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bernoullis principle

In: Physics

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Bernoulli’s principle is essentially the principle of conservation of energy applied to fluids.

It states that for an *inviscid* fluid (one with no viscosity), the following quantity is constant along a streamline:

v^2 /2+gh+p/d

where, v is the velocity of the fluid, p is the pressure, d is the density, g is acceleration due to gravity (9.81m/s^2), and z is the vertical coordinate. What this means is that, if there’s nothing adding energy to the fluid (like a pump) or dissipating energy from it (like viscosity), then any increase in the velocity of the fluid will result in a drop in pressure, and vice versa.

This happens because any kinetic energy gained by the fluid must come from somewhere – energy cannot be created out of nothing – and if it isn’t coming from any external source then it’s coming from the internal pressure of the fluid, which drops.

Bernoulli’s principle is responsible for the [venturi effect](https://en.wikipedia.org/wiki/Venturi_effect) – the drop in pressure when a fluid flows through a narrow part of the pipe. The narrower cross section means the fluid must flow faster, and in order for it to accelerate, the pressure must drop. When the pipe diameter expands, the velocity drops and the pressure rises.

Real fluids are not inviscid – they have viscosity, which works like friction, turning some of the fluids kinetic energy into heat. However, Bernoulli’s principle is still a useful approximation for flows which have low viscosity.