Selecting the correct pipe size is critical in fluid dynamics to ensure efficient transport without excessive pressure drop or erosion. The relationship between flow rate, velocity, and pipe diameter is governed by the Continuity Equation.
The Formula:
To find the internal diameter (D), we use the formula derived from Q = A × v:
D = √((4 × Q) / (π × v))
Q: Volumetric Flow Rate
v: Fluid Velocity
D: Inner Pipe Diameter
Typical Design Velocity Guidelines
When you don't have a specific velocity required, engineers use standard industry guidelines to prevent noise, water hammer, and pipe wear:
Service Type
Recommended Velocity (ft/s)
Recommended Velocity (m/s)
Water (Suction Line)
2 – 4 ft/s
0.6 – 1.2 m/s
Water (Discharge Line)
5 – 10 ft/s
1.5 – 3.0 m/s
Compressed Air
20 – 50 ft/s
6.0 – 15.0 m/s
Steam (Saturated)
80 – 120 ft/s
24 – 36 m/s
Real-World Example
Suppose you have a cooling system requiring a flow rate of 100 GPM and you want to maintain a velocity of 5 ft/s to minimize pressure loss. Using the calculator:
Input 100 into Flow Rate and select GPM.
Input 5 into Velocity and select ft/s.
The calculator converts units and solves for the area.
The resulting diameter is approximately 2.85 inches.
You would typically round up to the nearest standard nominal pipe size (e.g., a 3-inch pipe).
function calculatePipeSize() {
var flowRate = parseFloat(document.getElementById("flowRate").value);
var flowUnit = document.getElementById("flowUnit").value;
var velocity = parseFloat(document.getElementById("velocity").value);
var velocityUnit = document.getElementById("velocityUnit").value;
if (isNaN(flowRate) || flowRate <= 0 || isNaN(velocity) || velocity <= 0) {
alert("Please enter valid positive numbers for Flow Rate and Velocity.");
return;
}
// Convert Flow Rate to Cubic Feet per Second (CFS) as base
var q_cfs;
if (flowUnit === "gpm") {
q_cfs = flowRate / 448.831;
} else if (flowUnit === "m3h") {
q_cfs = flowRate / 101.941;
} else if (flowUnit === "lpm") {
q_cfs = flowRate / 1699.01;
} else if (flowUnit === "cfs") {
q_cfs = flowRate;
}
// Convert Velocity to Feet per Second (FPS) as base
var v_fps;
if (velocityUnit === "mps") {
v_fps = velocity * 3.28084;
} else {
v_fps = velocity;
}
// Calculation logic: Area (A) = Q / V
var area_sqft = q_cfs / v_fps;
// Diameter (D) = sqrt( (4 * A) / PI )
var diameter_ft = Math.sqrt((4 * area_sqft) / Math.PI);
// Conversions for results
var diameter_inches = diameter_ft * 12;
var diameter_mm = diameter_ft * 304.8;
var area_sqin = area_sqft * 144;
// Display Results
document.getElementById("resInches").innerHTML = diameter_inches.toFixed(3);
document.getElementById("resMM").innerHTML = diameter_mm.toFixed(2);
document.getElementById("resArea").innerHTML = area_sqin.toFixed(3);
document.getElementById("resultArea").style.display = "block";
}