# Steam turbine output power

The mass rate of flow into a steam turbine is 4500 kg/h and the heat transfer from the turbine is 8.8 kW. The following data are known for the steam entering and leaving the turbine.

Inlet Exit

Pressure 20 bar 1 bar

Temperature 420 C

Quality 100%

Velocity 60 m/s 150 m/s

Elevation above datum 5 m 3 m

Determine the output power of the turbine.

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Solution:

The useful power can be determined by applying the equation of energy:

(1)

where

steam (water) mass flow rate (kg/s)

inlet specific static enthalpy (and similarly for the outlet) (kJ/kg)

inlet, respectively outlet velocities (m/s)

elevations above datum (m)

g = gravity acceleration (g = 9.8 m/s2)

output (useful) power of turbine (kW)

heat transfer rate from turbine (kW)

ïƒ (2)

Assuming an isentropic process between inlet and outlet, the following formula applies:

(3)

where

k = adiabatic exponent (for superheated steam, k = 1.3)

T1 = 420ï‚°C = 420 + 273 = 693 K

specific heat of steam at constant pressure (kJ/kg.K)

Assuming a constant average value of specific heat during the process, we can use the formula:

(4)

where

R = steam gas constant, R = 461.9 J/kg.K

ïƒ

By substituting in (2), one yields:

(5)

ïƒ

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