How to Calculate Mass Flow Rate of Gas

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Mass Flow Rate of Gas Calculator .mfr-calculator-container { font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif; max-width: 800px; margin: 0 auto; padding: 20px; background-color: #f9fbfd; border: 1px solid #e1e4e8; border-radius: 8px; } .mfr-header { text-align: center; margin-bottom: 30px; color: #2c3e50; } .mfr-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 20px; } @media (max-width: 600px) { .mfr-grid { grid-template-columns: 1fr; } } .mfr-input-group { margin-bottom: 15px; } .mfr-label { display: block; margin-bottom: 5px; font-weight: 600; color: #4a5568; font-size: 0.95em; } .mfr-input { width: 100%; padding: 10px; border: 1px solid #cbd5e0; border-radius: 4px; font-size: 16px; box-sizing: border-box; } .mfr-select { width: 100%; padding: 10px; border: 1px solid #cbd5e0; border-radius: 4px; font-size: 16px; background-color: white; box-sizing: border-box; } .mfr-button { background-color: #007bff; color: white; border: none; 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margin-top: 20px; } .mfr-article ul { padding-left: 20px; } .mfr-article code { background-color: #f1f5f9; padding: 2px 5px; border-radius: 3px; font-family: monospace; } .hidden { display: none; } function toggleInputs() { var mode = document.getElementById("calculationMode").value; var velocitySection = document.getElementById("velocitySection"); var volumeSection = document.getElementById("volumeSection"); if (mode === "velocity") { velocitySection.style.display = "block"; volumeSection.style.display = "none"; } else { velocitySection.style.display = "none"; volumeSection.style.display = "block"; } } function calculateMassFlow() { var mode = document.getElementById("calculationMode").value; var density = parseFloat(document.getElementById("gasDensity").value); var resultBox = document.getElementById("resultBox"); // Validation if (isNaN(density) || density <= 0) { alert("Please enter a valid Gas Density greater than 0."); return; } var massFlowKgPerSec = 0; var areaM2 = 0; var velocity = 0; var volFlow = 0; if (mode === "velocity") { var velInput = parseFloat(document.getElementById("velocity").value); var diamInput = parseFloat(document.getElementById("diameter").value); var diamUnit = document.getElementById("diameterUnit").value; if (isNaN(velInput) || isNaN(diamInput) || velInput < 0 || diamInput <= 0) { alert("Please enter valid positive numbers for Velocity and Diameter."); return; } // Convert diameter to meters var diameterM = 0; if (diamUnit === "mm") { diameterM = diamInput / 1000; } else if (diamUnit === "cm") { diameterM = diamInput / 100; } else if (diamUnit === "m") { diameterM = diamInput; } else if (diamUnit === "inch") { diameterM = diamInput * 0.0254; } // Calculate Area (A = pi * r^2 = pi * (d/2)^2) areaM2 = Math.PI * Math.pow((diameterM / 2), 2); velocity = velInput; // Formula: m_dot = rho * v * A massFlowKgPerSec = density * velocity * areaM2; } else { var volFlowInput = parseFloat(document.getElementById("volFlowRate").value); var volUnit = document.getElementById("volFlowUnit").value; if (isNaN(volFlowInput) || volFlowInput < 0) { alert("Please enter a valid Volumetric Flow Rate."); return; } // Convert to m3/s var volFlowM3s = 0; if (volUnit === "m3s") { volFlowM3s = volFlowInput; } else if (volUnit === "m3h") { volFlowM3s = volFlowInput / 3600; } else if (volUnit === "cfm") { volFlowM3s = volFlowInput * 0.000471947; } else if (volUnit === "lpm") { volFlowM3s = volFlowInput / 60000; } // Formula: m_dot = rho * Q massFlowKgPerSec = density * volFlowM3s; } // Output Conversions var kgPerHour = massFlowKgPerSec * 3600; var lbPerSec = massFlowKgPerSec * 2.20462; var lbPerHour = kgPerHour * 2.20462; // Display Results document.getElementById("mainResult").innerHTML = massFlowKgPerSec.toFixed(4) + " kg/s"; document.getElementById("resKgH").innerHTML = "" + kgPerHour.toFixed(2) + " kg/h"; document.getElementById("resLbS").innerHTML = "" + lbPerSec.toFixed(4) + " lb/s"; document.getElementById("resLbH").innerHTML = "" + lbPerHour.toFixed(2) + " lb/h"; resultBox.style.display = "block"; }

Mass Flow Rate Calculator

Calculate the mass flow rate of gas based on density, velocity, or volumetric flow.

Using Velocity & Pipe Diameter Using Volumetric Flow Rate
Air at STP is approx 1.225 kg/m³
mm cm m inch
m³/s m³/h CFM L/min
Calculated Mass Flow Rate:
0.0000 kg/s
0.00 kg/h
0.00 lb/h
0.00 lb/s

How to Calculate Mass Flow Rate of Gas

Mass flow rate is a critical parameter in fluid dynamics, engineering, and thermodynamics. Unlike volumetric flow rate, which changes with pressure and temperature, mass flow rate measures the exact amount of matter (mass) passing through a specific point over time. It is denoted by the symbol ṁ (m-dot).

The Mass Flow Rate Formula

The fundamental equation to calculate the mass flow rate of a gas flowing through a pipe involves the gas density, the flow velocity, and the cross-sectional area of the pipe.

Formula: ṁ = ρ · V · A

  • ṁ = Mass Flow Rate (kg/s)
  • ρ (rho) = Density of the gas (kg/m³)
  • V = Velocity of the gas (m/s)
  • A = Cross-sectional Area of the pipe (m²)

Alternative Method: Using Volumetric Flow

If you already know the volumetric flow rate (Q), the calculation becomes simpler:

Formula: ṁ = ρ · Q

  • Q = Volumetric Flow Rate (m³/s)

Example Calculation

Let's say we have air flowing through a pipe. We want to find the mass flow rate with the following data:

  • Gas: Air (Density ≈ 1.225 kg/m³ at STP)
  • Pipe Diameter: 100 mm (0.1 meters)
  • Velocity: 5 m/s

Step 1: Calculate Area
Radius = 0.1m / 2 = 0.05m
Area = π · (0.05)² ≈ 0.00785 m²

Step 2: Calculate Mass Flow
ṁ = 1.225 kg/m³ · 5 m/s · 0.00785 m²
Result: ṁ ≈ 0.048 kg/s

Why is Mass Flow Rate Important?

In gas systems, volume changes drastically with temperature and pressure (Ideal Gas Law). Therefore, relying on volumetric flow (CFM or m³/h) can be misleading in combustion engines, chemical reactions, or HVAC systems. Mass flow rate remains constant regardless of expansion or compression along the pipe, adhering to the principle of conservation of mass.

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