Answered: Air at 20°C flows at V = 80.0 m/s over…

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

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,

$R e_{L} = \frac{V L}{ν}$

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

$ν = 1.516 \times 10^{- 5} m^{2} / s$

Calculate the Reynolds Number,

$\begin{array}{rcl} R e_{L} & = & \frac{V L}{ν} \\ = & \frac{(80 m / s) (17.5 m)}{1.516 \times 10^{- 5} m^{2} / s} \\ R e_{L} & = & 9.23 \times 10^{7} \end{array}$

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,

$\begin{array}{rcl} δ_{L} & = & \frac{0.16 (L)}{{(R e_{L})}^{1 / 7}} \\ = & \frac{0.16 (17.5 m)}{{(9.23 \times 10^{7})}^{1 / 7}} \\ δ_{L} & = & 0.2038 m \end{array}$

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

$\begin{array}{rcl} C_{f L} & = & \frac{0.027}{{(R e_{L})}^{1 / 7}} \\ = & \frac{0.027}{{(9.23 \times 10^{7})}^{1 / 7}} \\ C_{f L} & = & 1.965 \times 10^{- 3} \end{array}$

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