Calculate pipe volumetric flow based on diameter and velocity.
mm
inches
meters
m/s
ft/s
Use 1.0 for theoretical flow. Common range: 0.60 – 0.98 for orifices/nozzles.
Please enter valid positive numbers for diameter and velocity.
Calculation Results
Cubic Meters per Hour:–
Liters per Minute:–
Gallons per Minute (US):–
Cubic Feet per Second:–
Cross-Sectional Area:–
Understanding Actual Flow Rate Calculation
Flow rate is a critical metric in fluid dynamics, essential for engineering applications ranging from municipal water supply networks to industrial chemical processing and HVAC systems. While theoretical flow rate assumes ideal conditions, the Actual Flow Rate accounts for real-world factors such as friction, turbulence, and the geometry of the piping system.
The Difference Between Theoretical vs. Actual Flow
Theoretical flow rate is determined purely by the cross-sectional area of the conduit and the velocity of the fluid. However, in practice, no system is perfectly efficient. Engineers use a Discharge Coefficient (Cd) to correct theoretical calculations to match reality.
Theoretical Flow: Assumes inviscid, incompressible flow with no energy losses.
Actual Flow: Accounts for viscosity, vena contracta effects (in orifices), and friction losses.
The Flow Rate Formula
To calculate the volumetric flow rate ($Q$), the fundamental equation relates the cross-sectional area of the pipe ($A$) and the average velocity of the fluid ($v$). When adjusting for efficiency, we include the coefficient ($C_d$):
Q = A × v × Cd
Where:
Q = Volumetric Flow Rate (e.g., m³/s, GPM)
A = Cross-Sectional Area of the pipe (π · r²)
v = Average Fluid Velocity
Cd = Coefficient of Discharge (Dimensionless, typically 0.60 to 0.98)
How to Use This Calculator
This tool simplifies the complex conversions between different units used in fluid mechanics.
Input Pipe Diameter: Measure the internal diameter of the pipe. Wall thickness affects flow area, so internal dimensions are crucial. You can select Millimeters (mm), Inches (in), or Meters (m).
Input Fluid Velocity: Enter the speed at which the fluid is moving through the system. This is often determined by flow meters or pump specifications.
Discharge Coefficient: If you are calculating flow through a specific restriction (like an orifice plate) or want to account for efficiency losses, enter a value less than 1.0. For standard pipe flow calculations assuming known velocity, leave this as 1.0.
Applications of Flow Rate Data
Accurate flow rate calculations are vital for:
Pump Sizing: Ensuring a pump can deliver the required volume against system head.
Irrigation: Calculating water delivery to crops to prevent over or under-watering.
HVAC Balancing: Adjusting water flow in chillers and boilers for optimal heat transfer.
Chemical Dosing: Precise addition of reactants in manufacturing processes.
Common Unit Conversions
Fluid dynamics involves various units depending on the region and industry. This calculator automatically converts between:
m³/h (Cubic Meters per Hour): Standard metric unit for industrial flow.
L/min (Liters per Minute): Common for smaller pumps and hydraulics.
GPM (Gallons per Minute): The standard unit in the United States for water flow.
CFS (Cubic Feet per Second): Often used in large-scale civil engineering and open channel flow.
function calculateFlowRate() {
// 1. Get input elements
var diameterInput = document.getElementById("pipeDiameter");
var diameterUnit = document.getElementById("diameterUnit");
var velocityInput = document.getElementById("fluidVelocity");
var velocityUnit = document.getElementById("velocityUnit");
var coeffInput = document.getElementById("dischargeCoeff");
var errorDisplay = document.getElementById("errorDisplay");
var resultsDiv = document.getElementById("results");
// 2. Parse values
var d_val = parseFloat(diameterInput.value);
var v_val = parseFloat(velocityInput.value);
var cd_val = parseFloat(coeffInput.value);
// 3. Validation
if (isNaN(d_val) || isNaN(v_val) || d_val <= 0 || v_val < 0) {
errorDisplay.style.display = "block";
resultsDiv.style.display = "none";
return;
}
// Handle Coeff default or validation
if (isNaN(cd_val) || cd_val <= 0) {
cd_val = 1.0;
}
errorDisplay.style.display = "none";
// 4. Normalize inputs to Base SI Units (Meters for length, Meters/Second for velocity)
var diameterInMeters = 0;
if (diameterUnit.value === "mm") {
diameterInMeters = d_val / 1000;
} else if (diameterUnit.value === "in") {
diameterInMeters = d_val * 0.0254;
} else {
diameterInMeters = d_val; // already meters
}
var velocityInMetersPerSecond = 0;
if (velocityUnit.value === "ft_s") {
velocityInMetersPerSecond = v_val * 0.3048;
} else {
velocityInMetersPerSecond = v_val; // already m/s
}
// 5. Calculate Area (A = pi * r^2 = pi * (d/2)^2)
var radius = diameterInMeters / 2;
var areaM2 = Math.PI * Math.pow(radius, 2);
// 6. Calculate Flow Rate (Q = A * v * Cd) in Cubic Meters per Second
var flowM3s = areaM2 * velocityInMetersPerSecond * cd_val;
// 7. Convert to output units
// m3/h
var flowM3h = flowM3s * 3600;
// L/min (1 m3/s = 60000 L/min)
var flowLpm = flowM3s * 60000;
// GPM (US) (1 m3/s ≈ 15850.3231 GPM)
var flowGpm = flowM3s * 15850.3231;
// CFS (Cubic Feet per Second) (1 m3/s ≈ 35.3147 ft3/s)
var flowCfs = flowM3s * 35.3147;
// Area in cm2 for display
var areaCm2 = areaM2 * 10000;
// 8. Update DOM
document.getElementById("resM3h").innerHTML = flowM3h.toFixed(2) + " m³/h";
document.getElementById("resLpm").innerHTML = flowLpm.toFixed(2) + " L/min";
document.getElementById("resGpm").innerHTML = flowGpm.toFixed(2) + " GPM";
document.getElementById("resCfs").innerHTML = flowCfs.toFixed(3) + " ft³/s";
document.getElementById("resArea").innerHTML = areaCm2.toFixed(2) + " cm²";
resultsDiv.style.display = "block";
}