Practice Divergence Theorem (3.1.9) - Mass Conservation Equation- I - Fluid Mechanics

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8 questions

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Exercise
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6 sample questions

Question 1.
What does the divergence of a vector field measure?
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Think about sources and sinks.
Question 2.
What is mass flux?
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Consider how density and velocity combine.
3Question 3.
What does divergence tell us about fluid flow?
- Indicates fluid density change
- Represents temperature
- Measures pressure
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Think about how fluid expands.
4Question 4.
True or False: The Divergence Theorem can only be applied to incompressible flows.
- True
- False
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Consider the versatility of the theorem.
Question 5.
Consider a cylindrical tank with varying cross-section. Derive the mass conservation equation by applying the Divergence Theorem, considering inflows and outflows.
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Break down the regional inflow/outflow using the geometry of the cylinder.
Question 6.
A fluid is flowing through a pipe with varying diameter. Analyze how the Divergence Theorem applies and derive the implications for velocity and density changes.
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Use the principle of volume and area relation in flow.

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