Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
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The thread: Taught wrongly, everywhere — page 3

Page 3 of 14, continuing through the 124 essays this motif runs through.

124 essays carry this thread — page 3 of 14.

Every curved streamline has a pressure gradient across it. Twelve points in the flow past a cylinder, with the arrow at each showing the pressure gradient across the streamline. It points away from the centre of curvature everywhere, and its size is ρq²κ: the fluid is being pushed round a bend, and something has to do the pushing. Both sides are computed here and they share no arithmetic — one is Bernoulli's pressure differenced across the flow, the other is the turning rate of the velocity direction along it — and they agree to 6.7e-5. This is the whole content of the effect usually named after Coandă, and it is happening on every curved streamline of every flow. What is taught wrongly

The effect that explains nothing

A jet follows a curved wall and the wall feels a suction. Both are real, both are famous, and naming them after Coandă explains neither — what is happening is the normal component of Euler's equation, and it holds on every curved streamline in every flow.

 Two sides of one ball, at different pressures. The surface pressure coefficient round a ball, measured from the front stagnation point, on the side the seam trips and on the side it does not. Up to separation both follow the exact potential-flow distribution 1 − (9/4)sin²θ. After it both take the same wake pressure, which is what a manometer measures rather than what the ideal theory predicts. The asymmetry is the shaded area between them, and integrating it gives a side force of 0.2949 towards the later-separating side. Fluids at work

A ball that swings without spinning

A cricket ball curves in flight with no spin about any useful axis. The mechanism is not the Magnus effect; it is a seam tripping the boundary layer on one side so that side lets go later. Which way the ball then goes depends on one borrowed number, and this site's own inviscid solver supplies the value that gets it wrong.

 The bath is ten thousand times too small. The Rossby number — the ratio of the inertial term to the Coriolis term in the momentum equation — for eight flows at 45 degrees, on a logarithmic axis. Above one, rotation is a correction; below one, it is the physics. A draining bath sits at 3.2e+3 and a mid-latitude depression at 1.9e-1. The Coriolis term is not absent from the bath: it is present, computable, and four orders of magnitude smaller than the terms that decide what happens. Saying so is not the same as saying it is zero. What is taught wrongly

The bath does not know the hemisphere

The Coriolis term in a draining bath is not absent. It is present, computable, and about four hundred times smaller than what a hand left in the water an hour ago is still doing — which is a ratio rather than an opinion, and it is the same kind of argument as a Reynolds number.

 The pressure coefficient, read off the field. The closed-form surface pressure of a cylinder, and the same quantity computed from the speeds of the solved field at the same points. The coefficient is exactly one where the flow stops and exactly minus three at the shoulder, and those two numbers are properties of the shape rather than of the tunnel. Ideal flow

The number that does not depend on the tunnel

A pressure measured in a wind tunnel is a fact about that tunnel on that day. Divide it by the dynamic pressure and it becomes a fact about the shape — the same at any speed, in any fluid, at any scale, and equal to exactly one where the flow comes to rest.

 Three times the wind, on a reach. The polar diagram: boat speed in every direction, as a multiple of the true wind speed, for drag angles of 14 and 6 degrees. The shaded wedge at the top is the no-go zone, whose half-angle is exactly the sum of the two drag angles. Everywhere outside about twice that angle the boat is faster than the wind, and the maximum is 2.92 times the wind at 110 degrees — which is 1/sin λ at 90° + λ, both checked. Fluids at work

Faster than the wind that drives it

An ice yacht in a fifteen-knot breeze does forty. That is not a trick and it does not need a special sail — it follows from two drag angles and a triangle, and the best speed a boat can reach is one over the sine of their sum.

 Two drag laws, one derived and one fitted. Flat-plate drag coefficient against Reynolds number, laminar and turbulent, on log axes. The laminar curve is Blasius' similarity solution, solved by shooting; the turbulent one is the 1/7-power correlation, which was fitted to experiment and is drawn dashed-in-kind to keep the difference visible. Their slopes differ — −1/2 against −1/5 — so the gap between them widens rather than staying put. Viscosity

The cost of going turbulent

A turbulent boundary layer costs several times the friction of a laminar one, and the multiple is not a constant — it rises with Reynolds number, because the two laws have different exponents. That is why laminar flow is worth more on a long fast surface than on a short slow one.

 Two heights, and only one of them is in the answer. A siphon, with the two heights that get confused. The drop from the source surface to the outlet is what drives the flow: the exit speed is √(2gΔz) = 4.43 m/s and nothing else enters it. The rise to the crown decides the pressure at the top — 72.0 kPa absolute here, against an atmosphere of 101.3 — and therefore whether the column holds together at all. A siphon over a high wall and one over a kerb, draining to the same place, flow at exactly the same rate. What is taught wrongly

The siphon that does not need the air

A siphon is explained everywhere by the atmosphere pushing the liquid over the hump. The flow rate says otherwise, in the flattest way available — the height of the hump does not appear in it at all. What the atmosphere does is hold the column together, which is a different job with a different limit.

 The flap moves the curve and leaves its slope alone. Lift coefficient against incidence for several flap deflections. The lines are parallel: deflecting the flap gives the section lift at an incidence where it had none, and does not change how much lift each further degree of incidence buys. Circulation and lift

What a flap does, and what it does not

Lowering a flap gives a wing lift at an incidence where it had none. It does not make the wing more responsive to being pitched — the lift curve moves sideways and its slope does not change, and those are two quite different things to buy.

 There is a constriction, and it is a consequence rather than a cause. A cambered section at 5 degrees, with one streamtube traced above it and one below. The tube above narrows by 16 per cent at mid-chord and the tube below by -112 per cent, so the venturi story's premise is true: the flow over the top really is squeezed more than the flow underneath. The difficulty is that the tube's upper boundary is a streamline, not a wall. Nothing put it there but the solution of the whole flow — the same solution that already contains the lift — so the narrowing is a way of describing the answer rather than a reason for it. What is taught wrongly

Not half a venturi

The air above a wing really is squeezed into a narrower channel, it really does speed up, and the pressure really does fall. Every step of the story is true and the whole is still not an explanation, because the channel's upper wall is a streamline — and where a streamline went is part of the answer, not part of the question.

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