How do you calculate mass flow rate from pressure difference?

Calculating mass flow rate from pressure difference typically involves using a differential pressure flow meter and considering fluid properties. Often, the volume flow rate is first determined from the pressure difference (ΔP) and then multiplied by the fluid density (ρ) at the measured temperature (T) and pressure (P) to obtain the mass flow rate.

Here's a breakdown of the process:

Differential Pressure Flow Meters

Differential pressure flow meters, such as orifice plates, Venturi meters, and flow nozzles, are commonly used to measure flow rates based on the pressure drop created by constricting the flow. The pressure difference is related to the flow rate.

Steps to Calculate Mass Flow Rate

1. Measure the Pressure Difference (ΔP): Use a differential pressure sensor to measure the pressure drop across the flow meter.

2. Determine Volume Flow Rate (Q): Use the following general formula to determine the volume flow rate based on the pressure difference. This formula varies slightly depending on the type of flow meter being used (e.g., orifice plate, Venturi meter).

   $$Q = C \cdot A \cdot \sqrt{\frac{2 \Delta P}{\rho}}$$

   Where:

   • Q = Volume flow rate
   • C = Discharge coefficient (accounts for losses and geometry)
   • A = Cross-sectional area of the restriction (e.g., orifice area)
   • ΔP = Pressure difference
   • ρ = Fluid density

3. Determine Fluid Density (ρ): Measure the temperature (T) and pressure (P) of the fluid and use appropriate equations of state or look-up tables to determine the fluid density at those conditions. It is critical to use the fluid density at the measured temperature and pressure to ensure accuracy, per the reference.

4. Calculate Mass Flow Rate (ṁ): Multiply the volume flow rate by the fluid density to obtain the mass flow rate:

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

   Where:

   • ṁ = Mass flow rate
   • Q = Volume flow rate
   • ρ = Fluid density

Example

Let's say you have a volume flow rate of 0.01 m³/s and the fluid density, at the measured temperature and pressure, is 1000 kg/m³. The mass flow rate would be:

$$\dot{m} = 0.01 \, \text{m}^3/\text{s} \cdot 1000 \, \text{kg}/\text{m}^3 = 10 \, \text{kg}/\text{s}$$

Practical Considerations

• Discharge Coefficient (C): Accurately determining the discharge coefficient is crucial. This often requires calibration or consulting established correlations for the specific flow meter geometry.
• Fluid Properties: Ensure accurate fluid density data at the operating temperature and pressure. Use appropriate equations of state or reliable data sources.
• Flow Meter Selection: Choose the appropriate type of differential pressure flow meter based on the application, considering factors such as pressure drop, accuracy requirements, and fluid compatibility.