If the laminar velocity profile is approximated by the cubic-order polynomial where, a = u/U, and y = y/8 with U, and 6 being the edge velocity and boundary-layer thickness, respectively. a) Find out the velocity profile, by determining the unknown coefficients a,, a,, a, and a,. Plot the velocity profile. b) Find out the analytical expression for the boundary layer, displacement and momentum thickness and also find out their stream-wise variation as a function of x. Specifically prove that 8/x = 4.64/Re,, 8./1 = 1.74/VRe, and 0/r = 0.646//Re,
If the laminar velocity profile is approximated by the cubic-order polynomial where, a = u/U, and y = y/8 with U, and 6 being the edge velocity and boundary-layer thickness, respectively. a) Find out the velocity profile, by determining the unknown coefficients a,, a,, a, and a,. Plot the velocity profile. b) Find out the analytical expression for the boundary layer, displacement and momentum thickness and also find out their stream-wise variation as a function of x. Specifically prove that 8/x = 4.64/Re,, 8./1 = 1.74/VRe, and 0/r = 0.646//Re,
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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Transcribed Image Text:If the laminar velocity profile is approximated by the cubic-order polynomial
ū = a, + a,ỹ + a,5² + a,5³
where, ū = u/U, and ỹ = y/8 with U, and ô being the edge velocity and boundary-layer
thickness, respectively.
a) Find out the velocity profile, by determining the unknown coefficients a,, a,, az and a,.
Plot the velocity profile.
b) Find out the analytical expression for the boundary layer, displacement and momentum
thickness and also find out their stream-wise variation as a function of x. Specifically
prove that
8/x = 4.64/VRe,, 8./x = 1.74/VRe, and 0/x = 0.646/Re,
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