I need to calculate the diameter of an orifice to obtain 2.5 gpm flow at ?? pounds of water pressure?

Answer 1

I know that the velocity that water exits a hole in a tank depends on the depth of the water with the following formula. (Toricelli's Law if you want to look it up).

v = sqrt(2gy)
Where g is the acceleration of gravity ( 32f/s^2, or 9.8 m/s^2)
and y is the height of the water above the hole.

v depends on y because a higher height means more presssure.

The amount of fluid flowing out of the hole is equal to the area of the hole times the velocity.
A circular hole of radius r has an area of pi*r^2
Let f represent your fluid flow in ft^3/s and radius in feet
f = v * a = sqrt(2gy) * pi * r^2
r^2 = f / ( sqrt(2gy) * pi )
r = sqrt ( f / (sqrt(2gy) * pi))

Now you just need to figure out how the depth of water ( y) relates to water pressure and plug it in that formula. Also, don't forget that f is in cubic feet per second not gpm. You'll have to change from gpm to fps before putting it in the formula.

Answer 2

The answer from demiurge42 is good but you need to add a couple things. First, the flow area is not the area of your orifice. The edge effects on the orifice make the effective flow area (called the vena contracta) have a diameter about 0.60 times the diameter of the orifice. Second, the conversion between psi and head of water is just the density of the water. In practical terms this is 0.43 psi/ft.