PSI to GPM Calculator
### Fluid Dynamics & Hydrostatic Orifice Flow Pressure (pounds per square inch) and volumetric flow rate (gallons per minute) are governed by **Torricelli's Law** and the **Bernoulli Energy.
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📐 Formula
💡 Practical Example
Discharging water at 50.0 PSI through a 0.75-inch smooth bore nozzle: Generates 116.27 GPM and 3.39 Hydraulic Horsepower.
📖 About PSI to GPM Calculator
Fluid Dynamics & Hydrostatic Orifice Flow
Pressure (pounds per square inch) and volumetric flow rate (gallons per minute) are governed by Torricelli's Law and the Bernoulli Energy Equation. Fluid cannot flow through a pipe or orifice without a pressure differential Δ P.
Core Hydraulic Flow Equations
- Freeman's Nozzle Orifice Discharge: Q = 29.83 × C_d × d^2 × √(P)
- NFPA Fire Sprinkler Equation: Q = K × √(P) P = ((Q) / (K))^2
- Control Valve Sizing: Q = C_v × √((Δ P) / (SG))
- Torricelli Theoretical Jet Velocity: v = √(2 g h) = 12.19 × √(P)
- Hydraulic Horsepower: HHP = (P × Q) / (1,714)
Standard Orifice Discharge Coefficients (C_d)
- Smooth Bore Nozzle / Fire Monitor: C_d ≈ 0.97 - 0.99
- Standard Short Pipe / Spigot: C_d ≈ 0.80 - 0.82
- Square Sharp-Edged Orifice: C_d ≈ 0.60 - 0.
62.
How to Use This Calculator
Enter your Hydraulic System Model — choose from Nozzle / Orifice: Q = 29.83 × Cd × d² × √P, Fire Sprinkler / Hose: Q = K × √P, Control Valve: Q = Cv × √(ΔP / SG), Differential Water Pressure (PSI) (e.g. 50.0 in PSI), Orifice / Nozzle Diameter (d) (e.g. 0.75 in in), Discharge Coefficient (Cd) — choose from 0.98 - Smooth Bore Fire Nozzle / Well-Rounded, 0.80 - Short Pipe / Standard Tap, 0.62 - Sharp-Edged Orifice / Restriction Plate, and Valve Flow Coefficient (Cv) or Sprinkler K-Factor (e.g. 5.6). Results update instantly as you type — adjust any value to compare scenarios.
The Formula
Freeman's Nozzle Formula: Q = 29.83 Cd d^2 * sqrt(P)
Velocity V = 12.19 * sqrt(P) in ft/s for water (Torricelli)
NFPA Fire Sprinkler: Q = K * sqrt(P)
Valve Cv: Q = Cv * sqrt(dP)
Hydraulic Horsepower HHP = (P * Q) / 1714
Worked Example
Discharging water at 50.0 PSI through a 0.75-inch smooth bore nozzle: Generates 116.27 GPM and 3.39 Hydraulic Horsepower.
Understanding Your Result
Unit conversion precision: round to the same number of significant figures as your original measurement. Converting 6 feet to meters gives 1.8288 m — but if your measurement was approximate (±1 inch), expressing more than 2 decimal places is false precision. For international trade and technical specifications, SI units (meters, kilograms, liters) are the standard. US customary units (feet, pounds, gallons) differ from Imperial UK units: 1 US gallon = 3.785 L vs. 1 UK gallon = 4.546 L.
💡 Methodological Standards & Calculation Accuracy
- All calculations are performed client-side in your browser using verified, standards-compliant mathematical algorithms.
- Results are provided for educational and informational analysis; verify critical applications with certified domain specialists.
- Ensure input values are entered in consistent units matching the selector options to guarantee accurate outputs.
- Periodic recalibration is recommended whenever baseline assumptions, operating parameters, or external conditions change.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.