Please show all work clearly. Also, this problem is not meant to take the literal calculation of densities and pressure
Posted: Mon Jul 11, 2022 1:15 pm
Please show all work clearly. Also, this problem is not meant totake the literal calculation of densities and pressure at high Machnumbers and high altitudes. Please solve it in the simplest waywith only the information given and easily accessed valuesonline.
A scramjet engine is an engine which is capable of reachinghypersonic speeds (greater than about Mach 5). Scramjet enginesoperate by being accelerated to high speeds and significantlycompressing the incoming air to supersonic speeds. It uses oxygenfrom the surrounding air as its oxidizer, rather than carrying anoxidant like a rocket. Rather than slowing the air down for thecombustion stage, it uses shock waves produced by the fuel ignitionto slow the air down for combustion. The supersonic exhaust is thenexpanded using a nozzle. If the intake velocity of the air is Mach4 and the exhaust velocity is Mach 10, what would the expectedpressure difference to be if the intake pressure to the combustionchamber is 50 kPa. Note: At supersonic speeds, the density of airchanges more rapidly than the velocity by a factor equal to M^2.The inlet density can be assumed to be 1.876x10^-4 g/cm^3 at 50,000feet. The relation between velocity and air density change, takinginto account the significant compressibility due to the high Machnumber (the ration between the local flow velocity and the speed ofsound), is:
−𝑀^2 (𝑑𝑣/𝑣) = 𝑑𝜌/𝜌
The speed of sound at 50,000 ft is 294.96 m/s.
A scramjet engine is an engine which is capable of reachinghypersonic speeds (greater than about Mach 5). Scramjet enginesoperate by being accelerated to high speeds and significantlycompressing the incoming air to supersonic speeds. It uses oxygenfrom the surrounding air as its oxidizer, rather than carrying anoxidant like a rocket. Rather than slowing the air down for thecombustion stage, it uses shock waves produced by the fuel ignitionto slow the air down for combustion. The supersonic exhaust is thenexpanded using a nozzle. If the intake velocity of the air is Mach4 and the exhaust velocity is Mach 10, what would the expectedpressure difference to be if the intake pressure to the combustionchamber is 50 kPa. Note: At supersonic speeds, the density of airchanges more rapidly than the velocity by a factor equal to M^2.The inlet density can be assumed to be 1.876x10^-4 g/cm^3 at 50,000feet. The relation between velocity and air density change, takinginto account the significant compressibility due to the high Machnumber (the ration between the local flow velocity and the speed ofsound), is:
−𝑀^2 (𝑑𝑣/𝑣) = 𝑑𝜌/𝜌
The speed of sound at 50,000 ft is 294.96 m/s.