This calculator helps you determine the volumetric flow rate of air passing through a sharp-edged orifice under specific conditions. It's based on fundamental fluid dynamics principles.
Understanding Air Flow Rate Through an Orifice
The flow rate of air through an orifice is a critical parameter in many engineering applications, including ventilation systems, industrial process control, and aerodynamic testing. An orifice is essentially a precisely sized opening in a plate or wall through which fluid (in this case, air) passes.
The calculation for volumetric flow rate (Q) through an orifice is typically given by:
Q = Cd * A * sqrt(2 * P / rho)
Where:
Q is the volumetric flow rate (m³/s).
Cd is the discharge coefficient, a dimensionless factor accounting for energy losses due to friction and contraction of the flow stream as it passes through the orifice. Its value depends on the orifice geometry and the flow conditions, typically ranging from 0.6 to 0.8 for sharp-edged orifices.
A is the cross-sectional area of the orifice (m²).
P is the differential pressure across the orifice (Pa). In this calculator, we use the upstream gauge pressure as an approximation for the differential pressure, assuming atmospheric pressure on the downstream side. For more accurate calculations, the actual downstream pressure should be considered.
rho (ρ) is the density of the air (kg/m³). Air density is dependent on temperature and pressure.
Calculating Air Density:
The density of air can be estimated using the ideal gas law:
rho = P_abs / (R * T_K)
Where:
rho is the air density (kg/m³).
P_abs is the absolute upstream pressure (Pa). This is calculated by adding atmospheric pressure (assumed to be 101325 Pa at sea level) to the upstream gauge pressure.
R is the specific gas constant for dry air, approximately 287.05 J/(kg·K).
T_K is the absolute temperature of the air in Kelvin (°K). This is calculated by converting the input temperature in Celsius to Kelvin (T_K = T_C + 273.15).
This calculator uses these principles to provide an estimated airflow rate.
function calculateFlowRate() {
var orificeDiameter = parseFloat(document.getElementById("orificeDiameter").value);
var upstreamPressure = parseFloat(document.getElementById("upstreamPressure").value);
var temperatureCelsius = parseFloat(document.getElementById("temperatureCelsius").value);
var dischargeCoefficient = parseFloat(document.getElementById("dischargeCoefficient").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(orificeDiameter) || isNaN(upstreamPressure) || isNaN(temperatureCelsius) || isNaN(dischargeCoefficient) ||
orificeDiameter <= 0 || upstreamPressure < 0 || dischargeCoefficient 1) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields. Discharge coefficient must be between 0 and 1.";
return;
}
// Constants
var R_AIR = 287.05; // Specific gas constant for dry air in J/(kg·K)
var ATMOSPHERIC_PRESSURE = 101325; // Standard atmospheric pressure in Pascals (Pa)
// Calculate absolute upstream pressure
var absoluteUpstreamPressure = ATMOSPHERIC_PRESSURE + upstreamPressure;
// Convert temperature from Celsius to Kelvin
var temperatureKelvin = temperatureCelsius + 273.15;
// Calculate air density
var airDensity = absoluteUpstreamPressure / (R_AIR * temperatureKelvin);
// Calculate orifice area
var orificeArea = Math.PI * Math.pow(orificeDiameter / 2, 2);
// Calculate flow rate
// The term under the square root is related to kinetic energy: 0.5 * rho * v^2 = P
// v = sqrt(2 * P / rho)
// Q = A * v = A * Cd * sqrt(2 * P / rho)
// However, a more common form for orifice flow that accounts for the pressure drop and density:
// Q = Cd * A * sqrt(2 * deltaP / rho)
// Here, we are using upstream gauge pressure as deltaP.
var flowRate = dischargeCoefficient * orificeArea * Math.sqrt(2 * upstreamPressure / airDensity);
resultDiv.innerHTML = "Estimated Air Flow Rate: " + flowRate.toFixed(4) + " m³/s";
}