Fluid lies between two concentric cylinders. Theinner solid cylinder, of radius aa, rotates withangular velocity NaNa, and the outer hollowcylinder, of radius bb, rotates with angularvelocity NBN6. Assuming the flow is steady, findthe velocity of the fluid.

Given: Fluid is flowing in concentric cylinder. Assume the flow is laminar.

Answered: Fluid lies between two concentric…

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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Problem Consider a cylindrical pipe of length L and diameter D = 2R. The angle that the axis of the pipe forms with the vertical direction is a. Assume that when the fluid enters the pipe its velocity is uniform (i.e., it has the same value over the entire cross-section of the pipe) and equal to U in the axial direction. In the radial and angular directions, the velocity is zero. So, it is: 2 =0: v(r, 0, 2) = Ue, (1.1) Here v is the fluid velocity and e, is a vector of unit magnitude parallel to the coordinate axis z; furthermore, we have assumed that the pipe inlet is located at z = 0. Near the entrance of the pipe, the velocity profile varies in the axial direction. But after a certain entrance length, the profile becomes fully developed, no longer changing with z. The evolution of the velocity profile is sketched in Fig. 1, where, for clarity, the pipe inclination is not shown. The entrance length is denoted by L.. For z > L., the fluid velocity is no longer a function of the axial…
6.4 The three components of velocity in a flow field are given by u = x² + v² + z² v = xy + yz + z? w = -3xz – z2/2 + 4 Determine an expression for the rotation vector. Is this an irrotational flow field?
Find the location of the stagnation point for the flow due to a vortex +I at (2a, 0) and a vortex -25 at (-2a, 0).
prove that the flow is physically possible : v = Hzy
Problems 2 Find the stream Lines if 2 U = 2 x + Y V =-4xY 19
4.12. Show that the pattern due to a two-dimensional sink at the origin and sources at (0-5, 0) and (2, 0), all of strength 27, represents flow due to a source near a cylinder. Using angle measurements from a scale drawing, evaluate y for a series of points in the first and second quadrants and, by interpolation, draw the 37 streamlines =, and 4 !3!
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If the velocity of an incompressible fluid at a point (x,y,z) is given by (image below) prove that the motion is possible and that the velocity potential is −cosθ/r2. Find the equations of the streamlines where r^2 = x^2 +y^2 +z^2 and θ is the angle between r and the z-axis. Kindly, explain all the steps. :)
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3.14. Find the vorticity in polar coordinates for the following velocity com- ponents (a) v=rsin 0, ve = 2r cos 0 (b) v = cos 0, 11=0
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Fluid lies between two concentric cylinders. The inner solid cylinder, of radius aa, rotates with angular velocity NaNa, and the outer hollow cylinder, of radius bb, rotates with angular velocity O6Q6. Assuming the flow is steady, find the velocity of the fluid.