Pressure and Flow Rate Relationship Equation

Equations:

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

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 and Flow Rate Relationship?

Definition: These equations calculate fluid velocity and volumetric flow rate based on pressure differential, fluid density, and cross-sectional area.

Purpose: Essential for hydraulic system design, pipe sizing, and fluid dynamics analysis in engineering applications.

2. How Do the Equations Work?

The calculator uses two fundamental equations:

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

Where:

\( V \) — Fluid velocity (ft/s)
\( P_1 \) — Initial pressure (psi)
\( P_2 \) — Final pressure (psi)
\( \rho \) — Fluid density (lb/ft³)
\( Q \) — Volumetric flow rate (GPM)
\( A \) — Cross-sectional area (ft²)

Explanation: The first equation derives from Bernoulli's principle, converting pressure difference to velocity. The second converts velocity to flow rate.

3. Importance of These Calculations

Details: Proper calculations ensure efficient system design, prevent excessive pressure drops, and help select appropriate pump sizes.

4. Using the Calculator

Tips: Enter all pressure values in psi, density in lb/ft³ (water = 62.4), and area in square feet. Ensure P₁ > P₂ for valid results.

5. Frequently Asked Questions (FAQ)

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

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

Q3: What density should I use for water?
A: Pure water at 60°F has a density of 62.4 lb/ft³.

Q4: Can I use this for gases?
A: Only for incompressible fluids. Gases require compressible flow equations.

Q5: How does pipe diameter relate to area?
A: Area = π × (diameter/2)². Convert diameter from inches to feet first.