function calculateOrificeFlow() {
var d1_mm = parseFloat(document.getElementById('pipeDiameter').value);
var d2_mm = parseFloat(document.getElementById('orificeDiameter').value);
var dp = parseFloat(document.getElementById('pressureDiff').value);
var rho = parseFloat(document.getElementById('fluidDensity').value);
var cd = parseFloat(document.getElementById('dischargeCoeff').value);
if (isNaN(d1_mm) || isNaN(d2_mm) || isNaN(dp) || isNaN(rho) || isNaN(cd) || d1_mm <= 0 || d2_mm <= 0 || rho = d1_mm) {
alert("Orifice diameter must be smaller than pipe diameter.");
return;
}
// Conversions to SI units
var d1 = d1_mm / 1000; // meters
var d2 = d2_mm / 1000; // meters
// Area Calculation
var a1 = (Math.PI * Math.pow(d1, 2)) / 4;
var a2 = (Math.PI * Math.pow(d2, 2)) / 4;
// Beta Ratio
var beta = d2 / d1;
// Orifice Flow Formula: Q = Cd * A2 * sqrt( (2 * dP) / (rho * (1 – beta^4)) )
var numerator = 2 * dp;
var denominator = rho * (1 – Math.pow(beta, 4));
var flowRateM3S = cd * a2 * Math.sqrt(numerator / denominator);
var flowRateLMin = flowRateM3S * 1000 * 60;
var massFlowRate = flowRateM3S * rho;
document.getElementById('resBeta').innerText = beta.toFixed(4);
document.getElementById('resFlowM3S').innerText = flowRateM3S.toFixed(6);
document.getElementById('resFlowLMin').innerText = flowRateLMin.toFixed(2);
document.getElementById('resMassFlow').innerText = massFlowRate.toFixed(4);
document.getElementById('resultsArea').style.display = 'block';
}
Understanding Orifice Meter Calculations
An orifice meter is a type of flow meter used to measure the rate of fluid flow by creating a pressure drop across a restriction in a pipe. It operates on Bernoulli's Principle, which states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure.
The Core Formula
The volumetric flow rate (Q) is calculated using the following engineering equation:
Q = Cd × A2 × √[ (2 × ΔP) / (ρ × (1 – β4)) ]
Cd (Discharge Coefficient): This accounts for energy losses and the contraction of the fluid jet (vena contracta). For sharp-edged orifices, it is typically around 0.61.
A2: The cross-sectional area of the orifice hole.
ΔP: The pressure difference measured between the upstream and downstream taps.
ρ (Rho): The density of the fluid passing through the meter.
β (Beta Ratio): The ratio of the orifice diameter to the pipe diameter (d/D).
Key Application Guidelines
When using an orifice meter, engineers follow specific standards (like ISO 5167 or ASME MFC-3M) to ensure accuracy:
Beta Ratio Limits: For optimal performance, the beta ratio (β) should usually fall between 0.3 and 0.75.
Straight Pipe Runs: To ensure a fully developed flow profile, the meter requires several diameters of straight pipe upstream and downstream of the plate.
Fluid Type: Ensure the fluid density is constant (incompressible flow) for the most accurate results using this specific calculator.
Example Calculation
If you have a 100mm pipe with a 50mm orifice (β = 0.5), a fluid density of 1000 kg/m³ (water), and a measured pressure drop of 1000 Pa, the calculator determines the velocity and volume flow. With a Cd of 0.61, the resulting flow rate would be approximately 0.0011 m³/s or 68.7 L/min.