Mass Flow Rate From Continuity Relation For One Dimensional Flow In Tube Calculator

Mass Flow Rate Formula:

\[ \dot{m} = \rho_{Fluid} \times A_T \times u_m \]

Mass Flow Rate (ṁ):

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1. What is Mass Flow Rate?

Mass flow rate is the mass of a substance that passes per unit of time. Its unit is kilogram per second in SI units. It is a fundamental parameter in fluid dynamics and engineering applications.

2. How Does the Calculator Work?

The calculator uses the continuity relation formula:

\[ \dot{m} = \rho_{Fluid} \times A_T \times u_m \]

Where:

\( \dot{m} \) — Mass flow rate (kg/s)
\( \rho_{Fluid} \) — Density of fluid (kg/m³)
\( A_T \) — Cross sectional area (m²)
\( u_m \) — Mean velocity (m/s)

Explanation: This formula represents the continuity equation for one-dimensional flow in a tube, where the mass flow rate is constant for incompressible fluids.

3. Importance of Mass Flow Rate Calculation

Details: Mass flow rate calculation is crucial for designing piping systems, HVAC systems, chemical processes, and various engineering applications where fluid transport is involved.

4. Using the Calculator

Tips: Enter fluid density in kg/m³, cross-sectional area in m², and mean velocity in m/s. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between mass flow rate and volumetric flow rate?
A: Mass flow rate measures mass per unit time (kg/s), while volumetric flow rate measures volume per unit time (m³/s). They are related by density: mass flow rate = density × volumetric flow rate.

Q2: When is the continuity equation applicable?
A: The continuity equation applies to steady, incompressible flow where the fluid density remains constant throughout the flow.

Q3: What are typical units for mass flow rate?
A: In SI units, mass flow rate is measured in kilograms per second (kg/s). Other common units include grams per second (g/s) or pounds per second (lb/s).

Q4: How does cross-sectional area affect mass flow rate?
A: For a given velocity and density, increasing the cross-sectional area increases the mass flow rate proportionally.

Q5: Can this formula be used for compressible fluids?
A: For compressible fluids, the formula requires modification to account for density variations. This simplified version is primarily for incompressible fluids.