Flow Rate Equation Bernoulli

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 the Bernoulli Flow Rate Calculator?

Definition: This calculator determines the flow rate of a fluid through a pipe or channel using Bernoulli's equation, based on pressure difference, fluid density, and cross-sectional area.

Purpose: It helps engineers, plumbers, and fluid system designers calculate flow rates for various applications including piping systems, irrigation, and hydraulic systems.

2. How Does the Calculator Work?

The calculator uses two key 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 drives the flow, with velocity determined by the square root of the pressure difference divided by density. Flow rate is then calculated from velocity and area.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculations ensure proper system design, prevent pipe overpressure, optimize pump selection, and maintain efficient system operation.

4. Using the Calculator

Tips: Enter the pressure values (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 equation?
A: This converts psi (lb/in²) to lb/ft² (since 12 in × 12 in = 144 in² per ft²).

Q2: What does the 448.83 conversion factor do?
A: It converts ft³/s to gallons per minute (GPM).

Q3: When is Bernoulli's equation applicable?
A: For steady, incompressible flow with no friction losses or elevation changes.

Q4: What's a typical water density value?
A: Fresh water at 60°F is 62.4 lb/ft³. Saltwater is about 64 lb/ft³.

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