How to Calculate Flow Rate Using Pressure

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Flow Rate from Pressure Calculator

Water is approx. 1000 kg/m³
Standard orifice is 0.6 to 0.7

Calculated Flow Results

Gallons Per Minute (GPM) 0.00
Liters Per Minute (LPM) 0.00

Understanding Flow Rate and Pressure Relationship

In fluid dynamics, the relationship between flow rate and pressure is fundamental. When fluid passes through a restriction (like a pipe or an orifice), the potential energy (pressure) is converted into kinetic energy (velocity). This calculator uses Bernoulli's principle to determine how much fluid will flow based on the pressure difference across that restriction.

The Calculation Formula

The standard formula for calculating flow rate (Q) from pressure drop (ΔP) is:

Q = Cd * A * √(2 * ΔP / ρ)
  • Q: Flow Rate (Volume per unit time)
  • Cd: Discharge Coefficient (accounts for energy losses and turbulence)
  • A: Cross-sectional area of the opening
  • ΔP: Pressure difference (Pressure Drop)
  • ρ (rho): Density of the fluid

Key Variables Explained

Pressure Drop: This is the difference in pressure between two points in a system. The higher the pressure drop, the faster the fluid will move through the opening.

Discharge Coefficient (Cd): No system is 100% efficient. Factors like friction and the shape of the hole reduce the flow. A sharp-edged orifice usually has a Cd of about 0.62 to 0.65, while a smooth nozzle can be 0.95 or higher.

Fluid Density: Heavier fluids (higher density) require more pressure to move at the same speed as lighter fluids. Water has a density of approximately 1000 kg/m³ (62.4 lbs/ft³).

Example Calculation

If you have a 1-inch pipe with a 50 PSI pressure drop moving water (density 1000 kg/m³) with a discharge coefficient of 0.65:

  1. Convert PSI to Pascals: 50 PSI ≈ 344,738 Pa.
  2. Calculate Area: A = π * (0.0127m)² ≈ 0.0005067 m².
  3. Apply Formula: Q = 0.65 * 0.0005067 * √(2 * 344738 / 1000)
  4. Result: ~0.00865 m³/s, which converts to approximately 137 GPM.
function calculateFlowRate() { // Get Inputs var psi = parseFloat(document.getElementById('pressureDrop').value); var diameterInch = parseFloat(document.getElementById('pipeDiameter').value); var rho = parseFloat(document.getElementById('fluidDensity').value); var cd = parseFloat(document.getElementById('dischargeCoeff').value); // Validation if (isNaN(psi) || isNaN(diameterInch) || isNaN(rho) || isNaN(cd) || psi <= 0 || diameterInch <= 0 || rho <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // 1. Convert PSI to Pascals (N/m^2) // 1 PSI = 6894.76 Pascals var deltaP = psi * 6894.76; // 2. Convert Diameter (inches) to Radius (meters) // 1 inch = 0.0254 meters var radiusMeter = (diameterInch * 0.0254) / 2; // 3. Calculate Area (m^2) var area = Math.PI * Math.pow(radiusMeter, 2); // 4. Calculate Velocity (m/s) using Bernoulli // v = sqrt(2 * deltaP / rho) var velocity = Math.sqrt((2 * deltaP) / rho); // 5. Calculate Flow Rate Q (m^3/s) // Q = Cd * A * v var flowRateM3S = cd * area * velocity; // 6. Convert m^3/s to other units // 1 m^3/s = 15850.3 Gallons Per Minute (US) // 1 m^3/s = 60000 Liters Per Minute var gpm = flowRateM3S * 15850.323; var lpm = flowRateM3S * 60000; // Display Results document.getElementById('gpmOutput').innerText = gpm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('lpmOutput').innerText = lpm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('flowResult').style.display = 'block'; }

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