Pressure Flow Rate Equation

Flow Rate Formulas:

\[ V = \sqrt{\frac{2 \times (P_1 - P_2) \times 144}{\rho}} \] \[ Q = V \times A \times 448.83 \]

Initial Pressure (P₁):

psi

Final Pressure (P₂):

psi

Density (ρ):

lb/ft³

Area (A):

ft²

Velocity (V): ft/s

Flow Rate (Q): GPM

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1. What is the Pressure Flow Rate Equation?

Definition: This calculator determines the flow rate (in gallons per minute) through a pipe or orifice based on pressure difference and fluid density.

Purpose: It helps engineers and technicians calculate fluid flow rates in hydraulic systems, piping, and other fluid mechanics applications.

2. How Does the Calculator Work?

The calculator uses two formulas:

\[ V = \sqrt{\frac{2 \times (P_1 - P_2) \times 144}{\rho}} \] \[ Q = V \times A \times 448.83 \]

Where:

\( V \) — Velocity (feet per second)
\( P_1 \) — Initial pressure (psi)
\( P_2 \) — Final pressure (psi)
\( \rho \) — Fluid density (pounds per cubic foot)
\( Q \) — Flow rate (gallons per minute)
\( A \) — Cross-sectional area (square feet)

Explanation: The first equation calculates velocity from pressure difference, then the second converts this to volumetric flow rate.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations ensure proper system design, pump sizing, and process control in fluid systems.

4. Using the Calculator

Tips: Enter the pressure values (P₁ and P₂), fluid density (default 62.4 lb/ft³ for water), and cross-sectional area. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What does the 144 factor represent?
A: It converts psi to psf (pounds per square foot) since 1 psi = 144 psf.

Q2: Why is the flow rate multiplied by 448.83?
A: This converts cubic feet per second to gallons per minute (1 ft³/s = 448.83 GPM).

Q3: What's a typical density for water?
A: Pure water at 60°F is approximately 62.4 lb/ft³. This varies with temperature and impurities.

Q4: How do I calculate pipe cross-sectional area?
A: For circular pipes, \( A = \pi \times (D/2)^2 \) where D is diameter in feet.

Q5: Does this account for friction losses?
A: No, this is an ideal equation. For real-world applications, consider additional factors like pipe roughness and length.