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If the laminar velocity profile is approximated by the cubic-order polynomial ū = a1 + azỹ + azy² + a4ỹ³ where, ū = u/Ue and y = y/8 with U, and & being the edge velocity and boundary-layer thickness, respectively. a) Find out the velocity profile, by determining the unknown coefficients a1, a2, az and a4. Plot the velocity profile.

If the laminar velocity profile is approximated by the cubic-order polynomial ū = a1 + azỹ + azy² + a4ỹ³ where, ū = u/Ue and y = y/8 with U, and & being the edge velocity and boundary-layer thickness, respectively. a) Find out the velocity profile, by determining the unknown coefficients a1, a2, az and a4. Plot the velocity profile.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Problem-1 If the laminar velocity profile is approximated by the cubic-order polynomial ū = a1 + a2ỹ+ azy² + a4ÿ³ where, ū = u/Ue and y = y/8 with U, and & being the edge velocity and boundary-layer thickness, respectively. a) Find out the velocity profile, by determining the unknown coefficients a1, a2, az and a4. 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 %3D prove that 8/a = 4.64/VRe,, 8./x = 1.74// Re, and 0/x = 0.646//Re,
Transcribed Image Text:Problem-1 If the laminar velocity profile is approximated by the cubic-order polynomial ū = a1 + a2ỹ+ azy² + a4ÿ³ where, ū = u/Ue and y = y/8 with U, and & being the edge velocity and boundary-layer thickness, respectively. a) Find out the velocity profile, by determining the unknown coefficients a1, a2, az and a4. 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 %3D prove that 8/a = 4.64/VRe,, 8./x = 1.74// Re, and 0/x = 0.646//Re,
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