Question

4. A turbine operating under steady flow conditions receives steam at the following state. pressure 13.8 bar, specific volume 0.143 m3/kg, i.e., 2590 kJ/kg, velocity 30 m/s. The state of the steam leaving the turbine is pressure 0.35 bar, specific volume 4.37 m3/kg, i.e., 2360 kJ/kg, velocity 90 m/s. Heat is lost to the surroundings at the rate of 0.25 kJ/s. If the rate of steam flow is 0.38 kg/s, what is the power developed by the turbine?

Answer 1

Answer on Question #71022, Physics / Molecular Physics | Thermodynamics

A turbine operating under steady flow conditions receives steam at the following state. Pressure 13.8 bar, specific volume $0.143\mathrm{m}^3/\mathrm{kg}$, i.e., $2590\mathrm{kJ/kg}$, velocity $30\mathrm{m/s}$. The state of the steam leaving the turbine is pressure 0.35 bar, specific volume $4.37\mathrm{m}^3/\mathrm{kg}$, i.e., $2360\mathrm{kJ/kg}$, velocity 90 m/s. Heat is lost to the surroundings at the rate of $0.25\mathrm{kJ/s}$. If the rate of steam flow is $0.38\mathrm{kg/s}$, what is the power developed by the turbine?

Answer:

In the above equation :

- the mass flow is in kg/s

- velocity in m/s

- internal energy in J/kg

- pressure in Pa

- specific volume m3/kg

- the value of Q is in J/s

Then the unit of W will be J/s or W.

$$m \left[ u _ {1} + p _ {1} v _ {1} \frac {C _ {1} ^ {2}}{2} + Z _ {1} g \right] \pm Q = m \left[ u _ {2} + p _ {2} v _ {2} \frac {C _ {2} ^ {2}}{2} + Z _ {2} g \right] + W$$ $$W = m \left[ (u _ {1} - u _ {2}) + (p _ {1} v _ {1} - p _ {2} v _ {2}) \frac {C _ {1} ^ {2} - C _ {2} ^ {2}}{2} \right] - Q$$ $$Z _ {1} = Z _ {2} = 0$$ $$W = 0.38 \, \text{kJ/kg} \left[ \left(2590 \, \frac{\text{kJ}}{\text{kg}} - 2360 \, \frac{\text{kJ}}{\text{kg}}\right) + \left(13.5 \cdot 10^{5} \, \text{Pa} \times 0.143 \, \frac{\text{m}^{3}}{\text{kg}} - 0.35 \cdot 10^{5} \, \text{Pa} \times 4.37 \, \frac{\text{m}^{3}}{\text{kg}}\right) \right. \\ \left. + \left(\frac{30^{2} \, \frac{\text{m}}{\text{s}} - 90^{2} \, \frac{\text{m}}{\text{s}}}{2}\right) \right] - 0.25 \, \text{kJ/s} = 1.029 \cdot 10^{5} \, \text{J/s} \, \text{or} \, 102.9 \, \text{kW}$$

Answer: 102.9 kW

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