3.1.9 - Divergence Theorem
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Practice Questions
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What does the divergence of a vector field measure?
💡 Hint: Think about sources and sinks.
What is mass flux?
💡 Hint: Consider how density and velocity combine.
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Interactive Quizzes
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What does divergence tell us about fluid flow?
💡 Hint: Think about how fluid expands.
True or False: The Divergence Theorem can only be applied to incompressible flows.
💡 Hint: Consider the versatility of the theorem.
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Challenge Problems
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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.
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.
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