Calculate gas flow rate based on differential pressure, line pressure, and temperature.
The size of the opening the gas flows through.
The pressure drop across the orifice (Delta P).
Absolute pressure of the gas (Gauge + Atmospheric).
Operating temperature of the gas.
Default is 287.05 for Dry Air.
Calculated Gas Density:– kg/m³
Mass Flow Rate:– kg/h
Volumetric Flow Rate (Actual):– m³/h
Velocity at Orifice:– m/s
function calculateFlowRate() {
// 1. Get Input Values
var d_mm = parseFloat(document.getElementById("orificeDiameter").value);
var dp_mbar = parseFloat(document.getElementById("diffPressure").value);
var p_bar = parseFloat(document.getElementById("linePressure").value);
var t_celsius = parseFloat(document.getElementById("temperature").value);
var r_gas = parseFloat(document.getElementById("gasConstant").value);
// 2. Validate Inputs
if (isNaN(d_mm) || isNaN(dp_mbar) || isNaN(p_bar) || isNaN(t_celsius) || isNaN(r_gas)) {
alert("Please enter valid numerical values for all fields.");
return;
}
if (d_mm <= 0 || p_bar <= 0 || r_gas <= 0) {
alert("Diameter, Pressure, and Gas Constant must be positive values.");
return;
}
// 3. Convert to SI Units for Calculation
// Temperature: Celsius to Kelvin
var t_kelvin = t_celsius + 273.15;
// Pressure: Bar to Pascals (1 bar = 100,000 Pa)
var p_pascal = p_bar * 100000;
// Differential Pressure: mbar to Pascals (1 mbar = 100 Pa)
var dp_pascal = dp_mbar * 100;
// Diameter: mm to meters
var d_meter = d_mm / 1000;
// 4. Calculate Gas Density (Ideal Gas Law: rho = P / RT)
var rho = p_pascal / (r_gas * t_kelvin);
// 5. Calculate Area of Orifice (A = pi * r^2)
var area = Math.PI * Math.pow((d_meter / 2), 2);
// 6. Calculate Flow Rate using Bernoulli's Principle approximation for orifices
// Q_mass = C_d * A * sqrt(2 * rho * dP)
// Assuming Discharge Coefficient (C_d) is approx 0.62 (standard for sharp-edged orifices)
var c_d = 0.62;
// Check for negative sqrt issues
if (dp_pascal < 0) {
alert("Differential pressure cannot be negative for this calculation.");
return;
}
var massFlow_kg_s = c_d * area * Math.sqrt(2 * rho * dp_pascal);
// Convert Mass Flow to Volumetric Flow (Q = mass / density)
var volFlow_m3_s = massFlow_kg_s / rho;
// Calculate Velocity (v = Q / A)
var velocity_m_s = volFlow_m3_s / area;
// 7. Convert Results for Display
// Mass Flow: kg/s to kg/h
var massFlow_kg_h = massFlow_kg_s * 3600;
// Volumetric Flow: m3/s to m3/h
var volFlow_m3_h = volFlow_m3_s * 3600;
// 8. Update HTML
document.getElementById("resDensity").innerHTML = rho.toFixed(3) + " kg/m³";
document.getElementById("resMassFlow").innerHTML = massFlow_kg_h.toFixed(2) + " kg/h";
document.getElementById("resVolFlow").innerHTML = volFlow_m3_h.toFixed(2) + " m³/h";
document.getElementById("resVelocity").innerHTML = velocity_m_s.toFixed(2) + " m/s";
// Show results box
document.getElementById("results").style.display = "block";
}
How Pressure and Temperature Affect Flow Rate
Calculating flow rate requires understanding the relationship between the fluid's properties and the environmental conditions. In gas systems, unlike liquids, density is highly variable. The calculator above utilizes the Ideal Gas Law and Bernoulli's equation principles to determine how much gas flows through an orifice under specific conditions.
The Role of Density
The primary variable connecting pressure and temperature to flow rate is density. The equation for the flow of a compressible fluid through a restriction (like a valve or orifice) depends heavily on the density of that fluid upstream.
Density (ρ) = P / (R × T)
Where:
P is the absolute pressure (Pa).
T is the absolute temperature (Kelvin).
R is the specific gas constant (J/kg·K).
Key Relationships
By analyzing the formula, we can observe two critical rules of thumb for gas flow:
Pressure Effect: As the line pressure increases, the gas density increases. A denser gas results in a higher mass flow rate for the same differential pressure, because more molecules are packed into the same volume.
Temperature Effect: As temperature increases, gas density decreases (the gas expands). Consequently, for the same pressure conditions, a hotter gas will have a lower density.
The Flow Equation
This calculator estimates flow using the standard orifice equation:
Q = Cd × A × √(2 × ΔP / ρ)
Here, ΔP (Differential Pressure) provides the energy to drive the flow, while ρ (Density) acts as the resistance factor related to the fluid's mass. This demonstrates why you cannot calculate gas flow rate accurately without knowing both the line pressure and the operating temperature.
Example Calculation
Consider a system using compressed air with the following parameters:
Orifice Diameter: 10 mm
Differential Pressure: 50 mbar
Line Pressure: 5 bar (absolute)
Temperature: 25°C
First, we convert the temperature to Kelvin (298.15 K) and pressure to Pascals (500,000 Pa). Using the specific gas constant for air (287.05), we calculate the density to be approximately 5.84 kg/m³. Applying these values to the flow equation yields a mass flow rate of approximately 40-41 kg/h.