The gauge pressure measured at the nozzle or orifice.
The internal diameter of the opening where water exits.
Typically 0.90 for smooth nozzles, 0.60 for sharp-edged holes.
Flow Rate (GPM):–
Flow Rate (LPM):–
Fluid Velocity (ft/sec):–
function calculateFlowRate() {
// Get input values using var
var pressure = parseFloat(document.getElementById('pressurePsi').value);
var diameter = parseFloat(document.getElementById('diameterInch').value);
var cd = parseFloat(document.getElementById('dischargeCoeff').value);
var resultDiv = document.getElementById('result');
// Validation
if (isNaN(pressure) || isNaN(diameter) || isNaN(cd) || pressure < 0 || diameter <= 0) {
alert("Please enter valid positive numbers for Pressure and Diameter.");
resultDiv.style.display = "none";
return;
}
// Calculation Logic
// Formula: Q (GPM) = 29.83 * Cd * d^2 * sqrt(P)
// Where P is PSI, d is diameter in inches
var constant = 29.83;
var diameterSquared = Math.pow(diameter, 2);
var sqrtPressure = Math.sqrt(pressure);
var flowGPM = constant * cd * diameterSquared * sqrtPressure;
// Convert GPM to Liters per Minute (LPM)
var flowLPM = flowGPM * 3.78541;
// Calculate Velocity
// Velocity (ft/s) = (0.4085 * GPM) / (d^2)
// Alternatively: V = Cd * sqrt(2 * P_in_feet_head * g) … simpler to derive from GPM
var velocity = (0.4085 * flowGPM) / diameterSquared;
// Display Results
document.getElementById('resultGPM').innerHTML = flowGPM.toFixed(2) + " gal/min";
document.getElementById('resultLPM').innerHTML = flowLPM.toFixed(2) + " L/min";
document.getElementById('resultVelocity').innerHTML = velocity.toFixed(2) + " ft/s";
resultDiv.style.display = "block";
}
How to Calculate Flow Rate from PSI
Calculating the water flow rate through a nozzle, orifice, or leak based on pressure (PSI) is a fundamental task in fluid dynamics, plumbing, and fire protection engineering. This calculator uses the standard orifice discharge equation to estimate how much liquid will pass through an opening of a specific diameter at a given pressure.
The Flow Rate Formula
The relationship between Pressure (PSI) and Flow Rate (GPM) through an orifice is non-linear. The standard formula used in this calculator is:
Q = 29.83 × Cd × d² × √P
Where:
Q = Flow rate in Gallons Per Minute (GPM)
Cd = Discharge Coefficient (efficiency of the opening)
d = Diameter of the orifice in inches
P = Pressure at the orifice in PSI
29.83 = A mathematical constant derived from gravity and unit conversions
Understanding the Variables
1. Pressure (PSI)
This is the gauge pressure measured directly behind the opening. According to Bernoulli's principle, higher pressure results in higher velocity and consequently higher flow rate. Note that flow rate increases with the square root of pressure. To double the flow, you must quadruple the pressure.
2. Diameter
The physical size of the hole or nozzle exit. Because diameter is squared in the formula ($d^2$), small changes in diameter have a massive impact on flow rate. A 2-inch hole flows four times as much water as a 1-inch hole at the same pressure.
3. Discharge Coefficient ($C_d$)
Real-world fluids create friction and turbulence. The Discharge Coefficient ($C_d$) accounts for these losses. It represents the ratio of actual flow to the theoretical maximum flow.
Orifice Type
Typical $C_d$ Value
Description
Smooth Fire Nozzle
0.96 – 0.99
Highly efficient, tapered smooth bore.
Standard Sprinkler
0.75 – 0.90
Varies by design and manufacturer.
Square-Edged Orifice
0.60 – 0.62
A drilled hole in a pipe wall or plate (sharp edges).
Short Tube
0.80 – 0.82
A short pipe length extending from a tank.
Example Calculation
Imagine you have a garden hose with a smooth nozzle ($C_d$ = 0.90) that has an opening diameter of 0.5 inches. The pressure gauge reads 40 PSI.
d² = 0.5 × 0.5 = 0.25
√P = √40 ≈ 6.325
Calculation: 29.83 × 0.90 × 0.25 × 6.325
Result: ≈ 42.45 GPM
Limitations
This calculator assumes the fluid is water (specific gravity ≈ 1.0) and that it is discharging into the atmosphere (free discharge). If the water is discharging into a pressurized vessel, you must use the differential pressure ($\Delta P$) across the orifice rather than the gauge pressure.