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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does the divergence of a vector field measure?
💡 Hint: Think about sources and sinks.
Question 2
Easy
What is mass flux?
💡 Hint: Consider how density and velocity combine.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does divergence tell us about fluid flow?
- Indicates fluid density change
- Represents temperature
- Measures pressure
💡 Hint: Think about how fluid expands.
Question 2
True or False: The Divergence Theorem can only be applied to incompressible flows.
- True
- False
💡 Hint: Consider the versatility of the theorem.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a cylindrical tank with varying cross-section. Derive the mass conservation equation by applying the Divergence Theorem, considering inflows and outflows.
💡 Hint: Break down the regional inflow/outflow using the geometry of the cylinder.
Question 2
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.
💡 Hint: Use the principle of volume and area relation in flow.
Challenge and get performance evaluation