Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.6. If the pressure and temperature of air are 58 kPa and 270 K, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those for helium undergoing a normal shock under the same conditions.

A flow of air with Mach number M1 = 2, pressure p1 = 0.7 atm, and temperature 630 degR is turned away from itself through an angle of 26.38 deg. Determine the Mach number, the staticpressure, the static temperature, and the stagnation pressure after the turn (all pressures in atm).Also determine the Mach angles at the beginning and end of the expansion fan.

Q1: Air enters a converging-diverging nozzle of a supersonic wind tunnel at 1 MPa and 300 K with a low velocity. If a normal shock wave occurs at the exit plane of the nozzle at Ma = 2.4, determine the pressure, temperature, Mach number, velocity, and stagnation pressure after the shock wave.

In compressible flow, velocity measurements with a Pitot probe can be grossly in error if relations developed for incompressible flow are used. Therefore, it is essential that compressible flow relations be used when evaluating flow velocity from Pitot probe measurements. Consider supersonic flow of air through a channel. A probe inserted into the flow causes a shock wave to occur upstream of the probe, and it measures the stagnation pressure and temperature to be 620 kPa and 340 K, respectively. If the static pressure upstream is 110 kPa, determine the flow velocity.

Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.6. The pressure and temperature of air are 52 kPa and 270 K, respectively. Now, helium undergoes a normal shock under the same conditions. Calculate the entropy changes of air and helium across the normal shock. The properties of air are R = 0.287 kJ/kg-K and cp= 1.005 kJ/kg-K, and the properties of helium are R=2.0769 kJ/kg-K and cp=5.1926 kJ/kg.K. The entropy change for air is The entropy change for helium is kJ/kg-K. kJ/kg-K.

Ahead of the normal shock wave, the upstream pressure , temperature, and Mach number are 0.53 atm, 255 K, and 2.8, respectively. Determine the pressure downstream of the shock wave.

n aircraft is flying at an altitude of 12000 metres (T=216.65 K. p = 0.193 bar) at a Mach number of 0.82. The cross sectional area of the inlet diffuser before the L.P. compressor stage is 0.5 m. Determine (a) the mass of air entering the compressor per second (b) the speed of the aircraft (c) the stagnation %3D pressure and temperature of air at the diffuser entry.

- Air at 200 kPa, 100°C, and Mach number Ma = 0.8 lows through a duct. Calculate the velocity and the stagnation pressure, temperature, and density of the air.

(b) Air flows through a cylindrical duct at a rate of 2.3 kg/s. Friction between air and the duct and friction within air can be neglected. The diameter of the duct is 10cm and the air temperature and pressure at the inlet are T₁ 450 K and P₁ = 200 kPa. If the Mach number at the exit is Ma2 determine the rate of heat transfer and the pressure difference across the duct. The constant pressure specific heat of air is cp = 1.005 kJ/kg-K. The gas constant of air is R = 0.287 kJ/kg-K and assume k = 1.4. -

For non-isentropic constant-area flow with stagnation temperature change the following relation was determined: Y 1 To _ ²(y + 1)M² (1 + ¹ Z ¹ M²) 2 TO (1+yM²)² It is possible to use the above equation and calculate the downstream Mach number without resorting to iteration for a flow where the upstream Mach number, as well as the upstream and downstream stagnation temperatures, are known. This is a common calculation for flows through engine combustors. Presuming the left side is a known quantity, show that the above equation can be directly solved as a quadratic in M² and which roots correspond to the subsonic/supersonic solution. Rewrite the equation as: aM4 + bM² + c = 0, and then M² = (−b ± √b² - 4ac)/2a. Determine the appropriate expressions for a, b, and c.