Volumetric Flow Rate Equation with Pressure

Volumetric Flow Rate Formula:

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

Inlet Pressure (P₁):

psi

Outlet Pressure (P₂):

psi

Fluid Density (ρ):

lb/ft³

Cross-Sectional Area (A):

ft²

Velocity (V): ft/s

Volumetric Flow Rate (Q): GPM

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1. What is Volumetric Flow Rate with Pressure?

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

Purpose: It's essential for engineers and technicians working with fluid systems to design and analyze piping, valves, and flow systems.

2. How Does the Calculator Work?

The calculator uses two key equations:

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

Where:

\( V \) — Flow 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 and density. The second converts this to volumetric flow rate in gallons per minute.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations ensure proper system design, prevent cavitation, optimize pump sizing, and maintain efficient operation.

4. Using the Calculator

Tips: Enter both pressures in psi, fluid density (default 62.4 lb/ft³ for water), and cross-sectional area in square feet. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why multiply pressure by 144 in the equation?
A: This converts psi (lb/in²) to lb/ft² (1 ft² = 144 in²) for consistent units.

Q2: What's the 448.83 conversion factor for?
A: It converts ft³/s to gallons per minute (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. Density varies with temperature and impurities.

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

Q5: Does this account for friction losses?
A: No, this is an ideal equation. For real systems, consider additional factors like pipe roughness and length.