Feet per second (ft/s)
Meters per second (m/s)
Feet per minute (ft/min)
Calculation Results
Cross-Sectional Area:0 m²
Gallons per Minute
0 GPM
Liters per Minute
0 L/min
Cubic Meters per Hour
0 m³/h
Cubic Feet per Minute
0 CFM
function calculateTheoreticalFlow() {
var diameter = parseFloat(document.getElementById('diameter').value);
var dUnit = document.getElementById('diameterUnit').value;
var velocity = parseFloat(document.getElementById('velocity').value);
var vUnit = document.getElementById('velocityUnit').value;
if (isNaN(diameter) || isNaN(velocity) || diameter <= 0 || velocity <= 0) {
alert("Please enter valid positive numbers for diameter and velocity.");
return;
}
// Convert diameter to meters
var dInMeters;
if (dUnit === 'in') { dInMeters = diameter * 0.0254; }
else if (dUnit === 'mm') { dInMeters = diameter / 1000; }
else if (dUnit === 'cm') { dInMeters = diameter / 100; }
else { dInMeters = diameter; }
// Calculate Area in m2 (A = pi * r^2)
var radius = dInMeters / 2;
var areaM2 = Math.PI * Math.pow(radius, 2);
// Convert velocity to m/s
var vInMps;
if (vUnit === 'fps') { vInMps = velocity * 0.3048; }
else if (vUnit === 'fpm') { vInMps = (velocity * 0.3048) / 60; }
else { vInMps = velocity; }
// Calculate Flow Rate (Q = A * v) in m3/s
var qM3s = areaM2 * vInMps;
// Conversions from m3/s
var m3h = qM3s * 3600;
var lpm = qM3s * 60000;
var gpm = qM3s * 15850.3231;
var cfm = qM3s * 2118.880003;
// Display results
document.getElementById('areaResult').innerText = areaM2.toFixed(6);
document.getElementById('m3hResult').innerText = m3h.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + " m³/h";
document.getElementById('lpmResult').innerText = lpm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + " L/min";
document.getElementById('gpmResult').innerText = gpm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + " GPM";
document.getElementById('cfmResult').innerText = cfm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + " CFM";
document.getElementById('flow-results').style.display = 'block';
}
Understanding Theoretical Flow Rate
Theoretical flow rate is the calculated volume of fluid that passes through a specific cross-section (like a pipe or a duct) per unit of time, assuming ideal conditions without friction or turbulence losses. It is a fundamental calculation in hydraulics, HVAC design, and industrial piping.
The Theoretical Flow Rate Formula
To calculate the flow rate, we use the Continuity Equation for incompressible fluids:
Q = A × v
Q: Flow Rate (Volumetric flow)
A: Cross-sectional area of the conduit
v: Average velocity of the fluid
How to Calculate Step-by-Step
Determine the Area (A): If you have a circular pipe, calculate the area using the diameter (D): Area = π × (D / 2)².
Measure the Velocity (v): This is the speed at which the fluid moves (e.g., meters per second or feet per second).
Multiply: Multiply the Area by the Velocity to get the flow rate in cubic units per time.
Convert: Convert the result into your preferred units, such as Gallons per Minute (GPM) or Liters per Minute (L/min).
Example Calculation
Imagine you have a pipe with an internal diameter of 2 inches and water is moving at a velocity of 5 feet per second.
Radius: 1 inch (0.0254 meters)
Area: π × (0.0254)² ≈ 0.002027 m²
Velocity: 5 ft/s ≈ 1.524 m/s
Flow Rate (Q): 0.002027 × 1.524 ≈ 0.003089 m³/s
Result in GPM: Approximately 48.96 Gallons per Minute.
Why Calculate Theoretical Flow?
Calculating the theoretical flow rate is essential during the planning phase of any fluid system. It helps engineers size pumps correctly, ensure pipes are large enough to handle the volume without excessive pressure drops, and verify that fire sprinkler systems or cooling loops meet safety requirements. Keep in mind that "actual" flow rate is often slightly lower due to friction against pipe walls and fittings.