Orifice Flow Formula
Q = Cd x A x sqrt(2 x g x h). Solving for h (head in feet): h = (Q / (Cd x A))^2 / (2 x g). PSI = h x 0.4335. For PSI to GPM, solve for Q. Units: Q in cfs (GPM / 448.83), A in ft^2, g = 32.174 ft/s^2, h in ft.
Frequently Asked Questions
GPM and PSI are related through the orifice flow equation: Q = Cd x A x sqrt(2 x g x h), where Q is flow rate, Cd is the discharge coefficient (0.6-0.8 typically), A is the orifice area, g is gravity, and h is the pressure head in feet. This calculator handles the unit conversions.
In a simple orifice or nozzle, flow rate is proportional to the square root of pressure. Doubling the pressure multiplies flow by about 1.41 (square root of 2). Quadrupling pressure doubles flow. This non-linear relationship is why small pressure changes have diminishing returns at higher pressures.
The discharge coefficient (Cd) accounts for energy losses and flow contraction as fluid passes through an orifice. A sharp-edged orifice typically has Cd = 0.6. A well-rounded entrance can achieve Cd = 0.98. Sprinkler heads and nozzles typically range from 0.7-0.9.
Most residential water systems operate at 40-80 PSI. The ideal range is 60-80 PSI for typical fixtures. Pressures above 80 PSI can damage appliances and cause water hammer. Most local codes require a pressure-reducing valve (PRV) if line pressure exceeds 80 PSI.
For every foot of elevation drop, water gains approximately 0.433 PSI (or 0.299 PSI per foot for a tank elevated above the delivery point). A water tower 100 feet above the delivery point provides about 43 PSI of static pressure. Conversely, every foot of elevation rise reduces pressure by 0.433 PSI.
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