Fluid Mechanics

Where the Flow Is Faster, the Pressure Is Lower

Bernoulli p + ½ρv² + ρgh = const (one streamline); faster = lower pressure; Venturi, atomizer

Water passes through a pinched Venturi tube. Squeeze the throat to speed the water up and watch the pressure gauges to see what happens to the pressure.

Drag the probe along the tube and read the speed v and pressure p. Where it is wide and slow the pressure is high (tall column); at the narrow, fast throat it is low (short column).

Now pinch the throat. The tighter you squeeze, the higher the throat speed climbs and the lower its pressure drops. Speeding up and pressure falling happen together.

The three energy terms add to a constant: pressure p, kinetic ½ρv², height ρgh. Drag v and as the kinetic term grows, the pressure term shrinks by the same amount. Speed is bought by spending pressure.

As an equation, p + ½ρv² + ρgh = constant, Bernoulli's equation. Drag v and p drops to match instantly. (Assumes steady, inviscid, incompressible flow.)

Look at an atomizer. Blow air fast across the top of a tube and the pressure there drops, so the liquid below is sucked up and sprayed out. Drag the air speed up.

In PracticeTo sum up: along one streamline, p + ½ρv² + ρgh stays constant. So a faster spot has lower pressure and a slower spot higher pressure. If continuity said the flow speeds up where it narrows, Bernoulli adds that the pressure there is lower. This holds for steady, inviscid, incompressible flow, along a single streamline. A Venturi meter, an atomizer, the lift on an airplane wing, a curveball all run on this. In the next lesson, we follow the force that appears when a flow strikes an object and changes its momentum, through the momentum control volume.

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