Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Base pressure — where it appears

The pressure on the flat or blunt rear face of a body in a stream, usually well below the free-stream value because the separated wake behind it is at low pressure. Its deficit is the base drag, and it matters most on projectiles, rockets and nozzles whose exhaust fills or fails to fill the wake.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Three bluff bodies, whose Strouhal numbers agree once the wake's width is used. The measured Strouhal number of each body, and Roshko's universal number formed with the wake's width and the speed on the free streamline that bounds it. The raw numbers span a factor of 1.462; the collapsed ones span 1.0011, with a mean of 0.16281. The shedding was never body-dependent — the length in the number was.

The frequency a wake chooses

Bluff bodies shed at Strouhal numbers from 0.145 to 0.212, and the spread is not a fact about shedding — it is a fact about which length went into the number. Change the length to the wake's own width and three bodies agree to a tenth of a per cent. Then let the body move, and the number stops deciding anything at all.

regimes · Strouhal The suction a diffuser needs to beat Betz on its own exit. The best power per unit of exit area against the suction held behind the exit, as a pressure coefficient −c. The curve is (2/3√3)(1 + c)^(3/2) up to c = ½ and the dots are a direct search. It starts at 0.385, sixty-five per cent of Betz's limit, and crosses 16/27 at c = 1/3 exactly — the pressure on the back face of Betz's open disc. A diffuser with no suction at its exit is worse than a bare rotor as large as its exit; one that beats the limit on its exit area is holding more suction there than the open disc holds behind itself.

A duct beats Betz only on the area it chooses

Put a wind turbine inside a flaring duct and it can take more than 16/27 of the wind's power through its rotor, which is the claim. Measure the same power against the duct's exit, the area the device actually fills in the wind, and a plain diffuser takes less than a bare rotor of that size would. It crosses the limit only when the duct holds a suction behind its exit, and the suction it needs is exactly the pressure on the back face of Betz's own disc.

applied · Actuator disc

Named alongside it

The objects these essays reach for when they reach for this one.

Model limitActuator discThe Betz limitControl volumeDiffuserDimensionless numberEfficiencyFree-streamlineLock-inMeasurementMomentum theoremPoint vortex

All concepts