Mass Flow Rate Bernoulli Equation

Mass Flow Rate Formula:

\[ W = \rho \times V \times A \times 60 \]

Velocity Formula:

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

Density (ρ):

lb/gal

Pressure 1 (P₁):

psi

Pressure 2 (P₂):

psi

Cross-sectional Area (A):

ft²

Velocity (V): ft/s

Mass Flow Rate (W): lb/hr

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1. What is Mass Flow Rate Bernoulli Equation?

Definition: This calculator determines the mass flow rate of a fluid using Bernoulli's equation, which relates pressure difference to fluid velocity.

Purpose: It's used in fluid dynamics to calculate flow rates in pipes, nozzles, and other systems where pressure differences drive flow.

2. How Does the Calculator Work?

The calculator uses two formulas:

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

\[ W = \rho \times V \times A \times 60 \]

Where:

\( W \) — Mass flow rate (lb/hr)
\( \rho \) — Fluid density (lb/gal)
\( V \) — Fluid velocity (ft/s)
\( A \) — Cross-sectional area (ft²)
\( P_1, P_2 \) — Upstream and downstream pressures (psi)

Explanation: First calculates velocity from pressure difference, then computes mass flow rate using density and area.

3. Importance of Mass Flow Rate Calculation

Details: Accurate flow rate calculations are essential for designing piping systems, process control, and equipment sizing in chemical, petroleum, and mechanical engineering.

4. Using the Calculator

Tips: Enter fluid density (default 8.34 lb/gal for water), pressure values (P₁ > P₂), and cross-sectional area. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a 144 in the velocity formula?
A: This converts psi (lb/in²) to lb/ft² (since 12² = 144) for consistent units.

Q2: What's the 60 factor in mass flow rate?
A: It converts lb/min to lb/hr (60 minutes/hour).

Q3: What assumptions does this calculation make?
A: It assumes incompressible, inviscid flow with no elevation changes or friction losses.

Q4: Can I use this for gases?
A: No, this simplified form is for incompressible fluids only. Gases require more complex compressible flow equations.

Q5: What's a typical density value for water?
A: Water at 60°F is approximately 8.34 lb/gal, but this varies slightly with temperature.