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

Answer:

exit temperature 285 K

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 ×  $(\frac{v1^2}{2}-\frac{v2^2}{2})$   .....................1

so it will be

$h1 + \frac{v1^2}{2} = h2 + \frac{v2^2}{2}$      .....................2

put here value by using ideal gas table

and here for temperature 270K

h1 = 270.11 kJ/kg

$270.11 + \frac{180^2\times \frac{1}{1000}}{2} = h2 + \frac{48.4^2\times \frac{1}{1000}}{2}$  

solve it we get

h2 = 285.14 kJ/kg

so by the ideal gas table we get

T2 = 285 K