Bernoulli's Principle

slow → fast Gauge height shows pressure; lower = lower pressure

Wide-section speed

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Throat speed

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Throat pressure

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Pressure drop

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continuity A·v = Q (const) | Bernoulli P + ½·ρ·v² = const

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What you're looking at

Fluid flows left to right through a pipe that pinches into a narrow throat in the middle. The particles are coloured by speed, and the three tall tubes are pressure gauges — the fluid rises higher where the pressure is greater. Notice the gauge over the throat sits lowest, even though the fluid there is moving fastest.

First, continuity

The same amount of fluid has to pass every cross-section each second (it can't pile up). So where the pipe is narrow, the fluid must move faster to keep the flow rate the same:

A · v = Q = constant narrow area → high speed

Then, Bernoulli

For a steady, frictionless flow, energy is conserved along a streamline. Written as pressures, the sum of static pressure and "dynamic pressure" (½ρv²) is constant:

P + ½·ρ·v² = constant fast flow ⇒ low pressure

So when the fluid speeds up in the throat, its static pressure must drop to keep the total constant. Faster flow, lower pressure — that's the heart of Bernoulli's principle.

Why it matters

Air rushing faster over the curved top of a wing is at lower pressure than the slower air beneath — the difference is lift.
A carburettor or perfume atomiser uses a throat's low pressure to suck fluid in.
Two sheets of paper pulled close and blown between them are pushed together, not apart.

Things to try

Tighten the throat and watch the throat gauge plunge while the speed climbs. Raise the flow rate and every gauge responds. Increase the density and the pressure drop deepens (more ½ρv²).