Calculate flow rate based on duct diameter and velocity pressure.
The internal diameter of the duct or pipe in millimeters.
Measured differential pressure (Pascals).
Standard air density is 1.225 kg/m³ at sea level.
Calculation Results
Calculated Velocity:–
Flow Rate (m³/s):–
Flow Rate (m³/h):–
Flow Rate (CFM):–
Flow Rate (L/s):–
function calculateAirFlow() {
// Get Input Values
var diameterMM = parseFloat(document.getElementById("af_diameter").value);
var pressurePa = parseFloat(document.getElementById("af_pressure").value);
var density = parseFloat(document.getElementById("af_density").value);
// Validation
if (isNaN(diameterMM) || diameterMM <= 0) {
alert("Please enter a valid positive Diameter.");
return;
}
if (isNaN(pressurePa) || pressurePa < 0) {
alert("Please enter a valid Velocity Pressure (cannot be negative).");
return;
}
if (isNaN(density) || density <= 0) {
alert("Please enter a valid Air Density.");
return;
}
// 1. Calculate Area (A) in Square Meters
// Formula: A = PI * (D/2000)^2 (dividing by 2000 because D is mm and we need radius in m)
var radiusMeters = (diameterMM / 2) / 1000;
var area = Math.PI * Math.pow(radiusMeters, 2);
// 2. Calculate Velocity (v) in Meters per Second
// Formula: v = sqrt( (2 * Pressure) / Density )
// Derived from Bernoulli's equation for dynamic pressure: P = 0.5 * rho * v^2
var velocity = Math.sqrt((2 * pressurePa) / density);
// 3. Calculate Flow Rate (Q)
// Q = A * v
var flowCMS = area * velocity; // m³/s
// 4. Conversions
var flowCMH = flowCMS * 3600; // m³/h
var flowCFM = flowCMS * 2118.88; // Cubic Feet per Minute
var flowLS = flowCMS * 1000; // Liters per Second
// Display Results
document.getElementById("res_velocity").innerHTML = velocity.toFixed(2) + " m/s";
document.getElementById("res_cms").innerHTML = flowCMS.toFixed(4) + " m³/s";
document.getElementById("res_cmh").innerHTML = flowCMH.toFixed(1) + " m³/h";
document.getElementById("res_cfm").innerHTML = flowCFM.toFixed(1) + " CFM";
document.getElementById("res_ls").innerHTML = flowLS.toFixed(1) + " L/s";
// Show Result Box
document.getElementById("af_results_area").style.display = "block";
}
How to Calculate Air Flow Rate from Pressure and Diameter
Calculating the air flow rate within a duct or pipe using pressure readings and the diameter is a fundamental task in HVAC engineering, aerodynamics, and fluid dynamics. This process typically involves converting a Velocity Pressure (or dynamic pressure) reading into air velocity, and then multiplying that velocity by the cross-sectional area of the duct.
This calculator uses the Bernoulli principle and the continuity equation to determine the volumetric flow rate. Below is a detailed breakdown of the math involved.
1. The Physics: Dynamic Pressure vs. Static Pressure
To calculate flow, you cannot simply use static pressure (the pressure pushing against the duct walls). You must use Velocity Pressure (also known as Dynamic Pressure). This is usually measured using a Pitot tube, which measures Total Pressure and subtracts Static Pressure to find the pressure component caused solely by the air's motion.
2. Calculating Air Velocity
Once you have the velocity pressure ($P_v$) in Pascals (Pa) and the air density ($\rho$) in kg/m³, you can calculate the speed of the air using the following formula derived from Bernoulli's equation:
v = √ ( (2 × P) / ρ )
Where:
v = Velocity in meters per second (m/s)
P = Velocity Pressure in Pascals (Pa)
ρ = Air Density (Standard air is approx 1.225 kg/m³)
3. Calculating Cross-Sectional Area
To find the volume of air moving through the duct, we first need the area of the opening. For a round duct with a diameter ($d$) in millimeters:
Area (A) = π × ( (d / 1000) / 2 )²
We convert the diameter from millimeters to meters by dividing by 1000 before calculating the area in square meters ($m²$).
4. Calculating Volumetric Flow Rate (Q)
Finally, the Air Flow Rate ($Q$) is the product of the Area and the Velocity:
Q = Area × Velocity
Example Calculation
Let's assume you have a 200mm diameter duct and you measure a velocity pressure of 25 Pa.
Find Area: Radius is 0.1m. Area = 3.14159 × 0.1² = 0.0314 m².
This equates to approximately 720 m³/h or 425 CFM.
Why Air Density Matters
The standard air density of 1.225 kg/m³ applies at sea level at 15°C. If you are measuring hot air (which is less dense) or measuring at high altitude, you must adjust the density value in the calculator. A lower density results in a higher velocity for the same pressure reading.