Question

Water vapour at 90 kPa and 150°C enters a subsonic diffuser with a velocity of 150 m/s and leaves the diffuser at 190 kPa with a velocity of 55 m/s, and during the process, 1.5 kJ/kg of heat is lost to the surrounding. For water vapour, c_p is 2.1 kJ/kgK. The final temperature of water vapour will be
1. 154°C 
2. 158°C
3. 162°C
4. 166°C

Answer 1

Correct Answer - Option 1 : 154°C 

Concept:

Steady flow energy equation at input and output of the diffuser is

\({h_1} + \frac{{v_1^2}}{{2000}} + q = {h_2} + \frac{{v_2^2}}{{2000}}\)

Calculation:

\({C_p}{T_1} + \frac{{{{150}^2}}}{{2000}} + \left( { - 1.5} \right) = {C_p}{T_2} + \frac{{{{55}^2}}}{{2000}}\)

\(2.1 \times 423 + \frac{{{{150}^2}}}{{2000}} + \left( { - 1.5} \right) = 2.1 \times {T_2} + \frac{{55^ 2\;}}{{2000}}\)

∴ T₂ = 426.92 K

∴ T₂ = 153.92°C