Consider a laminar boundary layer flow over a flat plate for which the velocity profile can be approx- imated by, u/U = 2(y/δ) − 2(y/δ)3 + (y/δ)4Show that this profile satisfies the appropriate boundary conditions.Using the momentum integral relation, equ. (9.26), derive expressions for δ/x and τw(x). Inte- grate τw(x) and obtain an expression for the drag coefficient, CD, as a function of Rel, where l is length of plate. Check/compare with results in Table 9.2. e = ,(1 -) dy = #(1-#) dy Table 9.2Flat Plate Momentum Integral Results for Various AssumedLaminar Flow Velocity ProfilesProfile CharacterReCRea Blasius solutionb. Lincar/U = y/8e. Parabolie/U = 2y/8 - (y/8)d. Cubic/U - (y/8)/2 - (/8)2e. Sine wave/U = sin (y/8)/2)5000.6641.3283.460.578LI565480.7301.4604.640.6461.2924.790.6551310

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Answered: Consider a laminar boundary layer flow…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Consider a laminar boundary layer flow over a flat plate for which the velocity profile can be approx- imated by, u/U = 2(y/δ) − 2(y/δ)³ + (y/δ)⁴

Show that this profile satisfies the appropriate boundary conditions.
Using the momentum integral relation, equ. (9.26), derive expressions for δ/x and τw(x). Inte- grate τw(x) and obtain an expression for the drag coefficient, CD, as a function of Rel, where l is length of plate. Check/compare with results in Table 9.2.

Transcribed Image Text:Table 9.2 Flat Plate Momentum Integral Results for Various Assumed Laminar Flow Velocity Profiles Profile Character Re CRe a Blasius solution b. Lincar /U = y/8 e. Parabolie /U = 2y/8 - (y/8) d. Cubic /U - (y/8)/2 - (/8)2 e. Sine wave /U = sin (y/8)/2) 500 0.664 1.328 3.46 0.578 LI56 548 0.730 1.460 4.64 0.646 1.292 4.79 0.655 1310

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