Flow Rate Based on Pressure

Flow Rate Formulas:

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

Pressure at Point 1 (P₁):

psi

Pressure at Point 2 (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 Flow Rate Based on Pressure?

Definition: This calculator determines the flow rate of a fluid through a pipe or channel based on the pressure difference between two points using Bernoulli's equation.

Purpose: It helps engineers, plumbers, and fluid system designers calculate flow rates in piping systems, hydraulic systems, and other fluid applications.

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 (ft/s)
\( P_1 \) — Pressure at point 1 (psi)
\( P_2 \) — Pressure at point 2 (psi)
\( \rho \) — Fluid density (lb/ft³)
\( Q \) — Flow rate (GPM)
\( A \) — Cross-sectional area (ft²)

Explanation: The first equation calculates velocity from pressure difference, and the second converts velocity to flow rate using the cross-sectional area.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations are essential for proper system design, ensuring adequate fluid delivery, preventing pressure drops, and optimizing energy efficiency.

4. Using the Calculator

Tips:

Enter the pressure at two points in the system (P₁ and P₂)
Input fluid density (default 62.4 lb/ft³ for water)
Provide the cross-sectional area of the pipe/channel
All values must be positive numbers

5. Frequently Asked Questions (FAQ)

Q1: Why is there a 144 in the velocity equation?
A: This converts psi (lb/in²) to lb/ft² (since 1 ft² = 144 in²).

Q2: What's the 448.83 factor in the flow rate equation?
A: This converts ft³/s to gallons per minute (GPM).

Q3: What density should I use for other fluids?
A: Use 49.2 lb/ft³ for gasoline, 78.6 lb/ft³ for seawater, or look up specific densities for your fluid.

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

Q5: Does this account for friction losses?
A: No, this is the theoretical maximum flow. Actual flow will be less due to friction and other losses.