact given the two velocities · velocity-triangle · hero
• What a turning frame keeps — incompressible — the pressure rise is exact given the two velocities · velocity-triangle
• What a turning frame keeps — incompressible — the pressure rise is exact given the two velocities · velocity-triangle
• What a turning frame keeps — incompressible — the pressure rise is exact given the two velocities · velocity-triangle
• Where a vortex stops — two dimensions, incompressible — the identity needs both · observer-and-strain
• Which speed goes in the number — Ma below 1 — first order, and it fails where it says it does · transonic
• Why the list is this long — incompressible, no body force, unbounded; nu = 0.1 · oscillating-wall · hero
• Why the list is this long — incompressible, no body force, unbounded; nu = 0.1 · oscillating-wall
• Why the list is this long — incompressible, no body force; nu = 0.1, the residual floor is 10⁻⁸ · oscillating-wall
• Why the list is this long — incompressible, no body force; nu = 0.1, the boost is 0.8 and −0.5 · oscillating-wall
• Why the list is this long — incompressible Navier-Stokes in three dimensions, no body force · oscillating-wall
• Why the list is this long — incompressible, no body force; nu = 0.1, residuals over a grid at three times · oscillating-wall
• Why the list is this long — incompressible, no body force; nu = 0.1 · oscillating-wall

Every regime · All figures · All essays