Answered: Consider the boundary layer…

Engineering

Mechanical Engineering

Consider the boundary layer flow=1-(1-)1.5, 0

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

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Consider the boundary layer
flow=1-(1-)1.5,
0<y<8 and = 1, y ≥ 6. Using the von
Karman momentum integral equation Tw=pU2 de, write down the relation between 8 and x and calculate
when Re₂ = 104 (where Rez
U₂).
the local drag coefficient Cf=
=
08: 10vz Cf = 0.0067082
U 7
08=1
08=
08=
20vz
U 7
10vz
U
2012
U'
Cf = 0.0067082
Cf = 0.0139431
Cf = 0.0139431
Tw
PU²
=

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Step 1: Determine the relation and local drag coefficient.

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Step 2: Calculate the value of the shear stress.

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Step 3: Calculate the relation.

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Consider the boundary layer flow = 1 - (1 − 2)¹5, 0
Consider the boundary layer over a flat plate at 45° angle as shown. The exact flow field in this configuration is described by the Falkner-Skan similarity solution with n = 1/3 (see Figure 10.8 of the textbook, the Falkner-Skan profile chart). The objective is to find the approximate solution to this problem using the Thwaites method and calculate its error. Ve 11/4 Assume that for this approximate solution the free stream velocity is U₂(x) = ax" where a is an unknown constants and n = 1/3. Use the Thwaites method to find the momentum 0/x and 8*/x displacement thicknesses as well as the friction coefficient cf = 0.5, as functions of Re₂ = Uer/v, where is the shear stress at the wall. (No need to interpolate the Thwaites method table values; you can pick the nearest numbers.) Using the Falkner-Skan profile chart approximate the friction coefficient c; (by estimating the slope of the corresponding velocity profile at the wall). How does this value compare with your prediction in part…
D