First Set

Solutions should be very accurate, very neat and complete. Software you can use is on the main course web page.

1.

For the shock tube in acoustic approximation, find the deviations , , and , from the initial conditions in the driven section foras long times as you can. Initial conditions are for x<0, for x>0, and for all x. Take your own values for the other variables.

2.

For the problem 7.10, work out the pressure, temperature, velocity, and Mach number in all regions 1 through 6. Assume p₁ = 1 atm.

3.

Do problem 7.11. (Section 7.6 is a typo for section 7.7).

4.

For the problem 7.13, work out the pressure, temperature, velocity, and Mach number in all regions 1 through 6. Assume p₁ = 1 atm.

5.

Graphically represent (7.94) in three dimensions assuming air at both sides. Comment on how to optimize incident shock strength and what can be achieved. Next make corresponding graphs varying the driver gas -value and comment on what can be achieved.

6.

Study the linearized problem of Mach 1 flow found under the lecture notes heading ``Choked 2''. Examine what the restrictions are on small changes in mass flow, momentum flow plus pressure force, and stagnation enthalpy. Study what these restrictions mean physically.