Question

Air enters a gas turbine system with a velocity of 105 m/s and has a specific volume of 0.8m3 /kg. The inlet area of the gas turbine system is 0.05m2. At exit the air has a velocity of 135m/s and has a specific volume of 1.5 m3 /kg. In its passage through the turbine system, the specific enthalpy of air is reduced by 145kJ/kg and the air also has a heat transfer loss of 27 kJ/kg. Determine: (a) The mass flow rate of the air through the turbine system in kg/s? (b) The exit area of the turbine system in mạ ? (c) The power developed by the turbine system in kW?

Answer 1

$Q=AV=0.05\times105 m^3/s$

a.

$V= 0.8 m^3/kg \\ m= \frac{Q}{V}=6.5625 kg/s$

b.

$g_1 a_1 v_1=g_2 a_2 v_2 \; \;\;\;at steady \;\;\;stafe\\ \frac{1}{1.8}\times0.05\times105= \frac{1}{1.5} \times a_2 \times135 \\ a_2=0.0729m^2$

c.

$δq – δw =dH + d(ke)\\ -27 - δw = -145 + \frac{1}{2}(135^2 – 105_2)\times10^-3\\ -27 - δw = -145 +3.6\\ δw= 145 -3.6 -27\\ δw= 114.4 ks/kg\\$

$power developed = 114.4\times6.5625 kw\\ P=750.75 kw$