Flow Rate Through an Orifice

Flow Rate Formula:

\[ Q = C_d \times A \times \sqrt{\frac{2 \times \Delta P}{\rho}} \times 448.83 \]

Discharge Coefficient (C_d):

Orifice Area (A):

ft²

Pressure Difference (ΔP):

psi

Fluid Density (ρ):

lb/ft³

Flow Rate (Q): GPM

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1. What is Flow Rate Through an Orifice?

Definition: This calculator determines the volumetric flow rate of a fluid through an orifice based on the pressure difference and fluid properties.

Purpose: It's essential for engineers and technicians designing fluid systems, piping networks, and hydraulic applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = C_d \times A \times \sqrt{\frac{2 \times \Delta P}{\rho}} \times 448.83 \]

Where:

\( Q \) — Flow rate (gallons per minute, GPM)
\( C_d \) — Discharge coefficient (dimensionless, typically 0.62 for sharp-edged orifices)
\( A \) — Cross-sectional area of the orifice (square feet)
\( \Delta P \) — Pressure difference across the orifice (psi)
\( \rho \) — Fluid density (pounds per cubic foot)

Explanation: The formula calculates the theoretical flow rate through an orifice, accounting for fluid properties and the orifice characteristics.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations are critical for system design, pump sizing, process control, and ensuring proper operation of fluid systems.

4. Using the Calculator

Tips: Enter the discharge coefficient (default 0.62), orifice area in ft², pressure difference in psi, and fluid density in lb/ft³ (default 62.4 for water). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the discharge coefficient (C_d)?
A: It's a dimensionless number that accounts for energy losses and flow contraction through the orifice. Typical values range from 0.6 to 0.9.

Q2: How do I convert orifice diameter to area?
A: For circular orifices, \( A = \pi \times (d/2)^2 \), where d is diameter in feet.

Q3: What's the 448.83 constant for?
A: This converts the result from cubic feet per second to gallons per minute (GPM).

Q4: What density should I use for other fluids?
A: For oils use ~55 lb/ft³, for gasoline ~46 lb/ft³. Check material safety data sheets for exact values.

Q5: Does this work for compressible fluids like gases?
A: No, this formula is for incompressible fluids only. Different equations are needed for gases.