Relation Between Pressure and Flow Rate

Flow Rate Formulas:

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

Upstream Pressure (P₁):

psi

Downstream 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 the Relation Between Pressure and Flow Rate?

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

Purpose: It helps engineers and technicians analyze fluid systems, design piping networks, and understand flow characteristics.

2. How Does the Calculator Work?

The calculator uses these 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)
\( P_1 \) — Upstream pressure (psi)
\( P_2 \) — Downstream 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 (converted to lb/ft²) and density. The second converts velocity to flow rate in gallons per minute.

3. Importance of Pressure-Flow Relationship

Details: Understanding this relationship is crucial for designing efficient fluid systems, sizing pumps and pipes, and troubleshooting flow issues.

4. Using the Calculator

Tips: Enter upstream and downstream pressures (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: This converts psi to lb/ft² (1 psi = 144 lb/ft²).

Q2: Why 448.83 in the flow rate calculation?
A: This converts ft³/s to 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, use their specific density.

Q4: How do I find cross-sectional area?
A: For circular pipes, A = π × (diameter/2)². Convert diameter to feet.

Q5: Does this account for friction losses?
A: No, this is ideal flow. For real systems, consider additional pressure drop calculations.