Daniel Orifice Flow Calculator

Daniel Orifice Equation:

\[ Q = C A \sqrt{\frac{2 \Delta P}{\rho (1 - \beta^4)}} \]

Discharge Coefficient (C):

dimensionless

Orifice Area (A):

m²

Pressure Difference (ΔP):

Fluid Density (ρ):

kg/m³

Diameter Ratio (β):

dimensionless

Volumetric Flow Rate (Q):

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1. What is the Daniel Orifice Equation?

The Daniel orifice equation calculates the volumetric flow rate through an orifice plate based on the pressure difference across the orifice, fluid properties, and geometric characteristics. It's widely used in fluid mechanics and engineering applications.

2. How Does the Calculator Work?

The calculator uses the Daniel orifice equation:

\[ Q = C A \sqrt{\frac{2 \Delta P}{\rho (1 - \beta^4)}} \]

Where:

\( Q \) — Volumetric flow rate (m³/s)
\( C \) — Discharge coefficient (dimensionless)
\( A \) — Orifice area (m²)
\( \Delta P \) — Pressure difference across orifice (Pa)
\( \rho \) — Fluid density (kg/m³)
\( \beta \) — Diameter ratio (orifice diameter/pipe diameter)

Explanation: The equation accounts for energy losses through the orifice and the contraction of the flow stream.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate measurement is essential for process control, system design, and performance evaluation in piping systems, HVAC, and industrial processes.

4. Using the Calculator

Tips: Enter all parameters in consistent units. The diameter ratio (β) must be between 0 and 1. Typical discharge coefficients range from 0.6 to 0.9 depending on orifice geometry.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical discharge coefficient value?
A: For sharp-edged orifices, C is typically about 0.61. For rounded orifices, it can be higher (0.7-0.9).

Q2: What are the limitations of this equation?
A: The equation assumes steady, incompressible flow and a homogeneous fluid. It works best for turbulent flow conditions.

Q3: How does β affect the flow rate?
A: As β increases (approaches 1), the denominator term (1-β⁴) becomes very small, significantly increasing the flow rate for a given ΔP.

Q4: When is this equation not applicable?
A: Not suitable for compressible flows, very viscous fluids, or when the orifice is not perpendicular to the flow.

Q5: How accurate is this calculation?
A: With proper coefficient selection, accuracy within 1-2% is possible for standard orifice installations.