Energy Conservation in a Flowing Fluid
Daniel Bernoulli published his principle in 1738: in a steady, frictionless flow, the total mechanical energy per unit volume remains constant along a streamline. This means pressure, velocity, and elevation trade off — when one increases, the others must adjust. It is arguably the most widely applied equation in fluid mechanics, underpinning everything from aircraft lift to blood pressure measurement.
The Venturi: Speed Up, Pressure Down
A venturi is a convergent-divergent passage. As fluid enters the converging section, the continuity equation (A₁V₁ = A₂V₂) demands that velocity increases in proportion to the area ratio. Bernoulli then requires the pressure to drop. At the narrow throat, velocity peaks and pressure reaches its minimum. The diverging section downstream recovers most of the pressure, making the venturi an efficient device with minimal permanent loss.
Measuring Flow with Pressure
The venturi meter exploits this pressure-velocity trade-off to measure flow rate. Pressure taps at the inlet and throat yield ΔP, from which flow rate Q can be calculated. Venturi meters achieve discharge coefficients of 0.97-0.99, meaning 97-99% of the theoretical flow is realized. They are preferred in water supply and industrial applications where minimal head loss and long-term reliability are critical.
Cavitation & Practical Limits
If the throat pressure drops below the liquid's vapor pressure, dissolved gas comes out of solution and vapor bubbles form — cavitation. Collapsing cavitation bubbles generate shock waves that erode metal surfaces and produce noise. Practical venturi designs limit the area ratio and throat velocity to keep pressure safely above the cavitation threshold. This simulator shows when your parameters approach the danger zone.