Mass Flow Rate Calculator
Calculate flow rate based on differential pressure across an orifice.
Millimeters (mm)
Millimeters (mm)
Pascals (Pa)
kg/m³
Dimensionless (Typically 0.60 – 0.62)
Mass Flow Rate:
– kg/s
Hourly Flow Rate:
– kg/hr
Beta Ratio (β):
–
Velocity of Approach (E):
–
Understanding Mass Flow Rate via Differential Pressure
In fluid dynamics and industrial engineering, calculating the mass flow rate ($\dot{m}$) is crucial for process control, custody transfer, and efficiency monitoring. One of the most common methods to measure flow is by creating a constriction in the pipe (like an orifice plate, flow nozzle, or Venturi tube) and measuring the resulting pressure drop.
This calculator utilizes the standard incompressible flow equation derived from Bernoulli's principle. When a fluid flows through a constriction, its velocity increases while its pressure decreases. This difference in pressure ($\Delta P$) is directly proportional to the square of the flow rate.
The Calculation Formula
The mass flow rate is calculated using the following physics equation for orifice plates:
Qm = Cd × E × At × √(2 × ρ × ΔP)
Where:
- Qm ($\dot{m}$): Mass Flow Rate (kg/s)
- Cd: Discharge Coefficient (accounts for energy losses and flow profile, typically ~0.61 for orifice plates)
- At: Throat Area of the orifice (m²)
- E: Velocity of Approach Factor, calculated as $1 / \sqrt{1 – \beta^4}$
- β (Beta): Ratio of orifice diameter to pipe diameter ($d/D$)
- ρ (rho): Fluid Density (kg/m³)
- ΔP: Differential Pressure measured across the device (Pascals)
Key Input Parameters
To ensure accuracy in your calculation, precise inputs are required:
- Pipe & Orifice Diameter: These determine the "Beta Ratio". A Beta ratio between 0.2 and 0.75 is standard. If the orifice is too large (approaching pipe size), the differential pressure becomes too small to measure accurately.
- Differential Pressure: This is usually measured by a DP transmitter. Ensure units are converted to Pascals (Pa). Note: 1 bar = 100,000 Pa; 1 psi ≈ 6,895 Pa.
- Fluid Density: Density changes with temperature and pressure. For water at room temperature, it is approximately 998 kg/m³. For gases, density must be calculated at the specific line pressure and temperature.
Applications
This calculation is standard in various industries including:
- Oil & Gas: Measuring crude oil or natural gas flow in pipelines.
- Chemical Processing: Dosing reactants into mixing tanks.
- HVAC: Monitoring water flow in chiller systems.
- Water Treatment: Controlling filtration rates.