Bernoulli Equation Volumetric Flow Rate

Bernoulli Equation Formulas:

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

Pressure P₁:

psi

Pressure P₂:

psi

Density (ρ):

lb/ft³

Cross-sectional Area (A):

ft²

Velocity (V): ft/s

Volumetric Flow Rate (Q): GPM

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1. What is Bernoulli Equation Volumetric Flow Rate?

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

Purpose: It helps engineers and fluid system designers calculate flow rates in pipes and channels for various applications.

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)
\( P_1 \) — Upstream pressure (psi)
\( P_2 \) — Downstream pressure (psi)
\( \rho \) — Fluid density (lb/ft³)
\( Q \) — Volumetric flow rate (GPM)
\( A \) — Cross-sectional area (ft²)

Explanation: The pressure difference drives the flow, with velocity calculated first and then converted to flow rate.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate determination is crucial for system design, pump selection, and ensuring proper fluid transport in pipes.

4. Using the Calculator

Tips: Enter both pressures (P₁ > P₂ for forward flow), fluid density (default 62.4 lb/ft³ for water), and cross-sectional area. All values must be > 0.

5. Frequently Asked Questions (FAQ)

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

Q2: What's the 448.83 factor in flow rate?
A: This converts ft³/s to gallons per minute (1 ft³/s = 448.83 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 values.

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

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