Air enters a turbine with a stagnation pressure of 900 kPa and a stagnation temperature of 658K, and it is expanded to a stagnation pressure of 100 kPa. Assuming the expansion process is isentropic, determine the turbine power for a mass flow rate of 0.04 kg/s. What does the sign of the calculated power indicate

12.332 KW

The positive sign indicates work done by the system ( Turbine )

Explanation:

Stagnation pressure( P1 ) = 900 kPa

Stagnation temperature ( T1 ) = 658K

Expanded stagnation pressure ( P2 ) = 100 kPa

Expansion process is  Isentropic, also assume steady state condition

mass flow rate ( m ) = 0.04 kg/s

Calculate the Turbine power

Assuming a steady state condition

( p1 / p2 )^(r-1/r)  = ( T1 / T2 )

= (900 / 100)^(1.4-1/1.4) = ( 658 / T2 )

=  ( 9 )^0.285 = 658 / T2

∴ T2 = 351.22 K

Finally Turbine Power / power developed can be calculated as

Wt = mCp ( T1 - T2 )

    = 0.04 * 1.005 ( 658 - 351.22 )

    = 12.332 KW

The positive sign indicates work done by the system ( Turbine )

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