(The purpose of this problem is to calculate a two-dimensional expanding supersonic flow and compare it with the analogous quasi-one-dimensional flow in Problem 10.15.) Consider a two-dimensional duct with a straight horizontal lower wall, and a straight upper wall inclined upward through the angle
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- 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 = 287J 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 ) = 3.5. Find the area of the throat that lies between the reservoir and the test section. Give your answer in m² to two decimal places.arrow_forwardConsider a circular cylinder in a hypersonic flow, with its axisperpendicular to the flow. Let φ be the angle measured between radiidrawn to the leading edge (the stagnation point) and to any arbitrary pointon the cylinder. The pressure coefficient distribution along the cylindricalsurface is given by Cp = 2 cos2 φ for 0 ≤ φ ≤ π/2 and 3π/2 ≤ φ ≤ 2πand Cp = 0 for π/2 ≤ φ ≤ 3π/2. Calculate the drag coefficient for thecylinder, based on projected frontal area of the cylinder.arrow_forwardThe stagnation chamber of a wind tunnel is connected to a high pressure air bottle farm which is outside the laboratory building. The two are connected by a long pipe which has a inside diameter of 4 inches. If the static pressure ratio between the bottle farm and the stagnation chamber is 10 and the bottle farm static pressure is 100 atm, how long can the pipe be without choking and what is the change in entropy? Assume adiabatic,subsonic, one-dimensional flow with a friction coefficient of 0.005.arrow_forward
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- For Air Assume: y =1.4 and R = 287 J/kg K Question B1 a) Air is flowing at a Mach number of 0.6 in a two-dimensional duct at a location where the area is of 0.75 m². At this location the static pressure is 50 kPa and the static temperature is 300 K. 1- Calculate the mass flow rate through the duct; [2 marks] 2- What percentage in area change would be necessary to reach a Mach number of 0.75? [2 marks] 3- What percentage in area change would be necessary to reach a Mach number of 1.00? [2 marks] b) A normal shock wave occurs in a gas with an unknown specific heat ratio. The static pressure ratio across the normal shock wave is 10.6. The Mach number downstream of the shock wave is equal to 0.495, find the specific heat ratio of the gas and the velocity ratio across the shock wave. [8 marks] c) Explain why successive infinitesimal compression waves tend to reinforce and form a shock wave. Use sketches to illustrate your answer. [5 marks] d) Show that for a choked convergent nozzle further…arrow_forwardAir at 290°K and 105 P a approaches a normal shock. The temperature downstream of the shock is 540°K. Find: (a) The velocity downstream of the shock. (b) The pressure change across the shock, and compare it with that calculated for an isentropic flow with the same deceleration.arrow_forwardA uniform supersonic airstream travelling at a Mach number of 9.0 passes over a concave corner, as shown in Figure 4. An oblique shockwave, which makes an angle of 30° with the flow direction, is attached to the corner under the given conditions. If the pressure and temperature in the uniform flow are 45 kPa and -30 °C respectively, determine the Mach number and deflection angle behind the wave.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning