The energy balance for oneinletoneexit system is:
Applying the basic assumptions for turbines, the energy balance can
be rewritten as:
Water enters the turbine at 300 K and 750 kPa. At 300 K and 750 kPa,
water is compressed liquid. The enthalpy of compressed liquid can be
approximated by
h = h_{f@T} + v_{f} (P  P_{sat.})
where
h_{f@T} = the enthalpy of saturated water at
temperature
given
v_{f} = the specific volume of saturated water at
temperature
given
P_{sat.} = the saturation pressure at temperature given
From the water table, the saturated properties of water at 300 K are:
h_{f@300 k} = 104.89 kJ/kg
v_{f} = 0.001003 m^{3}/kg
P_{sat.} = 3.169 kPa
Hence, enthalpy
at 300 K and 750 kPa is:
h_{1 }= 104.89 + 0.001003(750
 3.169)
= 105.64
kJ/kg
At 300 K and 170 kPa, water is compressed liquid also. Using the same
approximation, the enthalpy of water at 300 K and 170 kPa is
h_{2} = 104.89 + 0.001003(170
 3.169)
= 105.06 kJ/kg
Substituting these enthalpies and the given mass flow rate to the energy
balance equation yields
 =
10,000/3,600(105.06  105.64) = 1.6 kW =
1.6 kW
The power is generated by the system, so it is positive.
The power needs for lighting an apartment is 500 W, which is smaller
than the power generated by the turbine.
500 W < 1.6 kW = 1,600 W
Hence, the result shows the turbine can be used to generate power for
the lighting system.
