body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 800px;
margin: 0 auto;
padding: 20px;
}
.calculator-container {
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border: 1px solid #e9ecef;
border-radius: 8px;
padding: 25px;
margin-bottom: 40px;
box-shadow: 0 2px 10px rgba(0,0,0,0.05);
}
.calc-title {
text-align: center;
margin-top: 0;
color: #2c3e50;
margin-bottom: 25px;
}
.form-group {
margin-bottom: 20px;
}
.form-group label {
display: block;
font-weight: 600;
margin-bottom: 8px;
color: #495057;
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transition: border-color 0.15s ease-in-out;
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box-shadow: 0 0 0 3px rgba(0,123,255,0.1);
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font-weight: 600;
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Understanding How to Calculate Air Pressure from Flow Rate
In fluid dynamics and HVAC engineering, calculating air pressure based on a known flow rate is a fundamental task. This calculation helps engineers determine the velocity pressure generated by air moving through a duct or pipe of a specific size. The relationship between flow rate (measured in CFM) and pressure is governed by the principles of air velocity.
The Core Concept: Velocity Pressure
When air moves through a system, it possesses kinetic energy proportional to its velocity. This energy exerts a pressure known as Velocity Pressure (Pv). This is distinct from Static Pressure, which is the pressure exerted against the duct walls.
To calculate the pressure derived solely from the movement of the air (dynamic pressure), we must first determine the velocity of the air stream and then apply the standard air formula.
Step 1: Calculate Velocity (V)
V = Q / A
Where:
Q = Air Flow Rate (CFM)
A = Cross-Sectional Area (ft²)
Step 2: Calculate Velocity Pressure (Pv)
Pv = (V / 4005)²
Where:
Pv = Velocity Pressure (Inches of Water Gauge)
V = Velocity (Feet Per Minute)
4005 = Constant for Standard Air Density
How the Calculation Works
Our calculator automates the conversion process using the following logic:
1. Determine the Area
First, the circular diameter of the duct (in inches) is converted into square feet. The formula used is:
Area (ft²) = π × (Diameter ÷ 24)²
(Note: We divide by 24 because the radius is half the diameter, and we must convert inches to feet).
2. Determine the Velocity
Next, the Air Flow Rate (CFM) is divided by the Area to find the Air Velocity in Feet Per Minute (FPM). High velocity typically indicates higher pressure and potential noise issues.
3. Determine the Pressure
Finally, the velocity is converted into Velocity Pressure using the standard coefficient 4005. This coefficient assumes standard air conditions (70°F, 29.92 in. Hg, dry air). The result is typically expressed in "Inches of Water Gauge" (in. wg), common in the US, or converted to PSI (Pounds per Square Inch) or Pascals (Pa).
Why is this important?
Understanding velocity pressure is crucial for:
- HVAC Duct Sizing: Ensuring ducts are large enough to transport air without excessive pressure drop.
- Fan Selection: Choosing a fan that can overcome the total pressure of the system.
- Sensor Calibration: Pitot tubes measure velocity pressure to determine flow rates in existing systems.
Example Calculation
Imagine you have 1,000 CFM of air flowing through a 12-inch diameter duct.
- Area: A 12-inch duct has an area of roughly 0.7854 ft².
- Velocity: 1,000 CFM / 0.7854 ft² = 1,273 FPM.
- Pressure: (1,273 / 4005)² = 0.101 in. wg.
This means the dynamic pressure exerted by the air movement is approximately 0.1 inches of water column.
function calculatePressure() {
// 1. Get input elements
var flowInput = document.getElementById('flowRate');
var diamInput = document.getElementById('diameter');
var resultsArea = document.getElementById('resultsArea');
var errorMsg = document.getElementById('errorMsg');
// 2. Parse values
var cfm = parseFloat(flowInput.value);
var diameterInches = parseFloat(diamInput.value);
// 3. Validation
if (isNaN(cfm) || isNaN(diameterInches) || cfm <= 0 || diameterInches <= 0) {
errorMsg.style.display = 'block';
resultsArea.style.display = 'none';
return;
}
errorMsg.style.display = 'none';
// 4. Calculate Area (ft^2)
// Radius in feet = (diameter in inches / 2) / 12 = diameter / 24
var radiusFt = diameterInches / 24;
var areaFt2 = Math.PI * Math.pow(radiusFt, 2);
// 5. Calculate Velocity (FPM – Feet Per Minute)
// Velocity = Flow Rate / Area
var velocityFPM = cfm / areaFt2;
// 6. Calculate Velocity Pressure (in. wg)
// Standard formula: Pv = (V / 4005)^2
var pressureWG = Math.pow((velocityFPM / 4005), 2);
// 7. Convert to other units
// 1 in. wg = 0.036127 PSI
var pressurePSI = pressureWG * 0.036127;
// 1 in. wg = 249.089 Pascals
var pressurePa = pressureWG * 249.089;
// 8. Update Result Elements
document.getElementById('resArea').innerHTML = areaFt2.toFixed(3) + " ft²";
document.getElementById('resVelocity').innerHTML = Math.round(velocityFPM).toLocaleString() + " FPM";
document.getElementById('resPressWG').innerHTML = pressureWG.toFixed(4) + " in. wg";
document.getElementById('resPressPSI').innerHTML = pressurePSI.toFixed(5) + " PSI";
document.getElementById('resPressPa').innerHTML = pressurePa.toFixed(1) + " Pa";
// 9. Show results
resultsArea.style.display = 'block';
}