The diffuser in a jet engine is designed to decrease the kinetic energy of the air entering the engine compressor without any work or heat interactions. Calculate the velocity at the exit of a diffuser when air at 100 kPa and 30°C enters it with a velocity of 357 m/s and the exit state is 200 kPa and 90°C. The specific heat of air at the average temperature of 60°C = 333 K is cp = 1.007 kJ/kg·K.

81.29 m/s

Explanation:

Given:

60°C = 333 K is cp = 1.007 kJ/kg·K.

at air inlet:

Pressure = 100 kPa

Temperature = 30°C

Velocity = 357 m/s

at air outlet:

Pressure = 200kPa

Temperature = 90°C

We can define the energy balance as:

- =  Δ = 0

therefore,        =  

m + m =m +  (taking m common and cancelling it)

4 + =    +  

The velocity at the exit of a diffuser:

= [ + 2 ( - )

= [ +  2  x   1000  x  1.007  x  (30-90)

= 81.29 m/s

therefore, the velocity at the exit of a diffuser is 81.29 m/s

the total distance traveled by the car is

30km + 49km = 79 km .