Standard sea level air density is approx 1.225 kg/m³.
0.60-0.62 for sharp orifice, ~0.98 for smooth nozzle.
Air Velocity:–
Volumetric Flow (m³/s):–
Volumetric Flow (CFM):–
Volumetric Flow (Liters/s):–
function calculateAirFlow() {
// Get input values
var pressure = parseFloat(document.getElementById('pressureDiff').value);
var diamMM = parseFloat(document.getElementById('diameter').value);
var density = parseFloat(document.getElementById('airDensity').value);
var cd = parseFloat(document.getElementById('dischargeCoeff').value);
// Validation
if (isNaN(pressure) || isNaN(diamMM) || isNaN(density) || isNaN(cd)) {
alert("Please enter valid numerical values for all fields.");
return;
}
if (pressure < 0 || diamMM <= 0 || density <= 0) {
alert("Pressure must be positive, and dimensions/density must be greater than zero.");
return;
}
// 1. Calculate Area (A) in square meters
// Diameter is in mm, convert to meters (d/1000)
// Area = PI * (r^2) = PI * (d/2)^2
var radiusM = (diamMM / 1000) / 2;
var area = Math.PI * Math.pow(radiusM, 2);
// 2. Calculate Velocity (v) using Bernoulli's principle derived formula
// v = Cd * sqrt( (2 * DeltaP) / rho )
var velocity = cd * Math.sqrt((2 * pressure) / density);
// 3. Calculate Flow Rate (Q)
// Q = v * A
var flowM3s = velocity * area;
// 4. Conversions
var flowCFM = flowM3s * 2118.88; // 1 m3/s = 2118.88 CFM
var flowLps = flowM3s * 1000; // 1 m3/s = 1000 L/s
// 5. Display Results
document.getElementById('results').style.display = 'block';
document.getElementById('resVelocity').innerText = velocity.toFixed(2) + " m/s";
document.getElementById('resM3s').innerText = flowM3s.toFixed(4) + " m³/s";
document.getElementById('resCFM').innerText = flowCFM.toFixed(2) + " CFM";
document.getElementById('resLps').innerText = flowLps.toFixed(2) + " L/s";
}
How to Calculate Air Flow Rate from Pressure
Understanding the relationship between air pressure and flow rate is fundamental in HVAC (Heating, Ventilation, and Air Conditioning), aerodynamics, and fluid dynamics engineering. Whether you are balancing a duct system, designing an intake manifold, or calculating ventilation requirements, knowing how to derive air flow (Q) from pressure differential ($\Delta P$) is a critical skill.
The Physics of Air Flow and Pressure
The calculation is primarily based on Bernoulli's Principle, which relates the pressure, velocity, and elevation of a fluid. In practical air flow applications where elevation changes are negligible, the relationship implies that as the velocity of a fluid increases, the static pressure decreases.
To calculate the flow rate through an opening (like an orifice, nozzle, or damper) based on the pressure drop across it, we use the following derived formula:
Q = Cd × A × √(2 × ΔP / ρ)
Where:
Q = Volumetric Air Flow Rate (m³/s)
Cd = Discharge Coefficient (dimensionless efficiency factor)
A = Cross-sectional Area of the opening (m²)
ΔP = Pressure Differential (Pascals)
ρ (rho) = Air Density (kg/m³, typically 1.225 at sea level)
Detailed Breakdown of Variables
1. Pressure Differential (ΔP)
This is the difference in static pressure between the two sides of the opening. In HVAC, this is often measured in Pascals (Pa) or Inches of Water Column (in. wg). A higher pressure difference creates a higher potential for air to move, resulting in higher velocity.
2. Discharge Coefficient (Cd)
Ideally, air would flow without resistance. However, due to turbulence, friction, and the shape of the opening (venacontracta), actual flow is less than theoretical flow. The discharge coefficient corrects for this:
Sharp-edged orifice: ~0.60 to 0.62
Rounded nozzle: ~0.95 to 0.98
Short tube: ~0.80
3. Air Density (ρ)
Air density changes with temperature and altitude. Standard air density at sea level (15°C / 59°F) is approximately 1.225 kg/m³. If you are calculating air flow in a hot exhaust stack or at high altitude, you must adjust the density value to get an accurate flow rate. Hotter air is less dense, which affects the mass flow.
Common Practical Applications
HVAC Duct Balancing
Technicians measure the static pressure before and after a damper or filter to estimate the volume of air (CFM) passing through the system. This ensures rooms receive the correct amount of conditioned air.
Cleanroom Pressurization
Cleanrooms must maintain positive pressure to prevent contaminants from entering. Calculating the leakage rate through cracks (openings) based on pressure difference is vital for sizing fans.
Engine Air Intake
Automotive engineers calculate flow through throttle bodies based on the pressure drop (vacuum) created by the pistons to optimize the air-fuel mixture.
Fan Performance
Fan curves are essentially graphical representations of the relationship between the pressure a fan can generate and the volume of air it can move.
How to Use This Calculator
To obtain an accurate air flow rate:
Measure Pressure: use a manometer to find the pressure difference (in Pascals) across the opening.
Determine Geometry: Measure the diameter of the duct or orifice in millimeters.
Estimate Efficiency: Choose a Discharge Coefficient. If you are unsure, 0.61 is a standard conservative estimate for a simple hole or sharp-edged opening.
Check Conditions: Ensure the air density matches your environment. Use 1.225 for standard conditions, or lower values for high altitudes/temperatures.
Note: This calculator assumes incompressible flow, which is accurate for standard HVAC and ventilation speeds (generally below Mach 0.3).