Venturi effect

In ideal steady flow, a contraction of a pipe increases the speed and lowers the pressure. For constant mass density, equal body-force potential at the ends and approximately uniform endpoint speeds, conservation of mass and the Bernoulli equation give $\dot{M}=S_1{S}_2\sqrt{2\rho (p_1-p_2)/(S_1^2-S_2^2)}$ for flow from a wider to a narrower section. Elevation changes contribute a body-force potential difference, and nonuniform profiles or viscous losses require additional information.

// Target: probability-and-statistics.bigb