Answered: Boundary layer U- 2 mm 2 mm L. L.

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 and 1 atm flow past the flat plate in Fig.
under laminar conditions. There are two equally spaced
pitot stagnation tubes, each placed 2 mm from the wall.
The manometer fluid is water at 20°C. If U = 15 m/s and
L = 50 cm, determine the values of the manometer readings
h₁ and h₂, in mm.

Expert Solution

Step 1

Given data

$U = 15 m / s L = 50 m$

Step 2

From Blasius's equation

$η_{1} = y [\frac{U}{v x_{1}}]$

Substitute the necessary values in above equation

$\begin{array}{rcl} η_{1} & = & (0.002 m) [\frac{15 m / s}{1.5 \times 10^{- 5} (0.5 m)}] \\ = & 2.83 \end{array}$

At this point from table 7.1

$f' = 0.816$

Now the velocity at this point

$\begin{array}{rcl} u_{1} & = & U f' \\ = & (15 m / s) (0.816) \\ = & 12.25 m / s \end{array}$

Step 3

Similarly,

$η_{2} = y {[\frac{U}{v x_{2}}]}^{1 / 2}$

Substitute the necessary values in above equation

$\begin{array}{rcl} η_{2} & = & (0.002 m) {[\frac{15 m / s}{1.5 \times 10^{- 5} (0.5 m)}]}^{1 / 2} \\ = & 2 \end{array}$

At this point from table 7.1

$f^{'} = 0.63$

The velocity at this point is

$\begin{array}{rcl} u_{2} & = & U f' \\ = & (15 m / s) (0.63) \\ = & 9.45 m / s \end{array}$

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