Hey everyone, having a lot of trouble solving this problem involving an adiabati

Question

Hey everyone, having a lot of trouble solving this problem involving an adiabatic turbine hopefully someone out there can help me!

An adiabatic turbine operates using steam as the working fluid. The steam enters the turbine at a pressure, temperature and flow velocity of 6 mPa, 600*C and 80 m/s respectivly. It leaves the turbine at 50 kPa, 100*C and 140 m/s. The power output of the turbine is known from experiments to be 5000 kW. Determine..

(a) The mass flow rate of the steam through the turbine.
(b) Whether the flow through the turbine is reversible or not.
(c) The entropy change of the the surroundings.
(d) The cross-sectional area of the inlet pipe to the turbine.

Thanks, Alex

Explanation / Answer

Pi = 6Mpa Ti = 600 deg C Vi = 80 m/s Po = 50 kPa To = 100 deg C Vo = 140 m/s W = 6 MW (a)Assume turbine as control volume with steady state condition 0 = Q - W + mdot(hi-ho+Vi^2/2-Vo^2/2), Adiabatic Q = 0 W = mdot(hi-ho+Vi^2/2-Vo^2/2) determine hi(Pi,Ti) and ho(Po,To) from steam table(super heat) then search for mdot, mass flow rate in kg/s (b) To determined reversible, compare entropy at inlet and at outlet, si(Pi,Ti) and so(Po,To). If the same in amount then reversible. Entropy outlet, So higher than entropy inlet, Si means irreversible. (c) ?s surr = So(Po,To) - Si(Pi,Ti) (d) mdot = Ao *Vo *?o(To,Po) Ao = mdot/Vo *?o(To,Po) mdot = mass flow rate, kg/s ?o(To,Po) = density at outlet state

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