Volume Flow Rate Equation Pressure

Volume Flow Rate Formula:

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

Pressure P₁:

psi

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 Volume Flow Rate Equation using Pressure?

Definition: This calculator determines the fluid velocity and volumetric flow rate based on pressure difference, fluid density, and cross-sectional area.

Purpose: It helps engineers and technicians calculate flow rates in pipes and channels when pressure measurements are available.

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 (ft/s)
\( P_1, P_2 \) — Upstream and downstream pressures (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, and the second converts velocity to flow rate.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations are essential for system design, pump sizing, and process control in fluid systems.

4. Using the Calculator

Tips: Enter the pressure values (P₁ and P₂), fluid density (default 62.4 lb/ft³ for water), and cross-sectional area. All values must be > 0 except P₂ which can be 0.

5. Frequently Asked Questions (FAQ)

Q1: What does the 144 factor represent?
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's a typical density for water?
A: Fresh water at 60°F is 62.4 lb/ft³. Salt water is about 64 lb/ft³.

Q4: Can I use this for gases?
A: This simplified form works best for incompressible fluids like liquids. Gases require additional factors.

Q5: How do I measure pipe area?
A: For circular pipes: \( A = \pi \times (diameter/2)^2 \). Convert diameter to feet.