Calculate volumetric flow rate based on pipe diameter and differential pressure.
Internal diameter of the opening.
Pressure drop across the opening (1 bar ≈ 14.5 psi).
Water = 1000, Air ≈ 1.2, Oil ≈ 850.
0.62 for sharp orifice, 0.98 for nozzle.
Calculation Results
Flow Rate (Liters/min)
–
Flow Rate (m³/hour)
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Flow Rate (US Gallons/min)
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Fluid Velocity (m/s)
–
function calculateFlowRate() {
// 1. Get Input Values
var diameterMM = parseFloat(document.getElementById('calc_diameter').value);
var pressureBar = parseFloat(document.getElementById('calc_pressure').value);
var density = parseFloat(document.getElementById('calc_density').value);
var coeff = parseFloat(document.getElementById('calc_coefficient').value);
// 2. Validation
if (isNaN(diameterMM) || diameterMM <= 0) {
alert("Please enter a valid positive diameter.");
return;
}
if (isNaN(pressureBar) || pressureBar < 0) {
alert("Please enter a valid pressure value.");
return;
}
if (isNaN(density) || density <= 0) {
alert("Please enter a valid fluid density.");
return;
}
if (isNaN(coeff) || coeff 1) {
alert("Please enter a Discharge Coefficient between 0 and 1.");
return;
}
// 3. Conversions to SI Units
var diameterM = diameterMM / 1000; // Convert mm to meters
var pressurePa = pressureBar * 100000; // Convert Bar to Pascals (N/m^2)
// 4. Calculate Area (A)
// Area = pi * (d/2)^2
var area = Math.PI * Math.pow((diameterM / 2), 2);
// 5. Calculate Velocity (v) using Bernoulli / Torricelli approximation
// v = Cd * sqrt(2 * DeltaP / rho)
var velocity = coeff * Math.sqrt((2 * pressurePa) / density);
// 6. Calculate Volumetric Flow Rate (Q)
// Q = A * v (result in cubic meters per second)
var flowM3s = area * velocity;
// 7. Convert Results for Display
var flowLmin = flowM3s * 60000; // m3/s to L/min (1 m3 = 1000L, 60s)
var flowM3h = flowM3s * 3600; // m3/s to m3/h
var flowGPM = flowLmin * 0.264172; // L/min to US Gallons per minute
// 8. Update DOM
document.getElementById('res_lmin').innerHTML = flowLmin.toLocaleString('en-US', {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('res_m3h').innerHTML = flowM3h.toLocaleString('en-US', {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('res_gpm').innerHTML = flowGPM.toLocaleString('en-US', {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('res_velocity').innerHTML = velocity.toLocaleString('en-US', {minimumFractionDigits: 2, maximumFractionDigits: 2});
// Show results container
document.getElementById('results').style.display = 'block';
}
Understanding Flow Rate, Pressure, and Diameter
Calculating the flow rate of a fluid through a pipe, nozzle, or orifice based on the pressure difference and the diameter of the opening is a fundamental task in fluid dynamics. This calculator uses principles derived from Bernoulli's equation to estimate how much fluid will pass through an opening given a specific driving pressure.
The Physics: Relationship Between Pressure and Velocity
The core principle behind this calculation is the conversion of potential energy (pressure) into kinetic energy (velocity). According to Torricelli's law, which is a specific case of Bernoulli's principle, the velocity of a fluid exiting under pressure is proportional to the square root of the pressure difference.
v = Cd × √(2 × ΔP / ρ)
Q = A × v
Where:
v: Fluid velocity (meters/second)
ΔP: Pressure difference (Pascals)
ρ (rho): Fluid density (kg/m³)
Cd: Discharge Coefficient
Q: Flow rate (m³/s)
A: Cross-sectional area of the opening (m²)
Key Parameters Explained
1. Pipe/Orifice Diameter
The physical size of the opening is the most critical factor. Since the area of a circle is calculated using the square of the diameter ($A = \pi \times r^2$), doubling the diameter increases the area (and thus the potential flow capacity) by a factor of four. This is why small changes in pipe size can have massive impacts on flow rate.
2. Pressure Difference
This is the "driving force" pushing the fluid. In this calculator, we assume the input is the differential pressure (e.g., the pressure inside a pipe versus the atmosphere, or the pressure drop across a valve). Higher pressure results in higher velocity.
3. Discharge Coefficient ($C_d$)
Theoretical equations assume a frictionless, ideal scenario. In the real world, friction and turbulence reduce the actual flow. The discharge coefficient corrects for this:
0.60 – 0.65: Sharp-edged orifices (lots of turbulence/contraction).
This type of calculation is widely used in various industries:
Fire Fighting: Determining water flow from a nozzle based on pump pressure.
Irrigation: Calculating emitter output based on water line pressure.
Industrial Hydraulics: Estimating flow through valves and restrictors.
Plumbing: Assessing leakage rates from pipe bursts or punctures.
Limitations of This Calculator
This tool assumes turbulent flow through an orifice or short pipe section where pressure is converted primarily to velocity. It does not account for friction loss over long pipe lengths (Darcy-Weisbach equation) or viscosity effects in laminar flow (Poiseuille's law). For long pipelines, you must also factor in pipe roughness and length to determine the pressure drop due to friction.