Air at 20°C flows at V = 80.0 m/s over a smooth flat plate of length L = 17.5 m. Plot the turbulent boundary layer profile in physical variables (u as a function of y) at x = L. Compare the profile generated by the one-seventh-power law, the log law, and Spalding’s law of the wall, assuming that the boundary layer is fully turbulent from the beginning of the plate.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Air at 20°C flows at V = 80.0 m/s over a smooth flat plate of length L = 17.5 m. Plot the turbulent boundary layer profile in physical variables (u as a function of y) at x = L. Compare the profile generated by the one-seventh-power law, the log law, and Spalding’s law of the wall, assuming that the boundary layer is fully turbulent from the beginning of the plate.

Expert Solution
Step 1

Write the expression of Reynolds Number,

ReL=VLν

The kinematic viscosity of air at 20 oC is taken as,

ν=1.516×10-5 m2/s

 

Calculate the Reynolds Number,

ReL=VLν=80 m/s17.5 m1.516×10-5 m2/sReL=9.23×107

 

The calculated Reynolds number is greater than the range of laminar flow so the flow will be turbulent.

 

Step 2

Calculate the boundary layer thickness at x=L,

δL=0.16LReL1/7=0.1617.5 m9.23×1071/7δL=0.2038 m

 

Calculate the skin friction coefficient at the end of the plate,

 

CfL=0.027ReL1/7=0.0279.23×1071/7CfL=1.965×10-3

 

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