Understanding the Relationship Between Flow Rate and Velocity
In fluid dynamics, the velocity of a liquid or gas traveling through a pipe is directly related to the volume of fluid moving past a point per unit of time (flow rate) and the size of the pipe (cross-sectional area). This relationship is governed by the Continuity Equation.
The Velocity Formula
To calculate velocity from volumetric flow rate, we use the following formula:
v = Q / A
Where:
v = Flow velocity (m/s or ft/s)
Q = Volumetric flow rate (m³/s or ft³/s)
A = Cross-sectional area of the pipe (m² or ft²)
Calculating the Cross-sectional Area (A)
Since most pipes are circular, the area is calculated using the internal diameter (D):
A = π × (D / 2)² — or — A = (π × D²) / 4
Practical Example
Suppose you have a pipe with an internal diameter of 100 mm and a flow rate of 50 Liters per minute (L/min).
Convert Flow Rate: 50 L/min is approximately 0.000833 m³/s.
Convert Diameter: 100 mm is 0.1 meters.
Calculate Area: A = π × (0.1 / 2)² = 0.007854 m².
Calculate Velocity: v = 0.000833 / 0.007854 = 0.106 m/s.
This calculator handles all unit conversions automatically, ensuring you get accurate results for engineering, plumbing, or industrial applications.
function calculateVelocity() {
var flowRate = parseFloat(document.getElementById("flowRate").value);
var flowUnit = document.getElementById("flowUnit").value;
var diameter = parseFloat(document.getElementById("diameter").value);
var diameterUnit = document.getElementById("diameterUnit").value;
if (isNaN(flowRate) || isNaN(diameter) || diameter <= 0 || flowRate < 0) {
alert("Please enter valid positive numbers for flow rate and diameter.");
return;
}
// Convert flow rate to cubic meters per second (m3/s)
var q_m3s = 0;
if (flowUnit === "m3s") {
q_m3s = flowRate;
} else if (flowUnit === "m3h") {
q_m3s = flowRate / 3600;
} else if (flowUnit === "lmin") {
q_m3s = flowRate / 60000;
} else if (flowUnit === "gpm") {
q_m3s = flowRate * 0.0000630901964;
} else if (flowUnit === "cfs") {
q_m3s = flowRate * 0.0283168;
}
// Convert diameter to meters (m)
var d_m = 0;
if (diameterUnit === "mm") {
d_m = diameter / 1000;
} else if (diameterUnit === "cm") {
d_m = diameter / 100;
} else if (diameterUnit === "m") {
d_m = diameter;
} else if (diameterUnit === "in") {
d_m = diameter * 0.0254;
}
// Calculate Area (A = pi * r^2)
var radius = d_m / 2;
var area = Math.PI * Math.pow(radius, 2);
// Calculate Velocity (v = Q / A)
var velocity_ms = q_m3s / area;
var velocity_fts = velocity_ms * 3.28084;
// Display Results
document.getElementById("velMs").innerText = velocity_ms.toFixed(4);
document.getElementById("velFts").innerText = velocity_fts.toFixed(4);
document.getElementById("calcArea").innerText = area.toFixed(6);
document.getElementById("results").style.display = "block";
}