Flow Rate and Pressure Relationship Formula

Flow Rate and Pressure 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 Flow Rate and Pressure Relationship Formula?

Definition: These formulas calculate fluid velocity and volumetric flow rate based on pressure difference and fluid density.

Purpose: Used in fluid dynamics to determine flow characteristics in pipes, valves, and other hydraulic systems.

2. How Do the Formulas 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 formula calculates velocity from pressure difference, and the second converts this to volumetric flow rate.

3. Importance of These Calculations

Details: Accurate flow rate calculations are essential for designing piping systems, selecting pumps, and ensuring proper system operation.

4. Using the Calculator

Tips: Enter the pressure values (psi), fluid density (default 62.4 lb/ft³ for water), and cross-sectional area (ft²). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a 144 in the velocity formula?
A: This converts psi (lb/in²) to lb/ft² (1 ft² = 144 in²).

Q2: What's the 448.83 conversion factor for?
A: It converts ft³/s to gallons per minute (1 ft³/s = 448.83 GPM).

Q3: What density should I use for other fluids?
A: Use 62.4 for water, 49.2 for gasoline, or look up specific densities for your fluid.

Q4: Does this account for friction losses?
A: No, this is theoretical maximum velocity. Actual flow will be less due to friction.

Q5: When would P₂ be greater than P₁?
A: This would indicate reverse flow, which the calculator doesn't handle.