Question

Question 1 A steam turbine drives an electric generator (so the turbine delivers shaft work). The inlet steam flows through a 12.0 cm diameter pipe to the turbine at the rate of 2.50 kg/s at 600.0 °C and 10.0 bar absolute. The exit steam discharges through a 25.0 cm diameter pipe at 400.0 °C and 1.00 bar absolute. The turbine is adiabatic, and the process is at steady state. Neglect the potential energy effects.

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(a) Calculate ∆Ek term for the steam. (Hint: Think how you can calculate velocity (m/s) of

steam from cross-sectional area of pipe (m2), mass flow rate (kg/s), and specific volume of steam (m3/kg). You can get steam properties including specific volume from the steam tables.)

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(b) Calculate ∆H term for the steam.

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(c) Comparingtheresultsfrom(a)and(b),whichone(∆Ekor∆H)hasthelargestcontribution

to the energy balance over the steam turbine.

(d) Calculate the shaft work delivered by the turbine in kW using the energy balance.

Answer 1

Given that,

A steam turbine drives an electric generator (so the turbine delivers shaft work).

The inlet steam flows through a diameter pipe to the turbine at the rate of at and absolute.

The exit steam discharges through a diameter pipe at and absolute.

Clearly we can see, since the both the temperatures of the steam are above 3730C (that is the critical point of water) both the steam are in superheated state.

(a) ∆Ek term, that means the change in kinetic energy is given by the equation,

To calculate the velocity of outlet and inlet stream we have the equation for mass flow rate as,

Here is the density of the gas at inlet condition, which can be found from the steam table as,

is the area of cross section of the inlet pipe, which can be calculated as,

To calculate the velocity of outlet and inlet stream we have the equation for mass flow rate as,

Here is the density of the gas at outlet condition, which can be found from the steam table as,

is the area of cross section of the outlet pipe, which can be calculated as,

So ∆Ek term, that means the change in kinetic energy is 21411.305 J/s

(b) for the steam can be calculated as,

Here is the specific enthalpy of the gas at outlet condition, which can be found from the steam table as,

Here is the specific enthalpy of the gas at inlet condition, which can be found from the steam table as,

So ∆H term, that means the change in enthalpy is -1049875 J/s

(c) So comparing the result from (a) and (b) the enthalpy term has the largest contribution to the energy balance over steam turbine.

(d) Using the energy balance equation we have,

Since the turbine is adiabatic , and the potentail energy change in the turbine is since it is negligible,

So shaft work delivered by the turbine in kW using the energy balance is 1028.463 kW