Orifice Sizing Calculator – Accurate Flow Rate Calculation

The flow rate of a fluid passing through an orifice or nozzle can be determined using the following equation:

Fluid Flow Through an Orifice or Nozzle

$q=\frac{C_d\cdot A}{\sqrt{1-{\beta }^4}}\cdot \sqrt{2\cdot g_n\cdot h_L}$

Where:

• q = Flow rate
• Cd = Coefficient of discharge
• A = Cross-sectional area
• β = Diameter ratio (d₁/d₂)
• gₙ = Acceleration due to gravity
• hL = Head loss

Instead of using the coefficient of discharge (Cd), a more practical approach is to apply the flow coefficient (C), which is defined as:

Flow Coefficient Formula

$C=\frac{C_d}{\sqrt{1-{\beta }^4}}$

$q=C\cdot A\cdot \sqrt{2\cdot g_n\cdot h_L}$

Where:

• C = Flow coefficient
• Cd = Coefficient of discharge
• β = Diameter ratio (d₁/d₂)

By utilizing the flow coefficient, engineers and fluid mechanics professionals can achieve more accurate calculations for fluid dynamics, hydraulic systems, and nozzle flow efficiency.

The coefficient of discharge (Cd) for orifice flow can be determined using the Reader-Harris/Gallagher (1998) equation as specified in ISO 5167:

Coefficient of Discharge Formula

Where:

• β = Diameter ratio (d₁/d₂)
• R_eD = Reynolds number based on the larger diameter
• d₁ = Smaller internal diameter
• d₂ = Larger internal diameter

Tap Configurations and Coefficient Adjustments

The values of L₁ and L₂ depend on the type of pressure tap used:

• Corner taps: L₁ = L₂ = 0
• D and D/2 taps: L₁ = 1, L₂ = 0.47
• 1-inch taps: L₁ = L₂ = 0.0254/d₁ (for d₁ in meters)

By applying these fluid flow equations, engineers can enhance flow measurement accuracy in hydraulic systems, pipelines, and industrial fluid applications.