How to Calculate Mass Flow Rate of Dry Air

Calculate the mass flow rate ($\dot{m}$) based on volumetric flow, temperature, and pressure using the Ideal Gas Law.

Unit: Cubic meters per second ($m^3/s$)

Unit: Degrees Celsius ($^\circ C$)

Unit: Kilopascals (kPa). Standard sea level is ~101.325 kPa.

Calculation Results

Calculated Air Density ($\rho$): –

Mass Flow Rate ($\dot{m}$): –

Mass Flow Rate (Hourly): –

Please enter valid numerical values for all fields. Temperature must be above -273.15°C.

How to Calculate Mass Flow Rate of Dry Air

Calculating the mass flow rate of dry air is a fundamental task in thermodynamics, HVAC engineering, and aerodynamics. While volumetric flow rate tells you how much space the air occupies as it moves, the mass flow rate tells you the actual amount of matter (mass) moving through a system per unit of time.

This distinction is critical because air is compressible; its volume changes significantly with temperature and pressure, but its mass remains constant. Engines, compressors, and cooling systems rely on mass flow calculations for efficiency and performance.

The Mass Flow Rate Formula

The general formula for mass flow rate ($\dot{m}$) relates air density ($\rho$) and volumetric flow rate ($Q$):

$\dot{m} = \rho \times Q$

• $\dot{m}$ = Mass Flow Rate ($kg/s$)
• $\rho$ = Air Density ($kg/m^3$)
• $Q$ = Volumetric Flow Rate ($m^3/s$)

Calculating Air Density Using the Ideal Gas Law

Since air density isn't usually measured directly, it is calculated using the Ideal Gas Law based on temperature and pressure. For dry air, the formula is:

$\rho = \frac{P}{R_{specific} \times T}$

Where:

• $P$ = Absolute Pressure in Pascals ($Pa$). (Note: $1 kPa = 1000 Pa$)
• $R_{specific}$ = Specific Gas Constant for dry air, approximately 287.058 $J/(kg\cdot K)$.
• $T$ = Absolute Temperature in Kelvin ($K$). ($K = ^\circ C + 273.15$)

Example Calculation

Let's assume you have an HVAC duct moving air under the following conditions:

• Volumetric Flow ($Q$): 2.5 $m^3/s$
• Temperature: 25 $^\circ C$
• Pressure: 101.325 $kPa$ (Standard Sea Level)

Step 1: Convert Temperature to Kelvin
$T = 25 + 273.15 = 298.15 K$

Step 2: Convert Pressure to Pascals
$P = 101.325 \times 1000 = 101,325 Pa$

Step 3: Calculate Density ($\rho$)
$\rho = 101,325 / (287.058 \times 298.15)$
$\rho \approx 101,325 / 85,586.34 \approx 1.184 kg/m^3$

Step 4: Calculate Mass Flow Rate ($\dot{m}$)
$\dot{m} = 1.184 kg/m^3 \times 2.5 m^3/s$
$\dot{m} \approx 2.96 kg/s$

Why Use Mass Flow vs. Volumetric Flow?

Volumetric flow (CFM or $m^3/s$) can be misleading in applications involving heat transfer or combustion. For example, hot air is less dense than cold air. A fan moving 100 $m^3/s$ of hot air moves significantly less oxygen (mass) than a fan moving 100 $m^3/s$ of cold air. Engineers calculate mass flow rate to ensure precise air-fuel ratios in combustion engines and accurate thermal load calculations in HVAC systems.

function calculateMassFlow() { // 1. Get DOM elements var volFlowInput = document.getElementById("volFlow"); var tempInput = document.getElementById("airTemp"); var pressInput = document.getElementById("airPress"); var resultContainer = document.getElementById("resultContainer"); var errorMsg = document.getElementById("errorMsg"); var resDensity = document.getElementById("resDensity"); var resMassFlowSec = document.getElementById("resMassFlowSec"); var resMassFlowHour = document.getElementById("resMassFlowHour"); // 2. Parse values var Q = parseFloat(volFlowInput.value); // m^3/s var Tc = parseFloat(tempInput.value); // Celsius var P_kpa = parseFloat(pressInput.value); // kPa // 3. Validation if (isNaN(Q) || isNaN(Tc) || isNaN(P_kpa)) { errorMsg.style.display = "block"; resultContainer.style.display = "none"; return; } // Absolute zero check if (Tc <= -273.15) { errorMsg.innerHTML = "Temperature cannot be below Absolute Zero (-273.15°C)."; errorMsg.style.display = "block"; resultContainer.style.display = "none"; return; } errorMsg.style.display = "none"; // 4. Constants and Conversions var R_specific = 287.058; // J/(kg*K) specific gas constant for dry air // Convert Temperature to Kelvin var Tk = Tc + 273.15; // Convert Pressure to Pascals (from kPa) var Pa = P_kpa * 1000; // 5. Calculate Density (Ideal Gas Law: rho = P / (R * T)) var rho = Pa / (R_specific * Tk); // 6. Calculate Mass Flow Rate (m_dot = rho * Q) var m_dot = rho * Q; // Calculate Mass Flow per Hour var m_dot_hour = m_dot * 3600; // 7. Display Results // Show density with 3 decimals resDensity.innerHTML = rho.toFixed(3) + " kg/m³"; // Show Mass Flow Rate with 3 decimals resMassFlowSec.innerHTML = m_dot.toFixed(3) + " kg/s"; // Show Hourly Flow resMassFlowHour.innerHTML = m_dot_hour.toFixed(1) + " kg/h"; // Make results visible resultContainer.style.display = "block"; }