Question

Steam enters a turbine operating at steady state with a mass flow of 30 kg/min, a specific enthalpy of 3100 kJ/kg. and a velocity of 30 m/s. At the exit, the specific enthalpy is 2600 kJ/kg and the velocity is 45 m/s. The elevation of the inlet is 3 m higher than at the exit. Heat transfer from the turbine to its surroundings occurs at a rate of 1.1 kJ per kg of steam flowing. Let.g=9.81 m/s² . Determine the power developed by the turbine, in kW.

Answer 1

The power developed by the turbine is 21000 kW.

Step-by-step explanation:

To determine the power developed by the turbine, we need to calculate the change in specific enthalpy and the change in kinetic energy.

The change in specific enthalpy can be calculated using the formula:

ΔH = Hexit - Hinlet

Using the given values, ΔH = 2600 kJ/kg - 3100 kJ/kg = -500 kJ/kg.

The change in kinetic energy can be calculated using the formula:

ΔKE = (1/2) * (Vexit2 - Vinlet2)

Using the given values, ΔKE = (1/2) * (45 m/s)2 - (30 m/s)2 = 225 - 450 = -225 m2/s2.

The power developed by the turbine can be calculated using the formula:

Power = (m_dot * (ΔH + ΔKE) - Q)

Where m_dot is the mass flow rate, Q is the heat transfer rate, and ΔH and ΔKE are the changes in specific enthalpy and kinetic energy, respectively.

Using the given values, Power = (30 kg/min * (-500 kJ/kg + (-225 m2/s2)) - 1.1 kJ/kg * 30 kg/min) = -21000 kW.

Since power cannot be negative, we can conclude that the power developed by the turbine is 21000 kW.