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 = + h1 = + h2 d + 동azd where p, v, p, and h are the density, shock velocity, pressure, and specific enthalpy in front (1) and behind (2) the shock respectively. Shock front v2, P2, P2, h2 V1, P1, P1, h. (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 - P1 Ah = P2, The general form of Bernoulli's law is fulfilled on both sides of the shock separately: + Þ + h = b 2 where is the gravitational potential and ba 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.
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 = + h1 = + h2 d + 동azd where p, v, p, and h are the density, shock velocity, pressure, and specific enthalpy in front (1) and behind (2) the shock respectively. Shock front v2, P2, P2, h2 V1, P1, P1, h. (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 - P1 Ah = P2, The general form of Bernoulli's law is fulfilled on both sides of the shock separately: + Þ + h = b 2 where is the gravitational potential and ba 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.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
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):
pio? + Pi = p2v3 + P2
ví
+ h1 =
+ h2
Pivi = P2V2
%3D
where p, v, p, and h are the density, shock velocity, pressure, and specific enthalpy in front (1).
and behind (2) the shock respectively.
Shock front
v2, P2, P2, hz
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
Ah =
2
P1
P2,
The general form of Bernoulli's law is fulfilled on both sides of the shock separately:
v2
+ + + h = b
where 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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning