Volumetric Flow Rate from Pressure

Flow Rate Formulas:

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

Inlet Pressure (P₁):

psi

Outlet 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 Volumetric Flow Rate from Pressure?

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

Purpose: It's essential for engineers and technicians designing fluid systems, pipelines, or hydraulic equipment.

2. How Does the Calculator Work?

The calculator uses two fundamental formulas:

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

Where:

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

Explanation: The first equation calculates velocity from pressure difference, then the second converts velocity to flow rate using the pipe area.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations ensure proper system design, prevent pipe overpressure, and help select appropriate pump sizes.

4. Using the Calculator

Tips: Enter pressure values (P₁ > 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's the 144 factor in the equation?
A: It converts psi to lb/ft² (1 psi = 144 lb/ft²) for consistent units in the calculation.

Q2: Why is there a 448.83 conversion factor?
A: This converts ft³/s to gallons per minute (GPM) - 1 ft³/s = 448.83 GPM.

Q3: What's a typical fluid density for water?
A: Pure water at 60°F is 62.4 lb/ft³. For other fluids, consult density tables.

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

Q5: Does this work for compressible fluids like air?
A: No, this simplified formula is for incompressible fluids only. Compressible flow requires more complex calculations.