Exhaust Gas Mass Flow Rate Calculator
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Calculate Mass Flow
Total Exhaust Mass Flow
0 kg/h
Intake Air Mass Flow:
0 kg/h
Fuel Mass Flow:
0 kg/h
Exhaust Flow (lbs/min):
0 lb/min
Exhaust Flow (g/s):
0 g/s
Understanding Exhaust Gas Mass Flow Rate
The exhaust gas mass flow rate is a critical parameter in internal combustion engine engineering, particularly for turbocharger sizing, exhaust system design, and after-treatment system development (such as catalytic converters and DPFs). Unlike volume flow, which changes drastically with temperature and pressure, mass flow remains conserved through the engine.
The Fundamental Principle: Conservation of Mass applies to the engine cycle. The mass of the gas exiting the exhaust is equal to the mass of the air entering the intake plus the mass of the fuel injected.
Formula: ṁexh = ṁair + ṁfuel
How to Calculate Exhaust Mass Flow
While modern ECUs measure air mass directly using a MAF sensor, it can be calculated theoretically using engine specifications. This calculator uses the "Speed-Density" approach combined with volumetric efficiency.
Step 1: Calculate Air Mass Flow (ṁair )
First, we determine the volume of air pumped by the engine, then convert it to mass using air density.
Formula: ṁair = (Vd × RPM × ηvol × ρair ) / (n × 60)Vd : Engine Displacement (converted to m³)ηvol : Volumetric Efficiency (percentage of the cylinder actually filled)ρair : Air Density (standard is ~1.225 kg/m³ at sea level)n: Number of revolutions per intake stroke (2 for 4-stroke, 1 for 2-stroke)
Step 2: Calculate Fuel Mass Flow (ṁfuel )
Using the Air-Fuel Ratio (AFR), we determine how much fuel is added to the air.
ṁfuel = ṁair / AFR
Step 3: Total Exhaust Flow
Finally, sum the two components to find the total mass exiting the exhaust valves.
Example Calculation
Consider a 2.0 Liter 4-stroke engine running at 6,000 RPM with a volumetric efficiency of 90% and an AFR of 12.5:1 (rich mixture for power).
Theoretical Volume Flow: 2.0L × (6000 / 2) = 6,000 L/minActual Volume Flow (with VE): 6,000 × 0.90 = 5,400 L/minAir Mass Flow: 5,400 L/min × 1.225 g/L = 6,615 g/min = 396.9 kg/h Fuel Mass Flow: 396.9 / 12.5 = 31.75 kg/h Total Exhaust Mass Flow: 396.9 + 31.75 = 428.65 kg/h
Why is this important?
Turbo Sizing: Turbine maps utilize corrected mass flow to determine if a turbocharger will choke or surge at specific RPMs.Exhaust Piping: To maintain optimal backpressure and velocity, pipe diameter must be matched to the peak mass flow rate.Emissions: Catalytic converters are rated for specific mass flow limits to ensure proper chemical reactions.
function calculateFlow() {
// Get input values
var dispStr = document.getElementById('displacement').value;
var rpmStr = document.getElementById('rpm').value;
var veStr = document.getElementById('ve').value;
var afrStr = document.getElementById('afr').value;
var rhoStr = document.getElementById('airDensity').value;
var cycleFactorStr = document.getElementById('engineType').value;
// Validation: Check if inputs are empty
if(!dispStr || !rpmStr || !veStr || !afrStr || !rhoStr) {
alert("Please fill in all fields to calculate flow.");
return;
}
// Parse values
var disp = parseFloat(dispStr); // Liters
var rpm = parseFloat(rpmStr); // RPM
var ve = parseFloat(veStr); // Percentage (e.g., 85)
var afr = parseFloat(afrStr); // Ratio
var rho = parseFloat(rhoStr); // kg/m^3
var cycleDivisor = parseFloat(cycleFactorStr); // 2 for 4-stroke, 1 for 2-stroke
// Validation: Check for logical numbers
if(disp <= 0 || rpm <= 0 || ve <= 0 || afr <= 0 || rho Fuel Mass = Air Mass / AFR
var fuelFlowKgH = airFlowKgH / afr;
// 5. Calculate Total Exhaust Mass Flow (kg/h)
// Conservation of Mass: Exhaust = Air + Fuel
var totalExhaustKgH = airFlowKgH + fuelFlowKgH;
// 6. Conversions for display
// kg/h to lb/min: 1 kg/h = 0.03674 lb/min
var totalExhaustLbMin = totalExhaustKgH * 0.0367437;
// kg/h to g/s: 1 kg/h = 0.277778 g/s
var totalExhaustGS = totalExhaustKgH * 0.277778;
// DISPLAY RESULTS
document.getElementById('results').style.display = 'block';
document.getElementById('airFlowKgH').innerHTML = airFlowKgH.toFixed(2) + " kg/h";
document.getElementById('fuelFlowKgH').innerHTML = fuelFlowKgH.toFixed(2) + " kg/h";
document.getElementById('totalFlowKgH').innerHTML = totalExhaustKgH.toFixed(2) + " kg/h";
document.getElementById('totalFlowLbMin').innerHTML = totalExhaustLbMin.toFixed(2) + " lb/min";
document.getElementById('totalFlowGS').innerHTML = totalExhaustGS.toFixed(2) + " g/s";
}