Please enter valid positive numbers for Flow Rate and Diameter.
Fluid Velocity (Metric): 0.00 m/s
Fluid Velocity (Imperial): 0.00 ft/s
Cross-Sectional Area: 0.0000 m²
function calculateVelocity() {
// Get Inputs
var flowRateInput = document.getElementById('flowRate').value;
var pipeDiameterInput = document.getElementById('pipeDiameter').value;
var flowUnit = document.getElementById('flowUnit').value;
var diameterUnit = document.getElementById('diameterUnit').value;
var errorDiv = document.getElementById('errorMsg');
var resultDiv = document.getElementById('resultBox');
// Validation
if (flowRateInput === "" || pipeDiameterInput === "" || parseFloat(flowRateInput) <= 0 || parseFloat(pipeDiameterInput) <= 0) {
errorDiv.style.display = 'block';
resultDiv.style.display = 'none';
return;
}
errorDiv.style.display = 'none';
var flow = parseFloat(flowRateInput);
var dia = parseFloat(pipeDiameterInput);
// 1. Standardize Inputs to SI Units (m³/s and meters)
// Convert Flow Rate to m³/s
var flowM3s = 0;
if (flowUnit === 'gpm') {
// 1 US GPM = 0.0000630901964 m³/s
flowM3s = flow * 0.0000630901964;
} else if (flowUnit === 'm3h') {
// 1 m³/h = 1/3600 m³/s
flowM3s = flow / 3600;
} else if (flowUnit === 'ls') {
// 1 L/s = 0.001 m³/s
flowM3s = flow / 1000;
} else if (flowUnit === 'cfm') {
// 1 CFM = 0.000471947443 m³/s
flowM3s = flow * 0.000471947443;
}
// Convert Diameter to meters
var diaM = 0;
if (diameterUnit === 'inch') {
// 1 inch = 0.0254 meters
diaM = dia * 0.0254;
} else if (diameterUnit === 'mm') {
// 1 mm = 0.001 meters
diaM = dia / 1000;
} else if (diameterUnit === 'm') {
diaM = dia;
}
// 2. Calculate Area (Circular Pipe)
// Area = pi * r² = pi * (d/2)²
var radiusM = diaM / 2;
var areaM2 = Math.PI * Math.pow(radiusM, 2);
// 3. Calculate Velocity
// v = Q / A
var velMs = flowM3s / areaM2;
// 4. Convert Results
var velFts = velMs * 3.28084; // Convert m/s to ft/s
// 5. Display Results
document.getElementById('resVelMetric').innerHTML = velMs.toFixed(2) + " m/s";
document.getElementById('resVelImperial').innerHTML = velFts.toFixed(2) + " ft/s";
document.getElementById('resArea').innerHTML = areaM2.toFixed(5) + " m²";
resultDiv.style.display = 'block';
}
Understanding Flow Rate to Velocity Calculations
In fluid dynamics, calculating the velocity of a fluid flowing through a pipe is a fundamental task for engineers, plumbers, and HVAC technicians. Whether you are sizing a pump, designing a water supply system, or analyzing air ducts, understanding the relationship between volumetric flow rate (Q) and fluid velocity (v) is critical for ensuring system efficiency and preventing issues like pipe erosion or excessive noise.
The Continuity Equation
The calculation performed by the tool above is based on the Continuity Equation for incompressible fluids. The principle states that the volumetric flow rate is equal to the cross-sectional area of the pipe multiplied by the velocity of the fluid.
Q = A × v
Where:
Q = Volumetric Flow Rate (e.g., GPM, m³/h, CFM)
A = Cross-Sectional Area of the pipe (derived from the inner diameter)
v = Fluid Velocity (e.g., ft/s, m/s)
To solve for Velocity (v), we rearrange the formula:
v = Q / A
Step-by-Step Calculation Logic
Because flow rates and pipe sizes are often provided in conflicting units (like gallons per minute for flow, but inches for diameter), manual calculation requires careful unit conversion. Here is how the process works mathematically:
Standardize Units: Convert the flow rate to cubic meters per second (m³/s) or cubic feet per second (ft³/s). Convert the diameter to meters or feet.
Calculate Area: For a circular pipe, calculate the cross-sectional area using the formula A = π × (d/2)².
Divide: Divide the standardized flow rate by the calculated area to get the velocity.
Why Fluid Velocity Matters
Maintaining the correct fluid velocity is essential for the longevity of piping systems:
Too High: High velocities (usually above 5-7 ft/s for water) can cause water hammer, pipe erosion, and increased friction loss, leading to higher energy bills for pumping.
Too Low: Low velocities (below 2 ft/s) may allow suspended solids to settle out of the fluid, causing clogs or sediment buildup in the pipes.
Calculation Examples
Here are a few realistic scenarios you might encounter in the field:
Scenario
Flow Rate
Pipe Diameter
Calculated Velocity
Residential Water Supply
10 GPM
1 Inch
4.08 ft/s (1.24 m/s)
Industrial Pump Line
50 m³/h
100 mm
1.77 m/s (5.80 ft/s)
HVAC Air Duct
500 CFM
12 Inches
636 ft/min (10.6 ft/s)
Common Unit Conversions
If you are calculating manually, keep these conversions handy:
1 GPM = 0.002228 ft³/s
1 Inch = 0.0833 Feet
1 m³/h = 0.2777 L/s
Using the calculator above eliminates the risk of conversion errors, ensuring accurate velocity data for your engineering or construction projects.