4.1.8 - Case Studies and Problems
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Practice Questions
Test your understanding with targeted questions
Define the continuity equation.
💡 Hint: Think about mass flow.
What is divergence in fluid mechanics?
💡 Hint: Consider vector fields.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the continuity equation express?
💡 Hint: Think about the principle of mass flow.
True or False: Incompressible flow assumes density varies with pressure.
💡 Hint: Reflect on the definitions of incompressible flow.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Consider a cylindrical tank with a piston compressing air. If the piston moves at a speed of 0.1 m/s, calculate how the density changes with time if initially, the density is known.
💡 Hint: Account for changes in the volume and apply the continuity equation.
Given a two-dimensional flow field represented as v(x,y) = (x, y^2), determine if the flow is incompressible or not.
💡 Hint: Remember to differentiate with respect to each variable and sum them.
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