Flow Rate Calculator (PSI to GPM)
Convert water pressure (PSI) into flow rate (GPM) based on the pipe diameter and the type of opening. This calculator uses fluid dynamics principles to estimate how much water will flow through an orifice or pipe given a specific pressure.
Understanding Flow Rate and PSI
The relationship between pressure (PSI) and flow rate (Gallons Per Minute or GPM) is governed by Bernoulli's principle. Simply put, higher pressure forces more fluid through an opening, while a larger opening (diameter) allows a greater volume of fluid to pass through at the same pressure.
This relationship is non-linear. Doubling the pressure does not double the flow rate; it increases it by the square root of 2 (approximately 1.41 times). However, doubling the diameter of the pipe quadruples the area, which significantly increases the flow rate.
Q = 29.84 × Cd × d² × √P
Where:
• Q = Flow Rate in GPM
• Cd = Discharge Coefficient
• d = Diameter in inches
• P = Pressure in PSI
What is the Discharge Coefficient (Cd)?
The Discharge Coefficient (Cd) represents the efficiency of the flow through an opening. Real-world fluids experience friction and turbulence, meaning the actual flow is always less than the theoretical maximum.
- Standard Orifice (0.60 – 0.62): Used for sharp-edged holes drilled in plates or tanks. This is the most common setting for leaks or simple drilled holes.
- Smooth Nozzle (0.98): Used for fire hoses or precision-machined nozzles designed to minimize friction.
- Venturi (0.80 – 0.95): Used in specialized tubes designed to measure flow or mix fluids.
Common Applications
This PSI to GPM calculator is essential for various industries and DIY projects:
- Plumbing: Estimating water flow from a broken pipe or determining if supply lines are adequate for new fixtures.
- Irrigation: calculating sprinkler output based on line pressure and nozzle size.
- Fire Fighting: Determining hydrant flow or hose output.
- Pressure Washing: Matching nozzle tips to pump pressure capabilities.
Why Diameter Matters Most
While increasing pressure increases flow, increasing the diameter of your pipe or orifice has a much more dramatic effect. Because the formula uses the diameter squared (d²), a 2-inch pipe carries four times as much water as a 1-inch pipe at the same pressure, assuming the discharge coefficient remains constant.