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

Diffuser — where it appears

A duct that widens in the direction of flow to turn a stream's speed into pressure. Subsonic flow slows in it and gains pressure, limited by the boundary layer's tendency to separate under the rising pressure; supersonic flow does the opposite, and in a nozzle the widening part accelerates it.

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

Six nozzles, six pump curves, and where each one is best. The head ratio a water jet pump delivers against the flow ratio it entrains, for six area ratios from a narrow nozzle to one filling four-fifths of the throat. A wide nozzle makes a tall, steep curve that is finished at a small flow; a narrow one makes a low, long curve. The dots are each curve's best-efficiency point. Nozzle, suction, throat-friction and diffuser losses are included at borrowed representative values, and the mixing loss is computed.

The nozzle that is best at one thing

Put the four losses back into a jet pump and three questions get three answers. The most head comes from a nozzle four-fifths of its throat, in closed form; the best efficiency from one a quarter of it; and the most flow from whichever nozzle is smallest, because flow has no optimum at all.

applied · Ejector 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.

EfficiencyPressure recoveryActuator discBase pressureThe Betz limitThe Borda–Carnot lossControl volumeEjectorEntrainmentLoss coefficientMixing lossModel limit

All concepts