Practice Continuity And Navier-stokes Equations (10.5.2)

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8 questions

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6 sample questions

Question 1.
What does the continuity equation represent?
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Think about the principle of mass in a closed system.
Question 2.
Describe irrotational flow.
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What happens to rotation in the fluid?
3Question 3.
What is the main purpose of the continuity equation?
- Energy conservation
- Mass conservation
- Momentum conservation
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Recap on what happens to mass in a closed system.
4Question 4.
True or False: The Navier-Stokes equations can only be applied to incompressible flows.
- True
- False
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Think about whether fluids can be compressed and how that impacts equations.
Question 5.
Given a velocity field of u = Ax + By and v = Cx - Dy, derive the continuity equation and analyze if it satisfies mass conservation.
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Utilize partial derivatives to solve.
Question 6.
For a flow scenario involving high-pressure gradients across a cylindrical pipe, derive the velocity profile using the Navier-Stokes equations.
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Remember to set gravity terms to zero for horizontal flow.

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