Volumetric Flow Rate from Pressure Calculator
How to Calculate Flow Rate from Pressure
In fluid dynamics, the relationship between pressure drop and volumetric flow rate is foundational for engineering and piping design. When a fluid passes through a restriction (like an orifice plate, nozzle, or venturi meter), its velocity increases and its pressure decreases. This phenomenon is described by Bernoulli's Principle.
Where:
- Q: Volumetric Flow Rate (m³/s)
- Cd: Discharge Coefficient (dimensionless, typically 0.6 to 0.98)
- A: Cross-sectional area of the opening (m²)
- ΔP: Pressure difference across the restriction (Pa)
- ρ (rho): Density of the fluid (kg/m³)
Understanding the Variables
Pressure Drop (ΔP): This is the difference in pressure between the upstream point and the point of restriction. The higher the pressure difference, the faster the fluid is pushed through the opening.
Discharge Coefficient (Cd): No system is perfectly efficient. Cd accounts for friction losses and the contraction of the fluid stream (vena contracta). For a standard sharp-edged orifice, 0.61 is a common value.
Fluid Density: Heavier fluids (like oil) require more pressure to move at the same rate as lighter fluids (like water or air).
Example Calculation
Suppose you have water (density 1000 kg/m³) flowing through a 50mm diameter orifice with a pressure drop of 5,000 Pascals and a discharge coefficient of 0.61.
- Convert diameter to meters: 50mm = 0.05m.
- Calculate Area: A = π × (0.05 / 2)² = 0.001963 m².
- Apply Formula: Q = 0.61 × 0.001963 × √(2 × 5000 / 1000).
- Q = 0.61 × 0.001963 × √10 = 0.61 × 0.001963 × 3.162.
- Result: Q ≈ 0.00378 m³/s (or approximately 227 Liters per minute).