Convert Pressure to Volumetric Flow Rate

Flow Velocity and Volumetric Flow Rate Formulas:

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

Initial Pressure (P₁):

psi

Final Pressure (P₂):

psi

Fluid Density (ρ):

lb/ft³

Cross-sectional Area (A):

ft²

Flow Velocity (V): ft/s

Volumetric Flow Rate (Q): GPM

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1. What is Pressure to Flow Rate Conversion?

Definition: This calculator converts pressure difference to flow velocity and volumetric flow rate using Bernoulli's principle.

Purpose: It helps engineers and technicians determine fluid flow characteristics in pipes and channels based on pressure measurements.

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:

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

Explanation: The pressure difference is converted to velocity head, then multiplied by area and conversion factor to get flow rate.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate determination is crucial for system design, pump sizing, and process control in fluid systems.

4. Using the Calculator

Tips: Enter both pressures (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's the 144 factor in the formula?
A: It converts psi to lb/ft² (1 psi = 144 lb/ft²) for consistent units in the calculation.

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?
A: Water at 60°F is 62.4 lb/ft³. Oil ranges 50-58 lb/ft³, air is about 0.075 lb/ft³ at STP.

Q4: How do I find cross-sectional area?
A: For circular pipes, A = π × (diameter/2)². For other shapes, use appropriate area formulas.

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