Pressure to Flow Rate Calculator

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 a Pressure to Flow Rate Calculator?

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

Purpose: It helps engineers, plumbers, and fluid system designers understand the relationship between pressure and flow in hydraulic systems.

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 (feet per second)
\( P_1 \) — Upstream pressure (psi)
\( P_2 \) — Downstream pressure (psi)
\( \rho \) — Fluid density (pounds per cubic foot)
\( Q \) — Flow rate (gallons per minute)
\( A \) — Cross-sectional area (square feet)

Explanation: The first equation calculates velocity from pressure difference using Bernoulli's principle. The second converts velocity to flow rate.

3. Importance of Pressure-Flow Calculations

Details: Accurate flow rate estimation ensures proper system design, prevents pipe damage from excessive velocity, and helps select appropriate pump sizes.

4. Using the Calculator

Tips: Enter the pressure difference (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 (lb/in²) to lb/ft² (since 1 ft² = 144 in²).

Q2: Why 448.83 in the flow rate formula?
A: This 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 changes with temperature and impurities.

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

Q5: Does this account for friction losses?
A: No, this is ideal flow. For real-world applications, consider additional factors like pipe roughness.