How To Calculate Flow Rate From Pressure

Orifice Flow Equation:

\[ Q = C_d \times A \times \sqrt{\frac{2 \Delta P}{\rho}} \]

Discharge Coefficient (C_d):

unitless

Cross-sectional Area (A):

m²

Pressure Difference (ΔP):

Density (ρ):

kg/m³

Flow Rate (Q):

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1. What is the Orifice Flow Equation?

The orifice flow equation calculates the volumetric flow rate of a fluid through an orifice based on pressure difference, fluid density, orifice area, and discharge coefficient. It's widely used in fluid mechanics and engineering applications.

2. How Does the Calculator Work?

The calculator uses the orifice flow equation:

\[ Q = C_d \times A \times \sqrt{\frac{2 \Delta P}{\rho}} \]

Where:

\( Q \) — Volumetric flow rate (m³/s)
\( C_d \) — Discharge coefficient (unitless)
\( A \) — Cross-sectional area of orifice (m²)
\( \Delta P \) — Pressure difference across orifice (Pa)
\( \rho \) — Fluid density (kg/m³)

Explanation: The equation derives from Bernoulli's principle and conservation of energy, accounting for energy losses through the discharge coefficient.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing piping systems, sizing pumps, process control in chemical plants, and optimizing fluid transport in various engineering applications.

4. Using the Calculator

Tips: Enter discharge coefficient (typically 0.6-0.8 for sharp-edged orifices), cross-sectional area in square meters, pressure difference in Pascals, and fluid density in kg/m³. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical discharge coefficient value?
A: For sharp-edged orifices, C_d is typically 0.6-0.65. For rounded orifices, it can be 0.8-0.98 depending on geometry.

Q2: How accurate is this equation?
A: The equation provides good estimates for incompressible fluids with turbulent flow. Accuracy depends on proper C_d selection and flow conditions.

Q3: Can this be used for gases?
A: For gases at low pressure differences, it can be used. For compressible flows or high pressure ratios, modified equations are needed.

Q4: What affects the discharge coefficient?
A: Orifice geometry, Reynolds number, edge sharpness, and upstream/downstream conditions all influence C_d.

Q5: When is this equation not applicable?
A: Not suitable for highly viscous fluids, laminar flow, compressible flows with large pressure changes, or non-Newtonian fluids.