Answered: Free surface P = Patm 40 = or 4, = u, =…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Engine oil at 60°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface
(z_surface as a function of r). (Hint: P = P_atm everywhere on the free surface. The flow is rotationally symmetric about the z-axis.)

Free
surface
P = Patm
40 = or
4, = u, = 0
Water

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