Answered: Write down the continuity equation and…

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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A subtle point, often missed by students of fluid mechanics (and even their professors!), is that an inviscid region of flow is not the same as an irrotational (potential) region of flow. Discuss the differences and similarities between these two approximations. Give an example of each.
By using the expression for the shear stress derived in class (and in BSL), show that the shear force on asphere spinning at a constant angular velocity in a Stokes’ flow, is zero.This means that a neutrally buoyant sphere (weight equal buoyancy force) that is made to spin in aStokes’ flow, will neither rise nor fall, nor translate in any preferential direction in the (x-y) plane. expressions for velocity are: v_r (r,θ)= U_∞ [1-3R/2r+R^3/(2r^3 )] cos⁡θ v_θ (r,θ)= -U_∞ [1-3R/4r-R^3/(4r^3 )] sin⁡θ Where v_r and v_θ are the radial and angle velocity, U_∞ is the velocity of fluid coming to sphere which very faar away from the sphere. And R is the radius of sphere.
Rain water is flowing through an inclined plane under gravity as shown in figure. A thin layer of thickness h is formed over the plate. An upward wind flow that exerts a shear stress on the upper surface (y = h) of the liquid layer. The wind flow tends to push the rain layer upward while gravity pulls the layer downward Write continuity and and Navier-Stokes equations to model this flow field. (Assume the flow is fully developed) Obtain expressions for the liquid velocity profile, the shear stress distribution, the volume flow rate, and the the expression for the thickness h of the liquid layer for which there is no net volume flow along the roof

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Write down the continuity equation and the Navier-Stokes equations in the x-, y-, and z- directions for an incompressible, three-dimensional flow. There should be a total of four equations. If we make the assumptions that the flow is steady and inviscid, what do these four equations simplify to?