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It states that along any streamline (a streamline is the path traced out by arbitrarily small element of the fluid), the following equality holds:

p + ½ρv² + ρgz = constant

p - static pressure

ρ - density

v - speed

g - gravitational acceleration

z - vertical position

The constant is the total pressure also called the stagnation pressure. This equation was derived for theoretically "frictionless" or zero viscosity fluids but it is a fair approximation for real fluids where friction is not playing a significant role in the flow. For the case of gases the last term is negligible, so you can say that wherever the flow speed decreases along that streamline, the static pressure will increase. Why along the streamline? Because that constant is only a constant for a given streamline.

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Q: What does bernoulli's principle state about fluids?
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