An incident shock within a shock tube is traveling through driven section where the pressure ratio is given as p2/p₁ = 860 across the incident shock. This incident shock reflects from the end wall of the tube and creating a reflected shock. Knowing that the fluid used in both sections is air with driven and treating the air as a section pressure of p₁ = 5 atm and temperature of T₁ = 270 K calorically perfect gas: a) Calculate the reflected shock wave velocity relative to the ground.

A

Air flows isentropically from a large reservoir maintained at 597°C and 1.0 MPa absolute into a converging-diverging duct. The flow at the exit plane of diverging duct is supersonic. The duct is 2 m long and has a circular cross sectional area with radius, r in m that varies in axial distance, x along the duct that is defined by r = 0.03x² +0.02 where x extends from -1.0 m to 1.0 m. (a) Sketch a 2D diagram of the above system on a graph of duct radius against axial distance with appropriate labelling. (b) Using the isentropic table provided, determine (i) the Mach number, pressure and temperature at the exit plane, and (ii) the mass flow rate through the duct. E.Q2 (c) If the radius of the duct as specified in E.Q2 is doubled, would the Mach number on the exit plane be increased, decreased or remain unchanged? Explain your answer briefly. Take heat specific ratio of 1.4 and specific gas constant of 0.287 kJ/(kg-K) for air.

The shock waves on a vehicle in supersonic flight cause a component ofdrag called supersonic wave drag Dw. Define the wave-drag coefficient asCD,w = Dw/q∞S, where S is a suitable reference area for the body. Insupersonic flight, the flow is governed in part by its thermodynamicproperties, given by the specific heats at constant pressure cp and atconstant volume cv. Define the ratio cp/cv ≡ γ . Using Buckingham’spi theorem, show that CD,w = f (M∞, γ ). Neglect the influence of friction.

A large reservoir at 20 °C and 800 kPa is used to fill a smallinsulated tank through a converging–diverging nozzle with1-cm2 throat area and 1.66-cm2 exit area. The small tankhas a volume of 1 m3 and is initially at 20 °C and 100 kPa. Estimate the elapsed time when (a) shock waves begin toappear inside the nozzle and (b) the mass flow begins todrop below its maximum value.

A supersonic wind tunnel is in the design stage. It is to be driven by a large upstream reservoir of compressed air and discharges to atmospheric conditions downstream. The test section has a constant cross-sectional area and lies downstream of a throat, which is a converging-diverging section that serves to accelerate the flow to supersonic conditions. For the duration of any given experiment, the reservoir can be considered to have constant stagnation conditions that are To = 313K and po = 6x105 Pa. The specific gas constant R = 287 J kg-¹ K-1 and the specific heat ratio is y = 1.4. The wind tunnel test section is designed to run with a cross-sectional area A (test section ) = 1.2 m² and Mach number M (test section ) = 4. Find the area of the throat that lies between the reservoir and the test section. Give your answer in m² to two decimal places.