Team enters a turbine operating at steady state at 2 MPa, 360°C with a velocity of 100 m/s. Saturated vapor exits at 0.1 MPa and a velocity of 50 m/s. The elevation of the inlet is 3 m higher than at the exit. The mass flow rate of the steam is 15 kg/s, and the power developed is 7 MW. Let g = 9.81 m/s2. Determine (a) the area at the inlet, in m2, and (b) the rate of heat transfer between the turbine and its surroundings, in kW.

-313.7 KW

Explanation:

Given

Fluid: Steam

Inlet 1:

Pressure = 2MPa

Temperature = 360°C

Velocity = 100 m/s

Exit 2:

Saturated vapor

Pressure = 0 .1 MPa

Velocity = 50 m/s  

Mass flow rate m = 15 Kg/s

The elevation of the inlet = 3 m

Gravitational force g = 9.81 m/s^2

Power developed W = +7 MW  

Required

a) The area at the inlet  

b) The rate of heat transfer between the turbine and its surroundings  

Assumption

Constant average values.

Steady flow.  

Solution

a) specific volume for steam at and from table

Mass flow rate could be defined by.

Then area at inlet could be calculated as following.

b)

Energy equation could be defined by.

specific enthalpy for steam at  and  from table

specific enthalpy for steam at and in saturated vapor state from table

Then The rate of heat transfer between the turbine and its surroundings could be calculated as following.

=-313.7 KW

As the sign is negative it means that the heat transfer is from turbine to the surrounding.

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