Average speed of the fluid moving through the cross-section.
Calculation Results
Cross-Sectional Area:0 m²
Volumetric Flow Rate (Cubic Meters/Sec):0 m³/s
Volumetric Flow Rate (Cubic Meters/Hour):0 m³/h
Volumetric Flow Rate (Liters/Min):0 L/min
Volumetric Flow Rate (CFM):0 CFM
Understanding Cross Flow Rate Calculations
In fluid dynamics and HVAC engineering, determining the Cross Flow Rate (often referred to simply as volumetric flow rate) is a fundamental task. This calculation helps engineers determine how much fluid (air, water, or gas) moves through a specific cross-sectional area over a given period. Whether you are sizing a duct for an HVAC system, designing a hydraulic pipe network, or analyzing wind tunnel data, understanding the relationship between velocity, area, and flow rate is critical.
The Fundamental Formula
The calculation relies on the continuity equation for incompressible flow. The basic formula used to calculate the volumetric flow rate ($Q$) is:
Q = A × v
Where:
Q = Volumetric Flow Rate (e.g., m³/s, CFM)
A = Cross-Sectional Area of the pipe or duct (m²)
v = Average Velocity of the fluid (m/s)
How to Calculate Area (A)
Before you can determine the flow rate, you must calculate the cross-sectional area of the conduit. The geometry of the duct or pipe dictates the math:
1. Circular Pipes
For a circular pipe, the area is calculated using the internal diameter ($D$):
Area = π × (D / 2)² or Area = (π × D²) / 4
Note: Ensure your diameter is converted to meters before calculating if your velocity is in meters per second.
2. Rectangular Ducts
For rectangular ducts, the area is simply the product of width ($W$) and height ($H$):
Area = W × H
Example Calculation
Let's assume you have a circular HVAC duct with an internal diameter of 300 mm (0.3 meters) and the air is moving at a velocity of 5 m/s.
Calculate Radius: 0.3m / 2 = 0.15m
Calculate Area: π × 0.15² ≈ 0.0707 m²
Calculate Flow Rate: 0.0707 m² × 5 m/s = 0.3535 m³/s
Maintaining the correct cross flow velocity is vital for system efficiency and longevity.
HVAC Systems: Velocity that is too high causes noise and excessive pressure drop. Velocity that is too low may result in poor temperature mixing or settling of particulates.
Filtration: In cross-flow filtration, the velocity of the feed stream parallel to the membrane surface prevents fouling.
Heat Exchangers: The flow rate directly impacts the heat transfer coefficient; higher flow usually increases heat transfer but requires more pumping power.
Using the Calculator
This tool simplifies the process by handling unit conversions automatically. Simply input your dimensions in millimeters and your velocity in meters per second. The calculator instantly provides the cross-sectional area and the volumetric flow rate in four distinct units (m³/s, m³/h, L/min, and CFM), covering the needs of both metric and imperial engineering standards.
function toggleInputs() {
var shape = document.getElementById("crossSectionShape").value;
var circInput = document.getElementById("circularInputs");
var rectInput = document.getElementById("rectangularInputs");
if (shape === "circular") {
circInput.classList.remove("hidden");
rectInput.classList.add("hidden");
} else {
circInput.classList.add("hidden");
rectInput.classList.remove("hidden");
}
}
function calculateFlowRate() {
// Inputs
var shape = document.getElementById("crossSectionShape").value;
var velocity = parseFloat(document.getElementById("velocity").value);
var area = 0; // in square meters
// Validation
if (isNaN(velocity) || velocity < 0) {
alert("Please enter a valid positive number for Velocity.");
return;
}
if (shape === "circular") {
var diameterMM = parseFloat(document.getElementById("diameter").value);
if (isNaN(diameterMM) || diameterMM <= 0) {
alert("Please enter a valid diameter in millimeters.");
return;
}
// Convert mm to meters
var diameterM = diameterMM / 1000;
var radiusM = diameterM / 2;
area = Math.PI * Math.pow(radiusM, 2);
} else if (shape === "rectangular") {
var widthMM = parseFloat(document.getElementById("width").value);
var heightMM = parseFloat(document.getElementById("height").value);
if (isNaN(widthMM) || widthMM <= 0 || isNaN(heightMM) || heightMM <= 0) {
alert("Please enter valid width and height dimensions in millimeters.");
return;
}
// Convert mm to meters
var widthM = widthMM / 1000;
var heightM = heightMM / 1000;
area = widthM * heightM;
}
// Calculate Flow Rate (Q = A * v) in m³/s
var flowCMS = area * velocity;
// Conversions
// 1 m³/s = 3600 m³/h
var flowCMH = flowCMS * 3600;
// 1 m³/s = 60000 L/min
var flowLPM = flowCMS * 60000;
// 1 m³/s = 2118.88 CFM (Cubic Feet per Minute)
var flowCFM = flowCMS * 2118.88;
// Display Results
document.getElementById("results-area").style.display = "block";
document.getElementById("resultArea").innerText = area.toFixed(6) + " m²";
document.getElementById("resultCMS").innerText = flowCMS.toFixed(5) + " m³/s";
document.getElementById("resultCMH").innerText = flowCMH.toFixed(2) + " m³/h";
document.getElementById("resultLPM").innerText = flowLPM.toFixed(2) + " L/min";
document.getElementById("resultCFM").innerText = flowCFM.toFixed(2) + " CFM";
}