fluid dynamics - Relation between water flow and pressure

Is there any equation that states the relation between pressure and water flow.

I.e. Let's say that in 1 hour with 8mca (water collum meters) pressure I obtain 50m3. What if (giving the same contditions) I execute the same test but now with 15mca?

Is that just proportional?

Answer

The water velocity into a region with atmospheric pressure goes as the square root of the pressure difference by Bernoulli's law. So if you quadruple the pressure difference, you get twice the speed.

This is not exact, because as the water fills up your container, unless it is coming from the very top, the building up water will produce a counterpressure.

The law is that when fluid is dynamically moving, the kinetic energy of the water coming out per unit mass, which is half the square of the velocity, is the loss in potential energy of the top of the imaginary water column of height h per unit mass, which is gh. So the velocity at the outlet is:

$$ v=\sqrt{2gh} = \sqrt{2P \over \rho}$$

Exactly the same as if you dropped the water from the top of the imaginary column to the point where you let out the water, and the answer doesn't depend on whether you have the pressure produced by a column as I imagined it above. This answer conserves energy, since water is disappearing from the top, and appearing at the bottom moving with the same speed as if you dropped it from the top of the column.