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

Test your understanding with targeted questions related to the topic.

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?

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 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.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation