Calculate Flow Rate from Pressure Difference

Flow Rate Calculator (Orifice Plate)

Understanding Flow Rate Calculation

The flow rate through an orifice plate is a crucial parameter in fluid dynamics, used in various industrial and scientific applications to measure or control the volume of fluid passing through a system per unit time. This calculator helps determine the volumetric flow rate (Q) based on fundamental fluid mechanics principles.

The formula used is derived from Bernoulli's principle and accounts for the contraction of the fluid stream (vena contracta) as it passes through the orifice. The basic relationship for flow through an orifice is:

Q = Cd * A * sqrt((2 * ΔP) / ρ)

Where:

• Q is the volumetric flow rate (in m³/s).
• Cd is the coefficient of discharge, a dimensionless factor that accounts for energy losses due to friction and the vena contracta. It typically ranges from 0.6 to 0.95 depending on the orifice geometry and flow conditions.
• A is the area of the orifice (in m²).
• ΔP is the pressure difference across the orifice (in Pascals, Pa).
• ρ (rho) is the density of the fluid (in kg/m³).

By inputting the pressure difference, orifice coefficient, orifice area, and fluid density, this calculator provides an estimated flow rate, assuming the fluid is incompressible and steady-state flow conditions.

Example Calculation:

Let's consider a scenario where:

• The pressure difference (ΔP) is 5000 Pascals.
• The orifice discharge coefficient (Cd) is 0.62.
• The orifice area (A) is 0.01 m².
• The fluid density (ρ) is 998 kg/m³ (for water at room temperature).

Using the formula: Q = 0.62 * 0.01 m² * sqrt((2 * 5000 Pa) / 998 kg/m³) Q = 0.0062 m² * sqrt(10000 Pa / 998 kg/m³) Q = 0.0062 m² * sqrt(10.02 m²/s²) Q = 0.0062 m² * 3.165 m/s Q ≈ 0.1962 m³/s

This means approximately 0.1962 cubic meters of fluid pass through the orifice per second under these conditions.