Practice Continuity and Navier-Stokes Equations - 10.5.2 | 10. The Navier-Stokes Equation III | Fluid Mechanics - Vol 3
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Continuity and Navier-Stokes Equations

10.5.2 - Continuity and Navier-Stokes Equations

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does the continuity equation represent?

💡 Hint: Think about the principle of mass in a closed system.

Question 2 Easy

Describe irrotational flow.

💡 Hint: What happens to rotation in the fluid?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the main purpose of the continuity equation?

Energy conservation
Mass conservation
Momentum conservation

💡 Hint: Recap on what happens to mass in a closed system.

Question 2

True or False: The Navier-Stokes equations can only be applied to incompressible flows.

True
False

💡 Hint: Think about whether fluids can be compressed and how that impacts equations.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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Reference links

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