Calculating Flow Rate with Pressure

Flow Rate & Pressure Differential Calculator

Calculate the volumetric flow rate of water through an orifice or nozzle based on the pressure drop.

PSI Bar

(Atmospheric = 0)

mm inch

Typically 0.60 to 0.98

Calculation Results:

Liters Per Minute

0.00

Gallons Per Minute

0.00

Understanding Flow Rate and Pressure

In fluid dynamics, the relationship between pressure and flow rate is governed by Bernoulli's Principle. When a fluid passes through a restriction (like an orifice or a nozzle), its potential energy (pressure) is converted into kinetic energy (velocity).

The Formula

The standard equation for flow through an orifice is:

Q = Cd × A × √ (2 × ΔP / ρ)

• Q: Volumetric flow rate
• Cd: Discharge coefficient (accounts for losses and turbulence)
• A: Cross-sectional area of the opening
• ΔP: Pressure difference between inlet and outlet (P1 – P2)
• ρ (rho): Density of the fluid (Water is approx. 1000 kg/m³)

Example Calculation

If you have an inlet pressure of 50 PSI discharging into the open air (0 PSI) through a 12mm hole with a Cd of 0.62:

1. Pressure difference is 50 PSI (converted to approx. 344,738 Pascals).
2. The cross-sectional area of a 12mm hole is approximately 0.000113 m².
3. The resulting flow rate would be approximately 73.8 Liters per Minute (LPM).

Common Discharge Coefficients (Cd)

Orifice Type	Typical Cd
Sharp-edged Orifice	0.60 – 0.65
Well-rounded Nozzle	0.95 – 0.98
Short Tube (Flush)	0.80

function calculateFlow() { var p1 = parseFloat(document.getElementById('inletPressure').value); var p2 = parseFloat(document.getElementById('outletPressure').value); var pUnit = document.getElementById('pUnit').value; var d = parseFloat(document.getElementById('diameter').value); var dUnit = document.getElementById('dUnit').value; var cd = parseFloat(document.getElementById('coeff').value); if (isNaN(p1) || isNaN(p2) || isNaN(d) || isNaN(cd)) { alert("Please enter valid numeric values."); return; } var deltaP = p1 – p2; if (deltaP <= 0) { alert("Inlet pressure must be higher than outlet pressure to calculate flow."); return; } // Convert Pressure to Pascals (N/m^2) var deltaPa = 0; if (pUnit === "psi") { deltaPa = deltaP * 6894.76; } else { deltaPa = deltaP * 100000; } // Convert Diameter to Meters var dMeters = 0; if (dUnit === "mm") { dMeters = d / 1000; } else { dMeters = d * 0.0254; } // Calculations var area = Math.PI * Math.pow((dMeters / 2), 2); var densityWater = 1000; // kg/m^3 // Torricelli / Bernoulli variation // v = Cd * sqrt(2 * deltaP / rho) var velocity = cd * Math.sqrt((2 * deltaPa) / densityWater); // Q = v * A (Result in m^3/s) var flowM3S = velocity * area; // Convert m^3/s to LPM (1 m^3/s = 60,000 LPM) var flowLPM = flowM3S * 60000; // Convert LPM to GPM (1 LPM = 0.264172 GPM) var flowGPM = flowLPM * 0.264172; // Display results document.getElementById('resultArea').style.display = 'block'; document.getElementById('resLPM').innerText = flowLPM.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('resGPM').innerText = flowGPM.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('velocityRes').innerText = "Exit Velocity: ~" + velocity.toFixed(2) + " m/s"; }