Calculate flow rate (GPM) from water pressure (PSI) and orifice diameter. Essential for hydraulics, plumbing, irrigation, and fluid dynamics.
Last updated: March 2026 | By Patchworkr Team
The relationship between pressure (PSI) and flow rate (GPM) is governed by fluid dynamics principles, specifically Bernoulli's equation and the orifice flow equation. When water flows through an orifice or opening, the flow rate depends on the pressure forcing the water through and the size of the opening.
The flow rate is proportional to the square root of the pressure difference. This means doubling the pressure doesn't double the flow rate—it increases flow by about 41% (√2 ≈ 1.41). The orifice diameter has an even stronger effect: flow rate is proportional to the square of the diameter, so doubling the diameter quadruples the flow rate.
The discharge coefficient (Cd) accounts for energy losses due to friction, turbulence, and contraction of the flow stream. A sharp-edged orifice typically has Cd ≈ 0.6, while a well-rounded nozzle can approach Cd ≈ 0.98. This coefficient significantly affects the actual flow rate compared to theoretical calculations.
Calculate flow rate for a garden hose nozzle:
A 0.5-inch diameter rounded nozzle at 60 PSI delivers approximately 46.2 gallons per minute, which equals about 175 liters per minute or 2.9 liters per second.
Flow rate is proportional to the square root of pressure (√P), not pressure itself. Doubling pressure (2×) increases flow by √2 ≈ 1.41×, or about 41%. This comes from Bernoulli's equation in fluid dynamics.
The discharge coefficient (Cd) accounts for energy losses due to friction, turbulence, and flow contraction. Real flow is always less than theoretical flow. Sharp-edged holes have Cd ≈ 0.6, while well-designed nozzles can achieve Cd ≈ 0.98.
Flow rate is proportional to the square of the diameter (d²). Doubling the diameter quadruples the flow rate. A 1-inch orifice delivers 4× more flow than a 0.5-inch orifice at the same pressure.
This calculator is calibrated for water at standard conditions. For other liquids, you need to account for different density and viscosity. The formula includes water's density in the constant 29.84.
Measure the pressure difference between the inlet and outlet (ΔP). If discharging to atmosphere, use gauge pressure at the inlet. Static pressure (no flow) will be higher than dynamic pressure (with flow).
Several factors affect real-world flow: pipe friction losses, fitting losses, elevation changes, temperature variations, and measurement accuracy. This calculator gives theoretical flow at the orifice itself.
For sharp-edged holes, use 0.6. For standard pipe fittings, use 0.7-0.75. For rounded nozzles, use 0.8-0.9. For precision applications, consult manufacturer specifications or measure actual flow.
This calculates flow through an orifice or restriction. For flow through a full pipe, you need the Hazen-Williams or Darcy-Weisbach equations which account for pipe length, roughness, and diameter differently.
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