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How to calculate mass flow rate of air in an engine?

Published in Engine Airflow 3 mins read

The mass flow rate of air in an engine can be calculated using the formula: Mass Flow Rate (ṁ) = V × A × ρ, where V is velocity, A is area, and ρ is density.

To determine the mass flow rate of air entering an engine, you need to know several key parameters:

Understanding the Formula

  • ṁ (Mass Flow Rate): This represents the mass of air passing through a given point per unit of time (e.g., kg/s).
  • V (Velocity): This is the average speed of the air moving through the intake passage (e.g., m/s).
  • A (Area): This is the cross-sectional area of the intake passage where the air is flowing (e.g., m2).
  • ρ (Density): This is the density of the air at the intake conditions (e.g., kg/m3).

Steps for Calculation

  1. Determine the Intake Area (A):

    • The intake area is the cross-sectional area of the air intake passage. For a circular intake, this is calculated as A = πr2, where r is the radius of the intake.
    • If the intake has a different shape, you'll need to use the appropriate formula to calculate the area.

  2. Measure or Estimate Air Velocity (V):

    • This is the trickiest parameter to determine accurately.
    • You can use an anemometer placed in the intake stream to measure the air velocity directly.
    • Computational Fluid Dynamics (CFD) simulations can also provide estimates of air velocity profiles within the intake.
    • Alternatively, you can use theoretical calculations based on engine speed (RPM), volumetric efficiency, and intake valve timing to estimate the average air velocity. However, these calculations will likely require simplifying assumptions.

  3. Determine Air Density (ρ):

    • Air density depends on temperature and pressure.

    • You can use a weather station or online resource to find the ambient temperature and pressure.

    • Use the ideal gas law (ρ = P / (R * T)) to calculate air density, where:

      • P is the absolute pressure (Pascals).
      • R is the specific gas constant for air (approximately 287 J/(kg·K)).
      • T is the absolute temperature (Kelvin).

  4. Calculate Mass Flow Rate (ṁ):

    • Once you have V, A, and ρ, simply plug the values into the formula: ṁ = V × A × ρ.
    • The result will be in kg/s if you use SI units (m/s, m2, kg/m3).

Example

Let's say we have the following values:

  • V (Velocity): 50 m/s
  • A (Area): 0.005 m2
  • ρ (Density): 1.2 kg/m3

Then, the mass flow rate would be:

ṁ = 50 m/s × 0.005 m2 × 1.2 kg/m3 = 0.3 kg/s

Practical Considerations

  • Units: Ensure that all units are consistent (SI units are recommended) before performing the calculation.
  • Assumptions: Be aware of the assumptions made in estimating air velocity and density. These assumptions can affect the accuracy of the result.
  • Pulsating Flow: Airflow in an engine intake is pulsating, not steady. The calculated mass flow rate represents an average value.
  • Temperature Changes: Account for any temperature changes of the air as it enters the engine.

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