Question

Air at 80 kPa and 10°C enters an adiabatic diffuser steadily with a velocity of 150 m/s and leaves with a low velocity at a pressure of 100 kPa. The exit area of the diffuser is 5 times the inlet area. Determine: i. the exit temperature of the air, and ii. the exit velocity of air.

Answer 1

The exit temperature is 293.74 K.

Step-by-step explanation:

Given that

At inlet condition(1)

P =80 KPa

V=150 m/s

T=10 C

Exit area is 5 times the inlet area

Now

`A_2=5A_1`

If consider that density of air is not changing from inlet to exit then by using continuity equation

`A_1V_1=A_2V_2`

So
`A_1* 150=5A_1V_2`

`V_2=30`m/s

Now from first law for open system

`h_1+(V_1^2)/(2)+Q=h_2+(V_2^2)/(2)+w`

Here Q=0 and w=0

`h_1+(V_1^2)/(2)=h_2+(V_2^2)/(2)`

When air is treating as ideal gas

`h=C_pT`

Noe by putting the values

`h_1+(V_1^2)/(2)=h_2+(V_2^2)/(2)`

`1.005* 283+(150^2)/(2000)=1.005* T_2+(30^2)/(2000)`

`T_2=293.74K`

So the exit temperature is 293.74 K.