Answered: A Newtonian fluid with absolute…

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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Question

A Newtonian fluid with absolute viscosity (Greek mu) flows past a flat surface. Due to the no-slip boundary condition, the velocity profile, u(y), develops near the surface and is given by u/U (shown in image provided) where the constant parameters U and delta have dimensions of velocity and length respectively.
a) Develop an expression for the shear stress acting in any horizontal plane.
b) Determine the shear stress acting on the surface at y = 0 and again at the edge of the boundary
layer, y = delta.

(Express your answers in terms of Greek mu, the outer velocity U, and the boundary layer thickness delta.)

Expert Solution

Step 1: given data

given velocity profile,

$u over U equals 3 over 2 open parentheses fraction numerator y over denominator space delta end fraction close parentheses minus 1 half open parentheses fraction numerator y over denominator space delta end fraction close parentheses cubed$

here $space delta$ basically represents the height of boundary layer.

some boundary conditions,

at y = 0 u = 0, due to no slip condition

y = $space delta$ u = U Here share stresses will be negligible.

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