This year's qualification round featured a spaceship escaping The crew survived and wants to study the shock wave in more the shock wave travels through a stationary flow of an ideal pol both sides of the shock. Properties in front and behind a shoe Rankine-Hugoniot jump conditions (mass, momentum, energy PIvi = P2v2 prvi + pi = Pao3 + p2 where o, 1, p. and h are the density, shock velocity, pressure
This year's qualification round featured a spaceship escaping The crew survived and wants to study the shock wave in more the shock wave travels through a stationary flow of an ideal pol both sides of the shock. Properties in front and behind a shoe Rankine-Hugoniot jump conditions (mass, momentum, energy PIvi = P2v2 prvi + pi = Pao3 + p2 where o, 1, p. and h are the density, shock velocity, pressure
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
![This year's qualification round featured a spaceship escaping from a shock wave (Problem B).
The crew survived and wants to study the shock wave in more detail. It can be assumed that
the shock wave travels through a stationary flow of an ideal polytropic gas which is adiabatic on
both sides of the shock. Properties in front and behind a shock are related through the three
Rankine-Hugoniot jump conditions (mass, momentum, energy conservation):
Pivi = P2V2
Pivi + P1 = p2u3 +p2
+ h2
+ hị =
2
where p, v, p, and h are the density, shock velocity, pressure, and specific enthalpy in front ().
and behind (2) the shock respectively.
Shock front
v2, P2; P2, h2
V1, P1, P1, h1
(a) Explain briefly the following terms used in the text above:
(i) stationary flow
(ii) polytropic gas
(iii) specific enthalpy
(b) Show with the Rankine-Hugoniot conditions that the change in specific enthalpy is given by:
P2 - Pi
1
Ah =
2
P1
P2
The general form of Bernoulli's law is fulfilled on both sides of the shock separately:
+ 4 + h = b
where d is the gravitational potential and b a constant.
(c) Assuming that the gravitational potential is the same on both sides, determine how the con-
stant b changes at the shock front.
(d) Explain whether Bernoulli's law can be applied across shock fronts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fdebdd2-ae29-4b46-af29-201b3dae5f5b%2F35d6b0e1-c469-4a24-94f8-7b0f32c9160c%2F8jdk9x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:This year's qualification round featured a spaceship escaping from a shock wave (Problem B).
The crew survived and wants to study the shock wave in more detail. It can be assumed that
the shock wave travels through a stationary flow of an ideal polytropic gas which is adiabatic on
both sides of the shock. Properties in front and behind a shock are related through the three
Rankine-Hugoniot jump conditions (mass, momentum, energy conservation):
Pivi = P2V2
Pivi + P1 = p2u3 +p2
+ h2
+ hị =
2
where p, v, p, and h are the density, shock velocity, pressure, and specific enthalpy in front ().
and behind (2) the shock respectively.
Shock front
v2, P2; P2, h2
V1, P1, P1, h1
(a) Explain briefly the following terms used in the text above:
(i) stationary flow
(ii) polytropic gas
(iii) specific enthalpy
(b) Show with the Rankine-Hugoniot conditions that the change in specific enthalpy is given by:
P2 - Pi
1
Ah =
2
P1
P2
The general form of Bernoulli's law is fulfilled on both sides of the shock separately:
+ 4 + h = b
where d is the gravitational potential and b a constant.
(c) Assuming that the gravitational potential is the same on both sides, determine how the con-
stant b changes at the shock front.
(d) Explain whether Bernoulli's law can be applied across shock fronts.
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