Bernoulli & the Venturi

Continuity comes first. For an incompressible flow the mass entering a duct each second must equal the mass leaving it, so A₁V₁ = A₂V₂. Halve the area and the velocity must double. Nothing about pressure has been said yet; this is bookkeeping on the fluid itself.

Bernoulli then pays the bill. Along a streamline, P + ½ρV² + ρgh is constant. The ½ρV² term is dynamic pressure and the P term is static pressure; their sum is total or stagnation pressure. Since the total cannot change, the extra dynamic pressure in the throat can only come out of the static pressure, which is why P₂ falls below P₁. Note that the drop goes with the square of velocity, so it grows very quickly as the throat is tightened.

This is the operating principle behind a large amount of aircraft hardware: the carburettor venturi, which uses the throat depression to draw fuel out of the jet; the pitot-static system, where total minus static gives the dynamic pressure the ASI reads as airspeed; and the pressure distribution over an aerofoil, where faster flow over the upper surface means lower static pressure there. The same reasoning explains why a diffuser, which is a venturi run backwards, converts velocity back into static pressure.

• Try this: Halve the area ratio and watch V₂ and ΔP. Velocity doubles, but by how much does the pressure drop change, and why?
• Try this: Reduce the density to simulate high altitude at the same indicated velocity. What happens to the throat depression, and what does that mean for a carburettor at altitude?
• Try this: Switch to carburettor mode and open the throat right up. Why does fuel delivery fall off, and what does that tell you about mixture at low power?