Flow Rate to Pressure Conversion Formula

Pressure and Flow Rate Formulas:

\[ P = \frac{V^2 \times \rho}{2 \times 144} \] \[ V = \frac{Q}{A \times 448.83} \]

Velocity (V):

Pressure (P):

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1. What is the Flow Rate to Pressure Conversion?

Definition: This calculator converts flow rate in gallons per minute (GPM) to pressure in pounds per square inch (psi) using fluid dynamics principles.

Purpose: It helps engineers and technicians determine the pressure generated by fluid flow in pipes and systems.

2. How Does the Calculator Work?

The calculator uses two formulas:

\[ P = \frac{V^2 \times \rho}{2 \times 144} \] \[ V = \frac{Q}{A \times 448.83} \]

Where:

\( P \) — Pressure (psi)
\( V \) — Velocity (ft/s)
\( \rho \) — Fluid density (lb/ft³)
\( Q \) — Flow rate (GPM)
\( A \) — Cross-sectional area (ft²)

Explanation: First converts flow rate to velocity, then calculates dynamic pressure based on velocity and fluid density.

3. Importance of Flow-Pressure Conversion

Details: Proper pressure calculation ensures system safety, pump sizing, and pipe strength requirements are met.

4. Using the Calculator

Tips: Enter flow rate in GPM, cross-sectional area in square feet, and fluid density (default 62.4 lb/ft³ for water). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the 448.83 factor used?
A: This converts GPM to ft³/s (1 GPM = 0.002228 ft³/s) and divides by area to get velocity.

Q2: What's the 144 factor for?
A: Converts lb/ft² to psi (1 psi = 144 lb/ft²).

Q3: What density should I use for other fluids?
A: Use 49.2 lb/ft³ for gasoline, 78.6 lb/ft³ for seawater, or specific density for your fluid.

Q4: Does this account for friction losses?
A: No, this calculates dynamic pressure only. For total system pressure, add static pressure and friction losses.

Q5: How do I find pipe cross-sectional area?
A: For circular pipes: \( A = \pi \times (D/2)^2 \) where D is diameter in feet.