A piston moves along a tube containing air at an initial sound speed of 330 m/s. When the piston velocity is 250 m/s, it drives a shock wave which propagates at a velocity of 500 m/s. When the piston velocity is 100 m/s, it drives a shock at 400 m/s. Use the hypersonic equivalence principle to calculate the shock angles (in degrees) on a flat plate: At an incidence of 6 degrees and a Mach number of 7.2
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- Consider a cone at zero angle of attack in a hypersonic flow. (Hypersonic flow is very high-speed flow, generally defined as any flow above a Mach number of 5.) The half-angle of the cone is θc, as shown inthe figure. An approximate expression for the pressure coefficient on the surface of ahypersonic body is given by the newtonian sine-squared law : Cp = 2 sin2 θcNote that Cp, hence, p, is constant along the inclined surface of the cone. Along the base of the body, we assume that p = p∞. Neglecting the effect of friction, obtain an expression for the drag coefficient of the cone, where CD is based on the area of the base Sb.A supersonic aircraft flies with a speed of 2750 km/h at 27 °C and 100 kPa weather conditions. Two oblique shock waves are generated at leading nose and front window edges as shown in Figure (1). The deflection angles of nose and window edges are 15° and 9° respectively. Determine: 1. Mach number upstream the first shock wave (M1) 2. Normal Mach number upstream the first shock wave (Ma1) 3. Normal Mach number downstream the first shock wave (Myı) 4. Mach number upstream the second shock wave (M) 5. Normal Mach number upstream the second shock wave (M2) 6. Normal Mach number downstream the second shock wave (My2) 7. Mach number downstream the second shock wave (M3) 8. The pressure downstream the second shock wave. Take (y=1.4 and R = 287 J/kg.K) for air. Oblique shock waves M3 ? T1=27°C 9° M2 P3 ? P1 =100 kPa HHAUR HANCE 15° 1.22 1.62 0.72 1.45 2.2A supersonic aircraft flies with a speed of 2750 km/h at 27 °C and 100 kPa weather conditions. Two oblique shock waves are generated at leading nose and front window edges as shown in Figure (1). The deflection angles of nose and window edges are 15° and 9° respectively. Determine: 1. Mach number upstream the first shock wave (M1) 2. Normal Mach number upstream the first shock wave (Ma1) 3. Normal Mach number downstream the first shock wave (My1) 4. Mach number upstream the second shock wave (M2) 5. Normal Mach number upstream the second shock wave (M2) 6. Normal Mach number downstream the second shock wave (My2) 7. Mach number downstream the second shock wave (M3) 8. The pressure downstream the second shock wave. Take (y=1.4 and R = 287 J/kg.K) for air. Oblique shock waves M3 ? T1=27°C 9° M2 P3 ? P1 = 100 kPa AR FRANe 15°
- The speed of a supersonic aircraft flying at an altitude of 1,100 meters corresponds to a Mach number of 2.5. Estimate the time elapsed, in seconds, between the instant the aircraft was directly over head of an observer and the instant the observer feels the disturbance due to the aircraft. Presume that the temperature at the given height is 280°K, with k = 1.4 and R = 2.87 J/kg·K, in determining the questions of the following three cases: A) When the observer is stationaryB) When the observer is moving in the direction of the aircraft at M = 0.5C) When the observer is moving in the opposite direction with M = 0.5.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.Air pass through a wind tunnel at 70 kPa and 15 °C and the speed of air is 200 m/s. Mach number is 1.728 2.576 1.701 0.5879
- A 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.The tank is filled with air at 20°C and 139 kPa in stationary condition. Air is leaving the tank with flowing in a nozzle under steady-state condition. The flow is under isentropic and subsonic condition. The nozzle exit area is 18,59 cm?. After leaving from the nozzle, air strikes a vertical plate. Define the force [N] required to hold the plate stationary. (Note: Assume Pe=1 atm, kair=1.4, Rair=287 J/kg.K) Pte F Yanıt:(b) A normal shock wave passes through stagnant air at 22°C and atmospheric pressure of 130 kPa with a speed of 465 m/s as shown in Figure 3. Assume y= 1.4 and R= 287 J/kg.K. P2 V1 V2 Stationary shock wave Figure 3 [Gambarajah 3] (i) Determine the pressure and temperature downstream of the normal shock wave. (ii) Determine the velocity in the air immediately behind the normal shock wave.
- The instrument fairing on an aircraft is shown below, consisting of a forward ramp at30◦, a horizontal section, and a rear ramp at 25◦. During a flight in air at Mach 5.5,the static pressure is 42.6 kPa and the static temperature is 250 K. An oblique shockforms at the turn of the forward ramp, two expansion fans form at the front and rear ofthe horizontal section, and a second oblique shock forms at the turn of the rear ramp. (a) Calculate the Mach numbers and pressures at regions 2, 3, 4, and 5. (b) Determine stagnation pressure ratio p05/p01. (c) Tabulate the angles of all oblique shocks waves leading/trailing expansion waves relative to horizontal (not relative to flow angle). Gamma = 1.4, R=287 J/kgK PLEASE SHOW ALL WORKWhat is the Mach of airflow with 150 m/s at a pressure of 0.95 atm and a Density of 1.15 kg/m^3?One type of supersonic wind tunnel is a blow-down tunnel, where air is stored in a high-pressure reservoir, and then, upon the opening of a valve, exhausted through the tunnel into a vacuum tank or simply into the open atmosphere at the downstream end of the tunnel. For this example, weconsider just the high-pressure reservoir as a storage tank that is being charged with air by a high-pressure pump. As air is being pumped into the constant-volume reservoir, the air pressure inside the reservoir increases. The pump continues to charge the reservoir until the desired pressure is achieved.Consider a reservoir with an internal volume of 30 m3. As air is pumped into the reservoir, the air pressure inside the reservoir continually increases with time. Consider the instant during the charging process when the reservoir pressure is 10 atm. Assume the air temperature inside the reservoir is held constant at 300 K by means of a heat exchanger.Air is pumped into the reservoir at the rate of 1…