Question

Air modeled as an ideal gas enters a well-insulated diffuser operating at steady state at 270 K with a velocity of 180 m/s and exits with a velocity of 48.4 m/s. For negligible potential energy effects, determine the exit temperature in K. The exit velocity is 48.4 m/s.

Answer 1

exit temperature 285 K

Step-by-step explanation:

given data

temperature T1 = 270 K

velocity = 180 m/s

exit velocity = 48.4 m/s

solution

we know here diffuser is insulated so here heat energy is negleted

so we write here energy balance equation that is

0 = m (h1-h2) + m ×
`((v1^2)/(2)-(v2^2)/(2))` .....................1

so it will be

`h1 + (v1^2)/(2) = h2 + (v2^2)/(2)` .....................2

put here value by using ideal gas table

and here for temperature 270K

h1 = 270.11 kJ/kg

`270.11 + (180^2* (1)/(1000))/(2) = h2 + (48.4^2* (1)/(1000))/(2)`

solve it we get

h2 = 285.14 kJ/kg

so by the ideal gas table we get

T2 = 285 K