Question

Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is 300 m/s, temperature is 330 K and pressure is 180 kPa. Assume that the air behaves as a perfect gas with constant ๐’„๐’‘ =1.005 kJ/kg.K. The stagnation temperature at this point is _________ K (round off to two decimal places).

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Answer :

Correct answer is : 374.77

V = 300 m/s, T = 330 K, ฮณ = 1.4, R = 287 J/kg-K.

M = V ฮณ R T = 300 1.4 ร— 287 ร— 330  = 0.823

We know that,

T 0 T = 1 + ( ฮณ โˆ’ 1 2 ) M 2

T 0 = T { 1 + ( 1.4 โˆ’ 1 2 ) 0.823 2 }

To = 330 (1 + 0.1355) = 374.71 K

โˆด Stagnation temperature To = 374.71 K

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