Question

An adiabatic gas turbine expands air at 1300 kPa and 500◦C to 100 kPa and 127◦C. Air enters the turbine through a 0.2-m2 opening with an average velocity of 40 m/s, and exhausts through a 1-m2 opening. Determine (a) the mass flow rate of air through the turbine (b) the power produced by the turbine

Answer 1

Given:

Pressure,
`P_(1)` = 1300 kPa

Temperature,
`T_(1)` =
`500^(\circ)`

`P_(2)` = 100 kPa

`T_(2) = 127^(\circ)`

velocity, v = 40 m/s

A = 1
`m^(2)`

Solution:

For air propertiess at

`P_(1)` = 1300 kPa

`T_(1)` =
`500^(\circ)`

`h_(1)` = 793kJ/K

`v_(1)` =
`0.172(m^(3))/(kg)`

and also at

`P_(2)` = 100 kPa

`T_(2) = 127^(\circ)`

`h_(2)` = 401 KJ/K

`v_(2)` =
`1.15(m^(3))/(kg)`

a) Mass flow rate is given by:

`m' = (Av)/(v_(1))`

Now,

`m = (0.2* 40)/(0.172)` = 46.51 kg/s

b) for the power produced by turbine,
`P = m'(h_(1) - h_(2))`

`P = 46.51*(793 - 401)` = 18.231 MW