Enter the gauge pressure at the nozzle or orifice.
The internal diameter of the opening.
0.98 – Smooth Tapered Nozzle
0.90 – Typical Fire Nozzle
0.80 – Short Tube
0.61 – Sharp Edged Orifice
Custom Value
Flow Rate (GPM):0.00 GPM
Flow Rate (LPM):0.00 LPM
Water Velocity:0.00 ft/s
How to Calculate Water Flow Rate from PSI
Understanding the relationship between water pressure (PSI) and flow rate (GPM) is essential for hydraulic engineering, irrigation planning, fire fighting, and plumbing. While pressure determines how much force the water has, flow rate measures the volume of water moving per unit of time.
The Orifice Flow Equation
To calculate the flow rate through a nozzle, pipe opening, or orifice based on pressure, we use a derivation of Bernoulli's principle. The standard formula for water flow through a circular orifice is:
Q = 29.84 × 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 in Pounds per Square Inch (PSI)
29.84 = Constant combining unit conversions and gravity
Understanding the Discharge Coefficient (Cd)
The discharge coefficient represents the efficiency of the nozzle or hole. It accounts for friction and the contraction of the water stream.
0.98: Highly efficient smooth nozzles (e.g., fire hoses).
0.80 – 0.90: Standard spray nozzles or short tubes.
0.61: A simple sharp-edged hole drilled in a tank or pipe (high turbulence).
Why Diameter Matters More Than Pressure
Looking at the formula, you will notice that the diameter (d) is squared, while the pressure (P) is under a square root. This means that doubling the diameter of your pipe increases flow by 4 times, whereas doubling the pressure only increases flow by roughly 1.4 times (approx 41%).
Common Use Cases
Pressure Washing: Determining the correct nozzle tip size for a specific PSI rating.
Irrigation: Calculating how much water a sprinkler head delivers based on system pressure.
Plumbing: Estimating leak rates from burst pipes or fittings.
// Handle Custom Coefficient Toggle
document.getElementById('dischargeCoeff').onchange = function() {
var val = this.value;
var customInput = document.getElementById('customCd');
if(val === 'custom') {
customInput.style.display = 'block';
} else {
customInput.style.display = 'none';
}
};
function calculateWaterFlow() {
// Get Inputs
var pressure = parseFloat(document.getElementById('pressurePsi').value);
var diameter = parseFloat(document.getElementById('diameterInch').value);
var cdSelect = document.getElementById('dischargeCoeff').value;
var cd = (cdSelect === 'custom') ? parseFloat(document.getElementById('customCd').value) : parseFloat(cdSelect);
// Validation
if (isNaN(pressure) || pressure < 0) {
alert("Please enter a valid positive pressure value.");
return;
}
if (isNaN(diameter) || diameter <= 0) {
alert("Please enter a valid diameter greater than 0.");
return;
}
if (isNaN(cd) || cd 1) {
alert("Please enter a valid discharge coefficient between 0 and 1.");
return;
}
// Calculation Logic
// Formula: Q (GPM) = 29.84 * Cd * d^2 * sqrt(P)
var constant = 29.84;
var flowGPM = constant * cd * Math.pow(diameter, 2) * Math.sqrt(pressure);
// Convert to Liters Per Minute (1 GPM = 3.78541 LPM)
var flowLPM = flowGPM * 3.78541;
// Calculate Velocity
// Formula: V (ft/s) = (Q_gpm * 0.4085) / d_inches^2
var velocity = (flowGPM * 0.4085) / Math.pow(diameter, 2);
// Display Results
document.getElementById('resGPM').innerHTML = flowGPM.toFixed(2) + " GPM";
document.getElementById('resLPM').innerHTML = flowLPM.toFixed(2) + " LPM";
document.getElementById('resVelocity').innerHTML = velocity.toFixed(2) + " ft/s";
// Show Results Section
document.getElementById('results').style.display = 'block';
}