How to Calculate Flow Rate from Pressure and Pipe Diameter
by
Flow Rate Calculator
Calculate water flow rate based on pressure and pipe size
0.62 for sharp orifice, 0.98 for smooth nozzle
Calculation Results:
Gallons Per Minute (GPM):
0
Liters Per Minute (LPM):
0
Velocity (ft/s):
0
Cubic Feet Per Second (CFS):
0
Understanding Flow Rate from Pressure
In fluid dynamics, the relationship between pressure and flow rate is governed by Bernoulli's Principle. When water is released from a pipe or an orifice, the potential energy (pressure) is converted into kinetic energy (velocity).
The Formula
This calculator uses the Discharge Formula for flow through an orifice, which is the most common way to estimate flow from a known pressure:
Q = Cd × A × √(2 × ΔP / ρ)
Where:
Q: Volumetric flow rate
Cd: Discharge coefficient (accounts for friction and fluid contraction)
A: Cross-sectional area of the pipe (π × r²)
ΔP: Pressure difference (the PSI you entered)
ρ (rho): Density of the fluid (water)
Practical Example
If you have a 1-inch pipe with a domestic water pressure of 50 PSI:
Area: A 1-inch diameter pipe has a radius of 0.5 inches. Area = π × 0.5² = 0.785 square inches.
Pressure: 50 PSI must be converted to absolute pressure units for standard calculations.
Coefficient: Using a standard discharge coefficient of 0.62 (typical for standard openings).
Result: The flow rate would be approximately 49.6 GPM (Gallons Per Minute).
Important Considerations
Real-world flow rates are affected by several factors not included in this basic calculation:
Pipe Length: Friction losses (head loss) increase as the pipe gets longer, significantly reducing flow.
Pipe Material: Rougher pipes (like old galvanized steel) create more friction than smooth pipes (like PEX or Copper).
Fittings: Elbows, tees, and valves create turbulence and reduce the effective flow.
function calculateFlowRate() {
// Inputs
var diameterInch = parseFloat(document.getElementById('pipeDiameter').value);
var pressurePsi = parseFloat(document.getElementById('pressurePsi').value);
var cd = parseFloat(document.getElementById('dischargeCo').value);
// Validate
if (isNaN(diameterInch) || isNaN(pressurePsi) || isNaN(cd) || diameterInch <= 0 || pressurePsi <= 0) {
alert("Please enter valid positive numbers.");
return;
}
// Constants
var rho = 62.42; // Density of water in lbs/ft^3
var gravity = 32.174; // ft/s^2
// 1. Calculate Cross-sectional Area in square feet
var radiusInch = diameterInch / 2;
var areaSqInch = Math.PI * Math.pow(radiusInch, 2);
var areaSqFt = areaSqInch / 144;
// 2. Convert PSI to lbs/sq ft (Pressure)
var pressurePsf = pressurePsi * 144;
// 3. Calculate Velocity (v = sqrt(2gh) or v = sqrt(2P/rho))
// Bernoulli simplified for exit velocity: v = sqrt(2 * pressure_diff / density)
// Result is in ft/s
var velocity = cd * Math.sqrt((2 * pressurePsf) / (rho / gravity) / gravity * 32.174);
// Correction for units: Velocity (ft/s) = Cd * sqrt(2 * Pressure_psf / (rho / g))
// Let's use the standard flow formula: Q = Cd * A * sqrt(2 * g * h) where h is head in feet
// h = (PSI * 2.31)
var headFeet = pressurePsi * 2.3067;
var calcVelocity = cd * Math.sqrt(2 * 32.174 * headFeet);
// 4. Calculate Flow Rate (Q = A * V)
var flowCFS = areaSqFt * calcVelocity;
// 5. Convert CFS to GPM (1 CFS = 448.831 GPM)
var flowGPM = flowCFS * 448.831;
// 6. Convert GPM to LPM (1 GPM = 3.78541 LPM)
var flowLPM = flowGPM * 3.78541;
// Output results
document.getElementById('resGPM').innerText = flowGPM.toFixed(2);
document.getElementById('resLPM').innerText = flowLPM.toFixed(2);
document.getElementById('resVelocity').innerText = calcVelocity.toFixed(2);
document.getElementById('resCFS').innerText = flowCFS.toFixed(4);
// Show result div
document.getElementById('flowResults').style.display = 'block';
}