Develop a closed-circuit wind tunnel. The test environment is to simulate flight at 70,000 feet with Mach number 4.6

Assumptions/Given: 1. The pipes leading to and from the compressor have a diameter equal to that of the exit of the diffuser.

2. The surface of the diffuser throat is coated with a very rough surface so that a shock is formed in the diffuser throat during steady-state operation.

3. There are no stagnation pressure losses in the system due to friction or heat through the pipes.

4.The test section is 6 feet in diameter.

5. The diffuser exit area is twice as large as the test section area.

6. The linear actuator used to narrow the area of the diffuser at a steady state is completely retracted at start-up. It has a maximum travel distance of 2.4ft and can be adjusted incrementally to stop at 0.3ft intervals. Assume that these intervals correlate with a change in the diffuse throat diameter (i.e. 0.3 ft of travel of the actuator is the same as narrowing the diameter by 0.3ft).

7. Due to oblique shocks in the test section it is predicted that there will be a 10% drop in stagnation pressure from the inlet of the test section to the outlet of the test section. However, the Mach number can be assumed to be constant throughout the test section.

8. The gas to be used has a gamma of 1.26 and a gas constant of air which can be treated as calorically perfect.

Find:

1. The area of the diffuser throat during steady-state operation. (in^2 & m^2)

2. The mass flow rate through the system. (lbm/s & kg/s)

3. The Mach number and velocity at the exit of the diffuser at a steady state. ( ft/s and m/s)

4. The cost to run an isothermal compressor ( stagnation temperature is the same on both sides) for one hour of operation given a usage cost of $0.15/ kWh. ($) Use an average temperature between the inlet and outlet to calculate the work.

5. The minimum diamter of the diffuser throat at start up. (This is where the linear actuator will be in the fully retracted position). (ft and m)

6. The diameter of the nozzle throat. ( ft and m)

7.The loss in total pressure through the diffuser at steady state. ( psi and kpa)

Include equations, calculations, and a simple schematic of the system to scale.