Cubic Meters per Second (m³/s)
Cubic Meters per Hour (m³/hr)
Liters per Minute (L/min)
Liters per Hour (L/hr)
US Gallons per Minute (GPM)
Cubic Feet per Second (cfs)
Cubic Feet per Minute (cfm)
Calculated Volumetric Flow Rate:
0.00
m³/s
Q = ṁ / ρ
How to Convert Mass Flow to Volumetric Flow
In fluid dynamics and engineering, converting between mass flow rate and volumetric flow rate is a fundamental calculation. This conversion is critical when sizing pumps, designing piping systems, or monitoring chemical processes where temperature and pressure changes might affect fluid volume but not mass.
The bridge between these two measurements is Density.
The Formula
The relationship between mass flow rate, volumetric flow rate, and density is defined by the following equation:
Q = ṁ / ρ
Where:
Q = Volumetric Flow Rate (e.g., m³/s, GPM, CFM)
ṁ (m-dot) = Mass Flow Rate (e.g., kg/s, lb/hr)
ρ (rho) = Fluid Density (e.g., kg/m³, lb/ft³)
Why is Density Important?
Mass is conserved; it does not change regardless of pressure or temperature. However, volume is dependent on the state of the fluid.
Gases: Highly compressible. A slight change in pressure or temperature drastically changes the density, meaning the volumetric flow rate will change even if the mass flow remains constant.
Liquids: Generally considered incompressible, but density still varies with temperature. For example, water at 4°C has a density of ~1000 kg/m³, while at 80°C it drops to ~971 kg/m³.
Calculation Example
Let's say you have a water pipe carrying 5,000 kg/hr of water. The water is at room temperature with a density of approximately 997 kg/m³.
Identify Mass Flow (ṁ): 5,000 kg/hr
Identify Density (ρ): 997 kg/m³
Apply Formula: Q = 5,000 / 997 = 5.015 m³/hr
If you need the result in Liters per Minute (L/min):
5.015 m³/hr × 1,000 = 5,015 L/hr
5,015 L/hr ÷ 60 = 83.58 L/min
Common Unit Conversions
When working with flow rates, unit mismatches are the most common source of error. Always ensure your mass and density units are compatible before dividing.
1 kg/s = 3600 kg/hr
1 m³ = 1000 Liters
1 m³ ≈ 264.172 US Gallons
1 lb ≈ 0.4536 kg
function calculateFlow() {
// 1. Get Input Elements
var massFlowInput = document.getElementById('massFlow');
var massUnitInput = document.getElementById('massUnit');
var densityInput = document.getElementById('density');
var densityUnitInput = document.getElementById('densityUnit');
var outputUnitInput = document.getElementById('outputUnit');
var resultContainer = document.getElementById('result-container');
var resultValueElement = document.getElementById('resultValue');
var resultUnitDisplay = document.getElementById('resultUnitDisplay');
var densityError = document.getElementById('densityError');
// 2. Get Values
var massFlow = parseFloat(massFlowInput.value);
var massUnit = massUnitInput.value;
var density = parseFloat(densityInput.value);
var densityUnit = densityUnitInput.value;
var outputUnit = outputUnitInput.value;
// 3. Validation
// Reset error
densityError.style.display = 'none';
if (isNaN(massFlow) || isNaN(density)) {
// If inputs are empty or not numbers, do not display result yet or handle gracefully
if(massFlowInput.value !== "" && densityInput.value !== "") {
alert("Please enter valid numeric values for Mass Flow and Density.");
}
resultContainer.style.display = 'none';
return;
}
if (density <= 0) {
densityError.style.display = 'block';
resultContainer.style.display = 'none';
return;
}
// 4. Normalize Inputs to Base Units (SI: kg/s for mass, kg/m³ for density)
var massFlowKgPerSec = 0;
// Convert Mass Flow to kg/s
switch(massUnit) {
case 'kg_s':
massFlowKgPerSec = massFlow;
break;
case 'kg_min':
massFlowKgPerSec = massFlow / 60;
break;
case 'kg_hr':
massFlowKgPerSec = massFlow / 3600;
break;
case 'lb_s':
massFlowKgPerSec = massFlow * 0.45359237;
break;
case 'lb_min':
massFlowKgPerSec = (massFlow * 0.45359237) / 60;
break;
case 'lb_hr':
massFlowKgPerSec = (massFlow * 0.45359237) / 3600;
break;
}
var densityKgPerM3 = 0;
// Convert Density to kg/m³
switch(densityUnit) {
case 'kg_m3':
densityKgPerM3 = density;
break;
case 'g_cm3':
densityKgPerM3 = density * 1000;
break;
case 'lb_ft3':
densityKgPerM3 = density * 16.018463;
break;
case 'lb_gal':
// 1 lb/gal (US) ≈ 119.826 kg/m³
densityKgPerM3 = density * 119.826427;
break;
}
// 5. Calculate Volumetric Flow in Base Unit (m³/s)
// Formula: Q = m_dot / rho
var volFlowM3PerSec = massFlowKgPerSec / densityKgPerM3;
// 6. Convert Result to Desired Output Unit
var finalResult = 0;
var unitLabel = "";
switch(outputUnit) {
case 'm3_s':
finalResult = volFlowM3PerSec;
unitLabel = "m³/s";
break;
case 'm3_hr':
finalResult = volFlowM3PerSec * 3600;
unitLabel = "m³/hr";
break;
case 'L_min':
finalResult = volFlowM3PerSec * 60000; // 1 m3/s = 60000 L/min
unitLabel = "L/min";
break;
case 'L_hr':
finalResult = volFlowM3PerSec * 3600000; // 1 m3/s = 3600000 L/hr
unitLabel = "L/hr";
break;
case 'gal_min':
// 1 m3/s ≈ 15850.3231 US GPM
finalResult = volFlowM3PerSec * 15850.3231;
unitLabel = "US GPM";
break;
case 'ft3_s':
// 1 m3 ≈ 35.314667 ft3
finalResult = volFlowM3PerSec * 35.314667;
unitLabel = "ft³/s (cfs)";
break;
case 'ft3_min':
finalResult = volFlowM3PerSec * 35.314667 * 60;
unitLabel = "ft³/min (cfm)";
break;
}
// 7. Display Result
// Format to 4 significant digits or suitable decimal places based on magnitude
var displayString = "";
if (finalResult 0) {
displayString = finalResult.toExponential(4);
} else {
displayString = finalResult.toLocaleString('en-US', { minimumFractionDigits: 2, maximumFractionDigits: 4 });
}
resultValueElement.innerText = displayString;
resultUnitDisplay.innerText = unitLabel;
resultContainer.style.display = 'block';
}