Pressure to Flow Rate Conversion

Flow Rate Formulas:

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

Inlet Pressure (P₁):

psi

Outlet Pressure (P₂):

psi

Fluid Density (ρ):

lb/ft³

Cross-Sectional Area (A):

ft²

Velocity (V): ft/s

Flow Rate (Q): GPM

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1. What is Pressure to Flow Rate Conversion?

Definition: This calculator converts pressure difference to flow rate (GPM) using Bernoulli's equation for incompressible fluids.

Purpose: It helps engineers and technicians determine fluid flow rates through pipes and orifices based on pressure measurements.

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)
\( P_1 \) — Inlet pressure (psi)
\( P_2 \) — Outlet pressure (psi)
\( \rho \) — Fluid density (lb/ft³)
\( Q \) — Flow rate (GPM)
\( A \) — Cross-sectional area (ft²)

Explanation: The pressure difference is converted to velocity, which is then multiplied by area and a conversion factor to get flow rate in gallons per minute.

3. Importance of Pressure-Flow Conversion

Details: Accurate flow rate calculation is essential for system design, pump sizing, and process control in hydraulic systems.

4. Using the Calculator

Tips: Enter pressure values (psi), fluid density (default 62.4 lb/ft³ for water), and cross-sectional area (ft²). All values must be > 0 except P₂ which can be 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the 144 factor in the equation?
A: It converts psi to lb/ft² (1 psi = 144 lb/ft²) for unit consistency.

Q2: Why 448.83 in the flow rate formula?
A: This converts ft³/s to GPM (1 ft³/s = 448.83 GPM).

Q3: What density should I use for other fluids?
A: Use 49.2 for gasoline, 78.6 for seawater, or look up specific values for your fluid.

Q4: Does this account for friction losses?
A: No, this is ideal flow. For real systems, include friction factors or use more complex formulas.

Q5: How do I calculate pipe cross-sectional area?
A: For circular pipes: \( A = \pi \times (diameter/2)^2 \) (convert diameter to feet).