Calculate Air Flow Rate from Pressure and Diameter
by
Airflow Rate Calculator
This calculator helps you estimate the airflow rate through a duct based on the pressure difference and the duct's diameter. This is commonly used in HVAC (Heating, Ventilation, and Air Conditioning) systems to ensure proper ventilation and comfort.
.airflow-calculator {
font-family: Arial, sans-serif;
border: 1px solid #ccc;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
background-color: #f9f9f9;
}
.airflow-calculator h2 {
text-align: center;
margin-bottom: 20px;
color: #333;
}
.airflow-calculator p {
text-align: justify;
margin-bottom: 20px;
color: #555;
line-height: 1.6;
}
.inputs {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
gap: 15px;
margin-bottom: 20px;
}
.form-group {
display: flex;
flex-direction: column;
}
.form-group label {
margin-bottom: 5px;
font-weight: bold;
color: #444;
}
.form-group input {
padding: 8px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box; /* Ensures padding doesn't affect width */
}
.airflow-calculator button {
display: block;
width: 100%;
padding: 10px 15px;
background-color: #4CAF50;
color: white;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
transition: background-color 0.3s ease;
}
.airflow-calculator button:hover {
background-color: #45a049;
}
.result {
margin-top: 20px;
padding: 15px;
background-color: #e7f3fe;
border: 1px solid #b3d7ff;
border-radius: 4px;
text-align: center;
font-size: 18px;
color: #333;
font-weight: bold;
}
function calculateAirflow() {
var pressure = parseFloat(document.getElementById("pressure").value);
var diameter = parseFloat(document.getElementById("diameter").value);
var length = parseFloat(document.getElementById("length").value);
var roughness = parseFloat(document.getElementById("roughness").value);
var airDensity = parseFloat(document.getElementById("airDensity").value);
var viscosity = parseFloat(document.getElementById("viscosity").value);
var resultDiv = document.getElementById("result");
if (isNaN(pressure) || isNaN(diameter) || isNaN(length) || isNaN(roughness) || isNaN(airDensity) || isNaN(viscosity) ||
pressure <= 0 || diameter <= 0 || length <= 0 || roughness < 0 || airDensity <= 0 || viscosity <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
// Calculation using Darcy-Weisbach equation for pressure drop
// and then deriving flow rate.
// This is an iterative process as friction factor depends on Reynolds number,
// which depends on flow rate. We'll use a simplified approach or an iterative solver.
// For simplicity, we will assume a fully turbulent flow initially to estimate flow,
// and then refine it. A more accurate method would involve the Colebrook equation and
// an iterative solver for the friction factor.
// Step 1: Estimate initial flow rate assuming a turbulent flow (e.g., using Haaland approximation for friction factor)
// Simplified approach: Assume a reasonable friction factor and iterate.
// Let's use the explicit Haaland equation for friction factor (f) as an approximation:
// 1/sqrt(f) = -1.8 * log10( (epsilon/D/3.7)^1.11 + 6.9/Re )
// Where Re = (rho * v * D) / mu = (rho * Q * 4) / (mu * pi * D)
// And pressure drop P = f * (L/D) * (rho * v^2 / 2) = f * (L/D) * (rho/2) * (4Q / (pi*D^2))^2
var flowRate;
var frictionFactor;
var reynoldsNumber;
var velocity;
var area = Math.PI * Math.pow(diameter / 2, 2);
// Initial guess for friction factor (e.g., turbulent flow assumption)
// Using Colebrook equation requires iteration. Let's use an explicit approximation.
// A common explicit approximation for friction factor is the Swamee-Jain equation:
// f = 0.25 / [log10( (roughness/D)/3.7 + 5.74/Re^0.9 )]^2
// This still requires iteration as Re depends on flow.
// Let's try to solve for Q iteratively.
// We know P = f * (L/D) * (rho * v^2 / 2).
// v = Q / A
// P = f * (L/D) * (rho/2) * (Q/A)^2
// P = f * (L/D) * (rho/2) * (Q^2 / (pi*D^2/4)^2)
// P = f * (L/D) * (rho/2) * (16 * Q^2 / (pi^2 * D^4))
// P = f * (L * rho * 16 * Q^2) / (2 * D * pi^2 * D^4)
// P = f * (8 * L * rho * Q^2) / (pi^2 * D^5)
// Q^2 = (P * pi^2 * D^5) / (8 * L * rho * f)
// Q = sqrt( (P * pi^2 * D^5) / (8 * L * rho * f) )
// And Re = (4 * rho * Q) / (mu * pi * D)
// And f is found via Colebrook or approximation.
// Iterative solution:
var Q_guess = 1.0; // Initial guess for flow rate in m³/s
var maxIterations = 100;
var tolerance = 1e-6;
var Q_new = Q_guess;
for (var i = 0; i < maxIterations; i++) {
velocity = Q_guess / area;
reynoldsNumber = (airDensity * velocity * diameter) / viscosity;
// Calculate friction factor using an explicit approximation (e.g., Swamee-Jain)
// for laminar flow (Re 4000) use Swamee-Jain
if (reynoldsNumber 4000) {
var logTerm = Math.log10( (roughness / diameter) / 3.7 + 5.74 / Math.pow(reynoldsNumber, 0.9) );
if (logTerm === 0) { // Avoid division by zero if logTerm is extremely close to 0
frictionFactor = Infinity; // Indicate an issue
} else {
frictionFactor = 0.25 / Math.pow(logTerm, 2);
}
} else { // Transitional flow – approximation can be less accurate. Interpolate or use a simple formula.
// For simplicity, let's use a weighted average or a smoother transition.
// A simpler approach is to use the turbulent approximation for this range as it's usually dominant.
var logTerm = Math.log10( (roughness / diameter) / 3.7 + 5.74 / Math.pow(reynoldsNumber, 0.9) );
if (logTerm === 0) {
frictionFactor = Infinity;
} else {
frictionFactor = 0.25 / Math.pow(logTerm, 2);
}
}
if (frictionFactor === Infinity || isNaN(frictionFactor) || frictionFactor <= 0) {
resultDiv.innerHTML = "Error calculating friction factor. Check inputs.";
return;
}
// Calculate new flow rate based on current friction factor
Q_new = Math.sqrt( (pressure * Math.PI * Math.PI * Math.pow(diameter, 5)) / (8 * length * airDensity * frictionFactor) );
// Check for convergence
if (Math.abs(Q_new – Q_guess) < tolerance) {
flowRate = Q_new;
break;
}
Q_guess = Q_new; // Update guess for next iteration
// If loop finishes without converging, use the last calculated value
if (i === maxIterations – 1) {
flowRate = Q_new;
}
}
if (isNaN(flowRate) || flowRate <= 0) {
resultDiv.innerHTML = "Calculation failed. Please check your input values.";
return;
}
// Convert to a more common unit like CFM (Cubic Feet per Minute) if desired, but sticking to m³/s for now as per standard SI.
// 1 m³/s = 2118.88 CFM
var airflow_cfm = flowRate * 2118.88;
resultDiv.innerHTML = "Estimated Airflow Rate: " + flowRate.toFixed(4) + " m³/s " +
"(" + airflow_cfm.toFixed(2) + " CFM)";
}