Flow Rate Calculation Using Pressure

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

Fluid Density (ρ):

lb/ft³

Cross-Sectional Area (A):

ft²

Velocity (V): ft/s

Flow Rate (Q): GPM

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1. What is Flow Rate Calculation Using Pressure?

Definition: This calculator determines the flow rate in gallons per minute (GPM) based on pressure difference, fluid density, and pipe cross-sectional area.

Purpose: It helps engineers and technicians estimate fluid flow rates in pipes and channels using pressure measurements.

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:

\( V \) — Fluid 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 velocity to flow rate.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate estimation is crucial for system design, pump sizing, and process control in hydraulic systems.

4. Using the Calculator

Tips: Enter both pressures (P₁ > P₂), fluid density (default 62.4 lb/ft³ for water), and pipe area. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the 144 factor in the equation?
A: This converts psi (lb/in²) to lb/ft² (1 ft² = 144 in²).

Q2: Why 448.83 in the flow rate equation?
A: This converts ft³/s to GPM (1 ft³/s = 448.83 GPM).

Q3: What's a typical fluid density?
A: Water is 62.4 lb/ft³ at 60°F. Oil is about 55 lb/ft³, while mercury is 849 lb/ft³.

Q4: How do I find pipe cross-sectional area?
A: For circular pipes: \( A = \pi \times (diameter/2)^2 \) (convert diameter to feet).

Q5: Does this work for compressible fluids?
A: No, this simplified equation is for incompressible fluids only.