Calculate water flow velocity and volume based on line pressure and pipe size.
Smooth Nozzle (0.98)
Sharp Edged Orifice (0.61)
Short Tube (0.80)
Water (62.4 lb/ft³)
Estimated Flow Results:
How to Calculate Flow Rate from Pressure and Diameter
Calculating the flow rate of water through an opening or pipe based on pressure is a fundamental task in hydraulics and plumbing. The calculation generally relies on Bernoulli's principle and the Law of Conservation of Energy.
The Formula
To calculate the theoretical flow rate (Q), we first determine the velocity of the fluid and then multiply it by the cross-sectional area of the pipe. The formula used in this calculator is:
Q = Cd × A × √(2 × ΔP / ρ)
Q: Flow Rate
Cd: Discharge Coefficient (accounts for friction and turbulence)
A: Cross-sectional area of the opening (π × r²)
ΔP: Pressure difference
ρ (Rho): Density of the fluid
Common Discharge Coefficients (Cd)
Opening Type
Coefficient Value
Smooth Nozzle
0.97 – 0.99
Short Pipe/Tube
0.80 – 0.82
Sharp-Edged Orifice
0.61 – 0.65
Step-by-Step Example
Suppose you have a 1-inch diameter pipe with a constant pressure of 40 PSI.
Convert Units: 40 PSI is approximately 5,760 lbs per square foot.
Calculate Velocity: For water, the theoretical velocity would be approximately 77 feet per second.
Calculate Area: A 1-inch pipe has an area of 0.785 square inches (0.00545 sq ft).
Determine Flow: Multiplying velocity by area and applying a discharge coefficient (e.g., 0.98) gives roughly 185 Gallons Per Minute (GPM) for an open discharge.
Note: Real-world results may vary based on pipe length, pipe roughness (friction loss), and elevation changes. This calculator assumes a discharge to atmosphere or a significant pressure drop across a short distance.
function calculateFlowRate() {
var psi = parseFloat(document.getElementById('flow_pressure').value);
var dia = parseFloat(document.getElementById('flow_diameter').value);
var cd = parseFloat(document.getElementById('flow_cd').value);
var density = 62.4; // lbs/ft3 for water
if (isNaN(psi) || isNaN(dia) || psi <= 0 || dia <= 0) {
alert("Please enter valid positive numbers for Pressure and Diameter.");
return;
}
// 1. Calculate Area (A) in square feet
// dia in inches to feet: dia / 12
var radiusFt = (dia / 2) / 12;
var areaSqFt = Math.PI * Math.pow(radiusFt, 2);
// 2. Convert PSI to lbs/sq foot (Pressure P)
// 1 PSI = 144 lbs/sq foot
var pressurePsf = psi * 144;
// 3. Calculate Velocity (v) in feet per second
// v = sqrt( (2 * g * P) / density ) where g is gravity 32.174
// Simplified Bernoulli: v = sqrt(2 * P / rho) in consistent units
// Velocity (ft/s) = sqrt(2 * pressurePsf / density)
var velocity = Math.sqrt((2 * pressurePsf) / (density / 32.174));
// 4. Calculate Flow Rate (Q) in cubic feet per second
var qCfs = cd * areaSqFt * velocity;
// 5. Convert CFS to Gallons Per Minute (GPM)
// 1 CFS = 448.831 GPM
var gpm = qCfs * 448.831;
// 6. Convert GPM to Liters Per Minute (LPM)
// 1 GPM = 3.78541 LPM
var lpm = gpm * 3.78541;
// Display Results
document.getElementById('flow_result_box').style.display = 'block';
document.getElementById('res_gpm').innerHTML = gpm.toFixed(2) + " GPM (Gallons/Min)";
document.getElementById('res_lpm').innerHTML = "Equivalent to " + lpm.toFixed(2) + " LPM (Liters/Min)";
document.getElementById('res_velocity').innerHTML = "Exit Velocity: ~" + velocity.toFixed(2) + " feet per second";
}