10.5.2 - Continuity and Navier-Stokes Equations
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Practice Questions
Test your understanding with targeted questions
What does the continuity equation represent?
💡 Hint: Think about the principle of mass in a closed system.
Describe irrotational flow.
💡 Hint: What happens to rotation in the fluid?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main purpose of the continuity equation?
💡 Hint: Recap on what happens to mass in a closed system.
True or False: The Navier-Stokes equations can only be applied to incompressible flows.
💡 Hint: Think about whether fluids can be compressed and how that impacts equations.
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Challenge Problems
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Given a velocity field of u = Ax + By and v = Cx - Dy, derive the continuity equation and analyze if it satisfies mass conservation.
💡 Hint: Utilize partial derivatives to solve.
For a flow scenario involving high-pressure gradients across a cylindrical pipe, derive the velocity profile using the Navier-Stokes equations.
💡 Hint: Remember to set gravity terms to zero for horizontal flow.
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