Answered: We saw in the text that, for k = 1.40,…

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

We saw in the text that, for k = 1.40, the maximum possible
deflection caused by an oblique shock wave occurs at
infinite approach Mach number and is θ_max = 45.58°.
Assuming an ideal gas, what is θmax for (a) argon and
(b) carbon dioxide?

Expert Solution

Step 1

In the limit as Ma1 → ∞, the normal-velocity ratio across a shock wave is

$\frac{V_{1}}{V_{2}} \to \frac{k + 1}{k - 1}$

It is this limiting ratio that we use to calculate θmax for the two gases above.

$\begin{array}{rcl} θ_{m a x} & = & \tan^{- 1} (\sqrt{r}) - \tan^{- 1} (\frac{1}{\sqrt{r}}) \\ r & = & \frac{k + 1}{k - 1} \end{array}$

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