Ideally 1.0. Typically 0.60-0.62 for sharp orifices.
Flow Rate (Cubic Meters/sec):–
Flow Rate (Liters/minute):–
Flow Velocity (m/s):–
function calculateFlow() {
// Get input values
var P = parseFloat(document.getElementById('pressureInput').value);
var A = parseFloat(document.getElementById('areaInput').value);
var rho = parseFloat(document.getElementById('densityInput').value);
var Cd = parseFloat(document.getElementById('cdInput').value);
// Validation
if (isNaN(P) || isNaN(A) || isNaN(rho) || isNaN(Cd)) {
alert("Please enter valid numeric values for all fields.");
return;
}
if (P < 0 || A <= 0 || rho <= 0 || Cd < 0) {
alert("Values must be positive. Density and Area cannot be zero.");
return;
}
// Calculation Logic based on Bernoulli's principle / Torricelli's Law for an orifice
// v = sqrt(2 * P / rho) — Theoretical Velocity
// Q = Cd * A * sqrt(2 * P / rho)
// 1. Calculate ideal velocity
var velocity = Math.sqrt((2 * P) / rho);
// 2. Calculate Flow Rate (Q) in m^3/s
var flowRateM3 = Cd * A * velocity;
// 3. Convert to Liters Per Minute (1 m^3/s = 60,000 L/min)
var flowRateLPM = flowRateM3 * 60000;
// Display Results
document.getElementById('resM3').innerHTML = flowRateM3.toFixed(6) + " m³/s";
document.getElementById('resLPM').innerHTML = flowRateLPM.toFixed(2) + " L/min";
document.getElementById('resVel').innerHTML = velocity.toFixed(2) + " m/s"; // Theoretical velocity at exit
// Show results container
document.getElementById('resultsArea').style.display = 'block';
}
Understanding Flow Rate Calculation
Calculating the volumetric flow rate of a fluid through an orifice or pipe based on pressure differential is a fundamental task in fluid dynamics. This calculator uses the principles derived from Bernoulli's equation to estimate how much fluid will pass through a specific area under a given pressure.
The Formula
The flow rate ($Q$) is calculated using the following equation:
Q = Cd × A × √(2 × P / ρ)
Where:
Q = Volumetric Flow Rate (m³/s)
Cd = Discharge Coefficient (dimensionless, usually 0.60–0.65 for orifices)
A = Cross-sectional Area of the opening (m²)
P = Pressure Differential across the opening (Pascals)
ρ (rho) = Fluid Density (kg/m³)
Key Inputs Explained
Pressure Differential (Pa)
This is the driving force of the flow. It represents the difference in pressure between the inside of the container (or pipe) and the outside environment. Higher pressure results in higher velocity and flow rate. Note that 1 PSI is approximately 6,895 Pascals.
Area (m²)
The physical size of the hole or pipe opening. A larger area allows more fluid to pass through. If you only have the diameter (d) of a circular pipe, calculate area using: A = π × (d/2)².
Fluid Density
Density affects how easily the fluid is accelerated. Heavier fluids (like mercury) flow slower than lighter fluids (like water) under the same pressure. Water has a density of approximately 1000 kg/m³.
Discharge Coefficient (Cd)
Real-world flow is never perfect. Friction and turbulence reduce the actual flow compared to the theoretical maximum. The Discharge Coefficient ($C_d$) corrects for this. A value of 0.61 is standard for a sharp-edged orifice, while a smooth nozzle might have a coefficient closer to 0.98.
Example Calculation
Let's say you have a water tank creating a pressure of 50,000 Pa (approx 0.5 bar) at a nozzle. The nozzle has an area of 0.001 m². The fluid is water (density 1000 kg/m³) and the discharge coefficient is 0.61.