Normal shock

Question 1

Write down basic relation for a normal shock

Question 2

Prove that a supersonic flow becomes subsonic after crossing a normal shock

Question 3

Derive Rankine-Hugoniot’s relation

Question 4

Derive Prandtl’s relation for a normal shock

Question 5

A supersonic flow is entering a CD-nozzle. A normal shock is observed in a converging part of the nozzle. The
exit flow is supersonic. (i) Sketch a plot of static and stagnation pressure variation along the nozzle. (ii)
Sketch a plot of static and stagnation temperature variation along the nozzle

Question 6

Derive the stagnation pressure ratio across the shock if the static pressure and temperature ratios are given.

Question 7

Derive the equation for calculation of the change of entropy across the shock if the ratio of static pressure
across the shock, 𝑝2/𝑝1, is given

Question 8

Derive equation for the static Pitot probe for operating in a compressible subsonic flow. Explain why this
equation does not contradicts the equation derived for an incompressible flow from the Bernoulli equation:
𝑀 = √(2/𝛾 )(𝑝0/𝑝− 1)

Question 9

Derive the equation for calculating Mach number in a supersonic flow by a static Pitot probe

Question 10

Derive basic relations of the moving normal shock starting with the basic relations for a steady state normal
shock

Question 11

Explain the term slip line in application to shock tubes