How to Calculate Volume Flow Rate from Mass Flow Rate
by
Mass Flow Rate to Volume Flow Rate Calculator
kg/s
kg/h
lb/s
lb/h
kg/m³
lb/ft³
g/L
Water is approx. 1000 kg/m³, Air is approx. 1.225 kg/m³ at sea level.
Cubic Meters per Second (m³/s)
Cubic Meters per Hour (m³/h)
Liters per Minute (L/min)
Gallons per Minute (GPM – US)
Cubic Feet per Second (ft³/s)
Result:
Understanding the Relationship
The conversion from mass flow rate to volume flow rate is a fundamental concept in fluid dynamics. It relies on the density of the fluid passing through the system. Unlike volume, mass is conserved regardless of changes in temperature and pressure (assuming no leaks), making mass flow measurement highly accurate for many industrial processes.
The Formula
To find the volume flow rate ($Q$), you divide the mass flow rate ($\dot{m}$) by the fluid's density ($\rho$):
Q = ṁ / ρ
Where:
Q: Volume Flow Rate (m³/s, L/min, etc.)
ṁ: Mass Flow Rate (kg/s, lb/h, etc.)
ρ (rho): Density of the fluid (kg/m³, lb/ft³, etc.)
Calculation Example
Suppose you have water flowing through a pipe with a mass flow rate of 5 kg/s. The density of water is approximately 1000 kg/m³.
Identify Values: ṁ = 5 kg/s, ρ = 1000 kg/m³.
Apply Formula: Q = 5 / 1000.
Result: Q = 0.005 m³/s.
Convert (optional): 0.005 m³/s is equal to 300 Liters per minute.
Why This Matters
In many chemical engineering and HVAC applications, meters measure mass flow because it is independent of thermal expansion. However, sizing pumps, pipes, and tanks requires knowing the actual volume occupied by that fluid, which is where this calculation becomes vital.
function calculateFlowRate() {
var massValue = parseFloat(document.getElementById("massFlowRate").value);
var massUnit = document.getElementById("massUnit").value;
var densityValue = parseFloat(document.getElementById("density").value);
var densityUnit = document.getElementById("densityUnit").value;
var targetUnit = document.getElementById("targetUnit").value;
var resultArea = document.getElementById("resultArea");
var finalOutput = document.getElementById("finalOutput");
var calcSteps = document.getElementById("calcSteps");
if (isNaN(massValue) || isNaN(densityValue) || densityValue <= 0) {
alert("Please enter valid positive numbers for both flow rate and density.");
return;
}
// Step 1: Normalize Mass Flow Rate to kg/s
var massKgs;
if (massUnit === "kgs") {
massKgs = massValue;
} else if (massUnit === "kgh") {
massKgs = massValue / 3600;
} else if (massUnit === "lbs") {
massKgs = massValue * 0.453592;
} else if (massUnit === "lbh") {
massKgs = (massValue * 0.453592) / 3600;
}
// Step 2: Normalize Density to kg/m³
var densityKgm3;
if (densityUnit === "kgm3") {
densityKgm3 = densityValue;
} else if (densityUnit === "lbft3") {
densityKgm3 = densityValue * 16.0185;
} else if (densityUnit === "gl") {
densityKgm3 = densityValue; // 1 g/L = 1 kg/m³
}
// Step 3: Calculate base Volume Flow Rate in m³/s
var volumeM3s = massKgs / densityKgm3;
// Step 4: Convert to target unit
var finalResult;
var unitLabel;
if (targetUnit === "m3s") {
finalResult = volumeM3s;
unitLabel = "m³/s";
} else if (targetUnit === "m3h") {
finalResult = volumeM3s * 3600;
unitLabel = "m³/h";
} else if (targetUnit === "lmin") {
finalResult = volumeM3s * 60000;
unitLabel = "L/min";
} else if (targetUnit === "gpm") {
finalResult = volumeM3s * 15850.3;
unitLabel = "GPM";
} else if (targetUnit === "cfs") {
finalResult = volumeM3s * 35.3147;
unitLabel = "ft³/s";
}
// Display Results
resultArea.style.display = "block";
finalOutput.innerHTML = finalResult.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 6}) + " " + unitLabel;
calcSteps.innerHTML = "Formula used: " + massValue + " [" + massUnit + "] / " + densityValue + " [" + densityUnit + "] converted to " + unitLabel;
}