Calculate fluid flow rate through an orifice based on pressure differential.
Difference between inlet and outlet pressure.
Inner diameter of the nozzle or hole.
Typically 0.60-0.65 for sharp orifices, 0.98 for smooth nozzles.
Water = 997, Hydraulic Oil ≈ 880, Gasoline ≈ 740.
Volumetric Flow Rate (GPM)
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Flow Rate (Liters/min)
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Fluid Velocity (ft/sec)
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Understanding Flow Rate vs Pressure
In fluid dynamics, the relationship between flow rate and pressure is fundamental to designing piping systems, irrigation networks, and hydraulic machinery. This calculator uses the physical principles governing flow through an orifice or nozzle to estimate how much fluid passes through an opening given a specific pressure difference.
How the Calculation Works
The core of this calculator is derived from Bernoulli's principle, often applied in the form of the orifice equation. The formula used is:
Q = Cd × A × √(2 × ΔP / ρ)
Where:
Q: Volumetric Flow Rate
Cd: Discharge Coefficient (Efficiency of the opening)
A: Cross-sectional Area of the opening
ΔP: Pressure Differential (Pressure drop across the opening)
ρ (rho): Fluid Density
Key Input Factors Explained
Pressure Difference (PSI): This is the "driving force" of the flow. It is the difference between the pressure pushing the fluid and the pressure downstream. Higher pressure results in a higher flow rate, but the relationship is non-linear (square root). To double the flow, you generally need four times the pressure.
Orifice Diameter: The size of the hole or pipe constriction. Small changes in diameter have a massive impact on flow because the area is a function of the square of the diameter.
Discharge Coefficient (Cd): This represents energy losses due to friction and turbulence. A perfect theoretical opening has a Cd of 1.0. A sharp-edged orifice plate typically has a Cd around 0.60 to 0.65, while a smooth, well-rounded nozzle may have a Cd close to 0.98.
Fluid Density: The weight of the fluid affects how easily it is accelerated by pressure. Heavier fluids (like mercury) flow slower than lighter fluids (like gasoline) under the same pressure.
Common Applications
Engineers and technicians use this logic for various tasks:
Fire Fighting: Calculating nozzle pressure required to deliver specific gallons per minute (GPM).
Irrigation: Determining the output of sprinkler heads at different system pressures.
Hydraulics: sizing orifices to control the speed of actuators.
Leak Testing: Estimating the volume of fluid lost through a puncture or crack of a known size.
Why Flow Does Not Double with Pressure
A common misconception is that doubling the pump pressure will double the flow rate. Due to the physics defined by Bernoulli's equation, flow rate is proportional to the square root of pressure. This means that to double the flow rate, you must increase the pressure by a factor of four.
function calculateFlowRate() {
// 1. Get DOM elements
var pressureInput = document.getElementById('fr_pressure');
var diameterInput = document.getElementById('fr_diameter');
var cdInput = document.getElementById('fr_cd');
var densityInput = document.getElementById('fr_density');
var resGPM = document.getElementById('res_gpm');
var resLMin = document.getElementById('res_lmin');
var resVel = document.getElementById('res_velocity');
var resultsDiv = document.getElementById('fr_results_container');
// 2. Parse values
var pressurePsi = parseFloat(pressureInput.value);
var diameterIn = parseFloat(diameterInput.value);
var cd = parseFloat(cdInput.value);
var densityKgM3 = parseFloat(densityInput.value);
// 3. Validation
if (isNaN(pressurePsi) || isNaN(diameterIn) || isNaN(cd) || isNaN(densityKgM3)) {
alert("Please enter valid numbers in all fields.");
return;
}
if (pressurePsi < 0 || diameterIn <= 0 || densityKgM3 <= 0) {
alert("Please ensure values are positive. Diameter and Density cannot be zero.");
return;
}
// 4. Conversions for Calculation (SI Units)
// PSI to Pascals (1 PSI = 6894.76 Pa)
var pressurePa = pressurePsi * 6894.76;
// Inches to Meters (1 Inch = 0.0254 m)
var diameterM = diameterIn * 0.0254;
// 5. Calculate Area (m^2)
var radiusM = diameterM / 2.0;
var areaM2 = Math.PI * Math.pow(radiusM, 2);
// 6. Calculate Flow Rate Q (m^3/s) Formula: Q = Cd * A * sqrt(2 * dP / rho)
// Check for negative inner sqrt term just in case
if (pressurePa < 0) {
resultsDiv.style.display = 'none';
alert("Pressure difference cannot be negative.");
return;
}
var flowM3s = cd * areaM2 * Math.sqrt((2 * pressurePa) / densityKgM3);
// 7. Calculate Velocity (m/s) Formula: V = Q / A
// Note: Theoretical velocity at the vena contracta or exit
var velocityMs = flowM3s / areaM2; // This simplifies to Cd * sqrt(2P/rho) if area cancels, but we keep explicit for clarity
// 8. Convert Results to User Units
// m^3/s to GPM (1 m^3/s = 15850.323141 GPM)
var flowGPM = flowM3s * 15850.323141;
// m^3/s to L/min (1 m^3/s = 60000 L/min)
var flowLMin = flowM3s * 60000;
// m/s to ft/s (1 m/s = 3.28084 ft/s)
var velocityFtS = velocityMs * 3.28084;
// 9. Update UI
resGPM.innerHTML = flowGPM.toLocaleString('en-US', { minimumFractionDigits: 2, maximumFractionDigits: 2 });
resLMin.innerHTML = flowLMin.toLocaleString('en-US', { minimumFractionDigits: 1, maximumFractionDigits: 1 });
resVel.innerHTML = velocityFtS.toLocaleString('en-US', { minimumFractionDigits: 1, maximumFractionDigits: 1 });
// Show results
resultsDiv.style.display = 'block';
}