In fluid dynamics and hydraulics, understanding the relationship between how much fluid moves (volumetric flow) and how fast it moves (linear flow) is crucial for sizing pipes, designing HVAC systems, and ensuring pump efficiency. This calculator helps engineers and technicians convert volumetric data into velocity data instantly.
The Difference Between Q and v
Volumetric Flow Rate (Q): Represents the volume of fluid passing a point per unit of time. Common units include Gallons Per Minute (GPM), Cubic Feet per Minute (CFM), and Liters Per Minute (LPM).
Linear Flow Rate (v): Also known as flow velocity, this represents the distance a fluid particle travels per unit of time. Common units are Feet per Second (ft/s) and Meters per Second (m/s).
The Conversion Formula
To convert volumetric flow to linear velocity, you need the cross-sectional area of the pipe or duct. The fundamental physics equation used is:
v = Q / A
Where:
v = Linear Velocity
Q = Volumetric Flow Rate
A = Cross-Sectional Area of the pipe
Since pipes are usually circular, the Area (A) is calculated using the diameter (D):
A = π × (D / 2)²
Why Velocity Matters
Calculating the linear flow rate is essential for several reasons:
Pipe Erosion: If the linear velocity is too high, it can scour pipe walls and cause premature failure, especially in copper pipes.
Noise Control: High velocity in HVAC ducts or water pipes often results in audible whistling or water hammer.
Sedimentation: If the velocity is too low, suspended solids in wastewater or slurry lines may settle and cause clogs.
Typical Velocity Guidelines
While specific applications vary, here are general guidelines for water flow in pipes:
Suction Lines: 2 to 5 ft/s (0.6 to 1.5 m/s)
Discharge Lines: 5 to 8 ft/s (1.5 to 2.4 m/s)
General Water Distribution: 3 to 7 ft/s (1 to 2 m/s)
function calculateLinearVelocity() {
// 1. Get Input Values
var flowRateInput = document.getElementById('flowRate').value;
var flowUnit = document.getElementById('flowUnit').value;
var diameterInput = document.getElementById('pipeDiameter').value;
var diameterUnit = document.getElementById('diameterUnit').value;
var errorMsg = document.getElementById('errorMsg');
var resultsDiv = document.getElementById('results');
// 2. Validation
errorMsg.style.display = 'none';
resultsDiv.style.display = 'none';
if (flowRateInput === "" || diameterInput === "") {
errorMsg.textContent = "Please enter both Flow Rate and Pipe Diameter.";
errorMsg.style.display = 'block';
return;
}
var flowRate = parseFloat(flowRateInput);
var diameter = parseFloat(diameterInput);
if (isNaN(flowRate) || isNaN(diameter) || diameter <= 0 || flowRate < 0) {
errorMsg.textContent = "Please enter valid positive numbers.";
errorMsg.style.display = 'block';
return;
}
// 3. Normalize to Base Units (SI: meters and seconds)
// Base Flow: Cubic Meters per Second (m³/s)
// Base Diameter: Meters (m)
var baseFlow = 0; // m³/s
var baseDiameter = 0; // m
// Convert Flow to m³/s
switch (flowUnit) {
case 'gpm': // US Gallons per Minute
baseFlow = flowRate * 0.0000630901964;
break;
case 'lpm': // Liters per Minute
baseFlow = flowRate / 60000;
break;
case 'cfm': // Cubic Feet per Minute
baseFlow = flowRate * 0.000471947443;
break;
case 'm3h': // Cubic Meters per Hour
baseFlow = flowRate / 3600;
break;
case 'm3s': // Cubic Meters per Second
baseFlow = flowRate;
break;
}
// Convert Diameter to Meters
switch (diameterUnit) {
case 'inch':
baseDiameter = diameter * 0.0254;
break;
case 'mm':
baseDiameter = diameter / 1000;
break;
case 'cm':
baseDiameter = diameter / 100;
break;
case 'm':
baseDiameter = diameter;
break;
}
// 4. Calculate Area (A = π * r²) in m²
var radius = baseDiameter / 2;
var areaM2 = Math.PI * Math.pow(radius, 2);
// 5. Calculate Velocity (v = Q / A) in m/s
var velocityMS = baseFlow / areaM2;
// 6. Convert to Imperial (ft/s)
// 1 m/s = 3.28084 ft/s
var velocityFPS = velocityMS * 3.28084;
// 7. Format Results
var displayMetric = velocityMS.toFixed(2) + " m/s";
var displayImperial = velocityFPS.toFixed(2) + " ft/s";
var displayArea = areaM2.toFixed(6) + " m²";
// 8. Update DOM
document.getElementById('resultMetric').textContent = displayMetric;
document.getElementById('resultImperial').textContent = displayImperial;
document.getElementById('resultArea').textContent = displayArea;
resultsDiv.style.display = 'block';
}