Flow Rate from Differential Pressure Calculator
Calculate the volumetric flow rate based on the pressure drop across an orifice plate, venturi meter, or flow nozzle using Bernoulli's principle.
Calculation Results:
Understanding Differential Pressure and Flow Rate
The relationship between differential pressure (ΔP) and flow rate (Q) is a fundamental concept in fluid mechanics, primarily derived from Bernoulli's Equation. When a fluid passes through a restriction (like an orifice plate or a venturi meter), its velocity increases, and its pressure decreases.
The Mathematical Formula
Q = Cd × A × √(2 × ΔP / ρ)
- Q: Volumetric Flow Rate (m³/s)
- Cd: Discharge Coefficient (accounts for energy losses and flow contraction)
- A: Cross-sectional area of the opening (m²)
- ΔP: Differential pressure across the restriction (Pa)
- ρ (rho): Density of the fluid (kg/m³)
Key Factors Affecting Results
Discharge Coefficient (Cd): This value varies depending on the type of device used. A sharp-edged orifice plate typically has a Cd of approximately 0.61, while a smooth Venturi tube can have a Cd as high as 0.98.
Fluid Density: Temperature and pressure affect fluid density. For liquid water at room temperature, 1000 kg/m³ is standard. For gases, the density must be calculated at the specific operating pressure and temperature.
Practical Example
Suppose you have an orifice plate with a diameter of 50mm (0.05m) installed in a water line. The differential pressure transmitter reads 5,000 Pascals (Pa). Using a discharge coefficient of 0.61:
- Area (A) = π × (0.025)² = 0.001963 m²
- Flow (Q) = 0.61 × 0.001963 × √(2 × 5000 / 1000)
- Q = 0.61 × 0.001963 × √10 ≈ 0.00378 m³/s
- Converted to Liters/min: 0.00378 × 60,000 ≈ 226.8 L/min