Answered: A viscous oil is 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

See similar textbooks

Related questions

Concept explainers

Question

Transcribed Image Text:A viscous oil is between two concentric cylinders. The inner cylinder has a radius of r, and is moving axially with a velocity, U. The outer cylinder has a much larger radius of R, and is stationary. There is a significant pressure supplied at the left end but the right end is open to the the atmosphere. Assume a purely axial fluid motion that is steady and fully developed. To find an equation for the velocity profile of the oil, which equation should you use? U а. ôu ôu др o'u au d'u ди ди + pgx -v+ ôt ôx b. dv dv u+ +pgy %3D ôt ôx ôx? ' ôy? C. dw dw + u dw + Pgz - + v + w- dz dz dz² he d. 1 Pv, , dv, + P8z dvz + Ur ar at + + Vz r a0 ar az? az dz r ar е. a (1 (rv,) ) + Pv, av, 2 dve az? dv, + Vz¯az de = - 1 P8r dv, + v, at Vg dv, dr ar f. 1 dve , dv, 2 ду, 合…。。需。“尝。学)--瑞 m) 制- 1 dp r a0 v,Vo + pgo + V, ar at Vg dVg + v, az az? ? d0 ar r a0

Expert Solution

Step 1

From the given problem, the following assumptions can be made,

Flow is steady and laminar.
Effect of gravity can be neglected in the z-direction.
The rate of change of pressure is zero.
The density of oil is constant.
The motion of the oil is in the axial direction only.

For cylindrical coordinates, the generalized expression for the momentum equation in the z-direction can be written as below,

$ρ (\frac{\partial v_{z}}{\partial t} + v_{r} \frac{\partial v_{z}}{\partial r} + \frac{v_{θ}}{r} \frac{\partial v_{z}}{\partial θ} + v_{z} \frac{\partial v_{z}}{\partial z}) = - \frac{\partial p}{\partial z} + μ [\frac{1}{r} \frac{\partial}{\partial r} (r \frac{\partial v_{z}}{\partial r}) + \frac{1}{r^{2}} \frac{\partial^{2} v_{z}}{\partial θ^{2}} + \frac{\partial^{2} v_{z}}{\partial z^{2}}] + ρ g_{z}$ ......(1)

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions