What's the formula?

Question

What is the formula to determine the rate of flow (gallons per minute) of water through 1/2 inch pipe at a given pressure?

Answer 1

Without pipe friction...
Bernoulli's Principle
P0 - P = 1/2 (rho) v^2 + (rho) (g) (h)

Then the volume flow is v * area. You have to apply the correct scaling factors to ensure consistent units.

With pipe friction: the RHS has an extra term that is empirically determined and depends on the length of pipe, the condition of the pipe, and the flow rate. Also the velocity gets modified to reflect a viscous flow profile, so that the effective velocity is a bit lower.

Answer 2

The velocity head is the static pressure, or pressure head in feet of liquid that would cause that velocity = h.

h = 0.00259 x gpm^2/d^4

where d = inside diameter of the pipe in inches.

you can convert feet of liquid head to psi by dividing the feet of liquid head by 2.3077.

This formula is taken from Cameron Hydraulic Data, 14th Edition.

Answer 3

♣ Bernoulli says: pressure p = 0.5*d*v^2 in Pa=N/m^2 units, where d=1000 kg/m^3, v is speed of jet in m/s units; hence v=√(2p/d)
♦ also volume per second r=v*s, where s=pi*D^2/4, D=0.5 inch = 0.5*0.0254 m;
♥ thus rate r= √(2p/d) * pi*(D/2)^2 =
= √(2p/1000) *pi* (0.25*0.0254)^2= 5.66516·10^(-6)√p m^3/s =
= 5.66516·10^(-6)√p (1000*60) = 0.340√p liters/min;
mind p is still in Pa; I did it in SI units since I do not know your pressure units and how many liters are in 1 gallon;