Mass Flow Rate Equation Using Pressure

Mass Flow Rate Formula:

\[ W = \rho \times V \times A \times 60 \] \[ V = \sqrt{\frac{2 \times (P_1 - P_2) \times 144}{\rho}} \]

Density (ρ):

lb/gal

Cross-sectional Area (A):

ft²

Upstream Pressure (P₁):

psi

Downstream Pressure (P₂):

psi

Mass Flow Rate (W): lb/hr

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1. What is Mass Flow Rate Using Pressure?

Definition: This calculator determines the mass flow rate of a fluid based on pressure difference, fluid density, and flow area.

Purpose: It's essential for engineers and technicians working with fluid systems to calculate flow rates in pipes, valves, and other components.

2. How Does the Calculator Work?

The calculator uses two key equations:

\[ V = \sqrt{\frac{2 \times (P_1 - P_2) \times 144}{\rho}} \] \[ W = \rho \times V \times A \times 60 \]

Where:

\( W \) — Mass flow rate (lb/hr)
\( \rho \) — Fluid density (lb/gal)
\( V \) — Flow velocity (ft/s)
\( A \) — Cross-sectional area (ft²)
\( P_1 \) — Upstream pressure (psi)
\( P_2 \) — Downstream pressure (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 critical for system design, performance analysis, and troubleshooting in hydraulic and pneumatic systems.

4. Using the Calculator

Tips: Enter fluid density, cross-sectional area, upstream and downstream pressures. All values must be positive with P₁ > P₂.

5. Frequently Asked Questions (FAQ)

Q1: Why is the 144 factor in the velocity equation?
A: This converts psi to lb/ft² (1 psi = 144 lb/ft²) for consistent units in the calculation.

Q2: What's the 60 factor in the mass flow equation?
A: This converts from lb/min to lb/hr (60 minutes/hour) for the final output.

Q3: What density units should I use?
A: The calculator expects density in pounds per gallon (lb/gal). For water at room temperature, this is about 8.34 lb/gal.

Q4: Does this work for compressible fluids?
A: This simplified model works best for incompressible fluids. Compressible flows require more complex calculations.

Q5: How do I measure the cross-sectional area?
A: For circular pipes, A = π × (diameter/2)². Convert diameter from inches to feet (divide by 12) before squaring.