How to Calculate Flow Rate of Water Using Pressure

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Water Flow Rate Calculator

Calculate water discharge (GPM) based on pressure and opening diameter.

The gauge pressure at the opening/nozzle.
Internal diameter of the pipe or nozzle.
0.98 – Smooth Nozzle 0.90 – Standard Fire Nozzle 0.80 – Short Tube 0.61 – Sharp-Edged Orifice 0.60 – Rough Opening Efficiency of the opening (friction loss factor).

Calculation Results

Flow Rate (US Gallons): 0 GPM
Flow Rate (Liters): 0 LPM
Water Velocity: 0 ft/sec

How to Calculate Flow Rate of Water Using Pressure

Understanding the relationship between water pressure and flow rate is essential for plumbing, irrigation, fire fighting, and industrial engineering. While pressure (measured in PSI) represents the potential energy of the water, the flow rate (measured in GPM) represents the actual volume of water moving through an opening over time.

The Orifice Flow Formula

To calculate the flow rate through an opening (like a nozzle, a pipe leak, or an orifice) based on pressure, we use a derivation of Torricelli's Law and Bernoulli's Principle. The practical formula used in US customary units 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 opening in inches
  • P = Pressure in PSI (Pounds per Square Inch)
  • 29.83 = A mathematical constant converting units

Understanding the Variables

Pressure (PSI): This is the gauge pressure reading right before the water exits the opening. Higher pressure forces water out faster.

Diameter (D): Small changes in diameter have a massive impact on flow. Because the formula squares the diameter ($D^2$), doubling the diameter roughly quadruples the flow rate.

Discharge Coefficient ($C_d$): Real-world openings create friction and turbulence. The $C_d$ accounts for this. A perfectly smooth nozzle might have a $C_d$ of 0.98, while a jagged hole in a pipe might only have a $C_d$ of 0.60.

Example Calculation

Imagine you have a fire hose with a 1-inch smooth nozzle ($C_d$ = 0.90) operating at 50 PSI.

  1. Square the diameter: 1² = 1
  2. Find the square root of pressure: √50 ≈ 7.07
  3. Apply the formula: 29.83 × 0.90 × 1 × 7.07
  4. Result: Approximately 189.8 GPM
function calculateWaterFlow() { // 1. Get input values var pressure = document.getElementById('pressurePsi').value; var diameter = document.getElementById('diameterInch').value; var cd = document.getElementById('dischargeCoeff').value; var resultsDiv = document.getElementById('resultsArea'); // 2. Validate inputs if (pressure === "" || diameter === "" || pressure < 0 || diameter <= 0) { alert("Please enter valid positive numbers for Pressure and Diameter."); return; } // Convert strings to floats var p = parseFloat(pressure); var d = parseFloat(diameter); var c = parseFloat(cd); // 3. Perform Calculations // Formula: Q (GPM) = 29.83 * Cd * d^2 * sqrt(p) var gpm = 29.83 * c * Math.pow(d, 2) * Math.sqrt(p); // Convert GPM to Liters Per Minute (LPM) // 1 US Gallon = 3.78541 Liters var lpm = gpm * 3.78541; // Calculate Velocity (Feet per Second) // Formula: V = (0.408 * Q) / d^2 var velocity = (0.408 * gpm) / Math.pow(d, 2); // 4. Update the DOM with results document.getElementById('resGPM').innerHTML = gpm.toFixed(2) + " GPM"; document.getElementById('resLPM').innerHTML = lpm.toFixed(2) + " LPM"; document.getElementById('resVelocity').innerHTML = velocity.toFixed(2) + " ft/sec"; // Show the results box resultsDiv.style.display = "block"; }

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