Answered: Maj = 3 P = 100 kPa Maz. P2 5°

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

Supersonic airflow takes a 5° expansion turn, as in
Fig. Compute the downstream Mach number and
pressure, and compare with small-disturbance theory.

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Step 2

$F r o m p r o p e r t i e s t a b l e o f g a s e s, S p e c i f i c h e a t r a t i o o f t h e a i r, k = 1.4 F r o m t a b l e o f' P r a n d t l - M e y e r S u p e r s o n i c e x p a n s i o n f u n c t i o n' f o r, k = 1.4 P r a n d t l - M e y e r a n g l e f o r u p s t r e a m c o n d i t i o n o f m a c h n u m b e r (M a_{1}) = 3 i s ω_{M a_{1}} = 49 . 76^{o} E x p a n s i o n t u r n i n g a n g l e i s t h e d i f f e r e n c e i n P r a n d t l - M e y e r a n g l e s f o r t h e t w o c o n d i t i o n s ∆ ω = ω_{M a_{2}} - ω_{M a_{1}} H e n c e, t h e p r a n d t l M e y e r a n g l e f o r t h e d o w n s t r e a m c o n d i t i o n o f a r c i s g i v e n b y, ω_{M a_{2}} = ω_{M a_{1}} + ∆ ω ω_{M a_{2}} = 49.76 + 5 ω_{M a_{2}} = 54 . 76^{o} F r o m t h e t a b l e o f P r a n d t l M e y e r s u p e r s o n i c e x p a n s i o n f u n c t i o n f o r k = 1.4, t h e a p p r o x i m a t e d o w n s t r e a m m a c h n u m b e r f o r t h e a n g l e o f, ω_{M a_{2}} = 54 . 76^{o} i s M a_{2} = 3.274 H e n c e t h e m a c h n u m b e r o f t h e s t r e a m a f t e r d e f l e c t i o n, M a_{2} = 3.274$

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