Unit: Millimeters (mm) – Must be smaller than Pipe Diameter
Unit: Pascals (Pa)
Unit: kg/m³
Typical range: 0.60 – 0.62
Beta Ratio (β):
Volumetric Flow Rate (Q):
Volumetric Flow Rate (Hourly):
Mass Flow Rate (ṁ):
function calculateFlowRate() {
// Get input values
var D_mm = parseFloat(document.getElementById('pipeDiameter').value);
var d_mm = parseFloat(document.getElementById('orificeDiameter').value);
var deltaP = parseFloat(document.getElementById('pressureDrop').value);
var rho = parseFloat(document.getElementById('fluidDensity').value);
var Cd = parseFloat(document.getElementById('dischargeCoeff').value);
// Validation
if (isNaN(D_mm) || isNaN(d_mm) || isNaN(deltaP) || isNaN(rho) || isNaN(Cd)) {
alert("Please ensure all fields contain valid numbers.");
return;
}
if (D_mm <= 0 || d_mm <= 0 || rho <= 0 || Cd = D_mm) {
alert("Orifice diameter (d) must be smaller than pipe diameter (D).");
return;
}
if (deltaP < 0) {
alert("Differential pressure cannot be negative.");
return;
}
// Conversions and Intermediate Calculations
var D_m = D_mm / 1000.0; // Convert mm to meters
var d_m = d_mm / 1000.0; // Convert mm to meters
// Beta Ratio (beta = d/D)
var beta = d_m / D_m;
var beta4 = Math.pow(beta, 4);
// Orifice Area (Ao) in m²
var Ao = Math.PI * Math.pow((d_m / 2.0), 2);
// Velocity of Approach Factor (1 / sqrt(1 – beta^4))
var approachFactorDenominator = Math.sqrt(1.0 – beta4);
if (approachFactorDenominator === 0) {
alert("Calculation error: Beta ratio implies infinite velocity.");
return;
}
// Standard Orifice Equation for Incompressible Flow:
// Q = (Cd * Ao * sqrt(2 * deltaP / rho)) / sqrt(1 – beta^4)
var numerator = Cd * Ao * Math.sqrt((2 * deltaP) / rho);
var Q_m3_s = numerator / approachFactorDenominator; // m³/s
var Q_m3_h = Q_m3_s * 3600; // m³/h
var massFlow = Q_m3_s * rho; // kg/s
// Display Results
document.getElementById('resBeta').innerText = beta.toFixed(4);
document.getElementById('resVolumetricSec').innerText = Q_m3_s.toFixed(6) + " m³/s";
document.getElementById('resVolumetricHour').innerText = Q_m3_h.toFixed(2) + " m³/h";
document.getElementById('resMassFlow').innerText = massFlow.toFixed(4) + " kg/s";
document.getElementById('resultsBox').style.display = "block";
}
How to Calculate Flow Rate in Orifice Meter
Calculating the flow rate through an orifice meter is a fundamental task in fluid dynamics and industrial engineering. Orifice meters are widely used to measure the flow rate of fluids (liquids and gases) in pipes by measuring the pressure difference created by a restriction plate.
Understanding the Orifice Meter Principle
An orifice meter works on Bernoulli's principle, which states that there is a relationship between the pressure and the velocity of a fluid. When a fluid passes through a constriction (the orifice plate), its velocity increases, resulting in a decrease in pressure.
By measuring the pressure drop (ΔP) across the orifice plate, we can determine the flow rate using standard ISO equations.
The Flow Rate Formula
For incompressible fluids (like water), the volumetric flow rate (Q) is calculated using the following equation:
Q = (Cd × Ao × √(2 × ΔP / ρ)) / √(1 – β4)
Where:
Q: Volumetric flow rate (m³/s)
Cd: Discharge Coefficient (dimensionless, typically ~0.61)
Ao: Area of the orifice (m²)
ΔP: Differential pressure across the orifice (Pascals)
ρ (rho): Density of the fluid (kg/m³)
β (beta): Ratio of orifice diameter to pipe diameter (d/D)
Key Variables Explained
1. Beta Ratio (β)
The beta ratio is simply the orifice bore diameter divided by the internal pipe diameter (d/D). This ratio determines the velocity of approach factor. A typical beta ratio ranges between 0.3 and 0.75. If the ratio is too high or too low, the accuracy of the measurement may decrease.
2. Discharge Coefficient (Cd)
This coefficient accounts for energy losses (friction and turbulence) and the contraction of the fluid jet (vena contracta) after passing the orifice. While exact values depend on the Reynolds number and exact tap locations (flange taps, corner taps, etc.), a value of 0.60 to 0.62 is often used for general estimates.
3. Differential Pressure (ΔP)
This is the most critical dynamic variable. It represents the drop in pressure measured between the upstream and downstream sides of the plate. Because flow rate is proportional to the square root of the pressure drop, a small error in pressure reading can significantly affect the calculated flow.
Step-by-Step Calculation Example
Let's assume we are measuring water flow with the following parameters:
Pipe Diameter (D): 100 mm (0.1 m)
Orifice Diameter (d): 50 mm (0.05 m)
Pressure Drop (ΔP): 2500 Pa
Fluid Density (ρ): 1000 kg/m³
Discharge Coefficient (Cd): 0.61
Step 1: Calculate Beta Ratio
β = 50 / 100 = 0.5
Step 2: Calculate Orifice Area (Ao)
Radius = 0.05 / 2 = 0.025 m
Ao = π × (0.025)² ≈ 0.0019635 m²