Pressure to Flow Rate Formula

Pressure to 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

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Pressure to Flow Rate Formula?

Definition: These formulas convert pressure difference to fluid velocity and then to volumetric flow rate.

Purpose: Used in fluid dynamics to determine flow rates through pipes, valves, and other hydraulic systems based on pressure measurements.

2. How Do the Formulas 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 (gallons per minute)
\( A \) — Cross-sectional area (ft²)

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

3. Importance of Pressure to Flow Conversion

Details: Essential for designing hydraulic systems, sizing pipes, selecting pumps, and troubleshooting flow problems in industrial processes.

4. Using the Calculator

Tips: Enter pressures in psi, density in lb/ft³ (62.4 for water), and area in ft². All values must be positive, with P₁ ≥ P₂.

5. Frequently Asked Questions (FAQ)

Q1: Why multiply pressure by 144 in the formula?
A: Converts psi to psf (pounds per square foot) since density is in lb/ft³.

Q2: What's the 448.83 factor in the flow rate formula?
A: Conversion factor to change ft³/s to gallons per minute (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 other fluids.

Q4: Does this account for friction losses?
A: No, this is ideal flow. For real-world applications, consider additional factors like pipe roughness.

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