EM 510 Continuum Mechanics
Homework Set 3
For the problems of this set, it is recommended to use software like Matlab, Mathematica, or
Maple to perform the matrix computations. And, unless otherwise stated, the components of
vectors and tensors are to be
Reading: Ryden chs. 3 & 4, Shu chs. 15 & 16. For the enthusiasts, Shu chs. 13 & 14.
A good article for further reading: Shull & Draine, The physics of interstellar shock waves, in
Interstellar processes; Proceedings of the Symposium, Grand Teton
Normal Shock Waves
Where there are supersonic ows, there are usually also shock waves. A fundamental type of shock wave
is the normal shock wave the shock wave normal to the ow direction. We will examine that type
of shock wave in this chapter.
AerE 532 Homework 2 (5 points)
1. Liepmann and Roshko 2.2
2. Liepmann and Roshko 2.4
3. Consider air entering a heated duct at ! = 1 atm and ! = 288K. Ignore the
effect of friction. Calculate the amount o
1st Order ODE with Three Variables
Find the integral curves of the following equations.
( Hint: Find equations of two surfaces in the form f(x,y,z)=C , g(x,y,z)=D )
2 ( )
)2 + + ( + +
1. One solution of the differential equation
4 + 4 2
Is . Determine the full solution of the equation, by using the method of Wronskian.
2. Find two linearly independent solutions of the equation
2 + 6 = 0
Are the solutions
ME 131B Fluid Mechanics
Solutions to Week Seven Problem Session:
Rayleigh Flow (2/24/98)
1. What do all the states on the same Rayleigh curve have in common?
The Rayleigh curve is derived from the conservation of mass and the conservation
of linear momen