### Problem StatementWater vapor enters a turbine operating at steady state at 500°C and 40 bar, with a velocity of 200 m/s, and expands adiabatically to the exit, where it is saturated vapor at 0.8 bar, with a velocity of 150 m/s and a volumetric flow rate of 9.48 m³/s. Find the power developed by the turbine, in kW.### ExplanationThis problem involves calculating the power generated by a steam turbine under specified conditions. The process is adiabatic, meaning no heat is transferred to or from the surroundings. The power output is determined by the change in enthalpy and kinetic energy of the steam as it passes through the turbine.---Here are the steps to solving the problem:1. **Determine Initial and Final Conditions:** - Initial: 500°C, 40 bar, 200 m/s - Final: 0.8 bar, 150 m/s, 9.48 m³/s2. **Apply the Energy Balance Equation for Adiabatic Process:** The power developed (Ẇ) can be calculated using: \[ Ẇ = \dot{m} \times (\Delta h + \frac{\Delta (v^2)}{2}) \] where: - \(\dot{m}\) is the mass flow rate. - \(\Delta h\) is the change in specific enthalpy. - \(\Delta (v^2)\) is the change in specific kinetic energy.3. **Calculate Mass Flow Rate:** Mass flow rate \(\dot{m}\) can be derived from the volumetric flow rate using the final specific volume: \[ \dot{m} = \frac{\text{Volumetric flow rate}}{\text{Specific Volume}} \]4. **Use Steam Tables or Mollier Chart:** - Find specific enthalpies at initial and final conditions using steam tables.5. **Compute Change in Enthalpy and Kinetic Energy:** Substitute into the energy equation to find power developed.This method provides an understanding of how turbines harness the energy from steam to produce power, emphasizing thermodynamics and fluid dynamics principles.

Answered: Image /qna-images/answer/91abb175-b157-4c88-ab32-dcb93da50c50.jpg

2) Water vapor enters a turbine operating at steady state at 500°C, 40 bar, with a velocity of 200 m/s, and expands adiabatically to the exit, where it is saturated vapor at 0.8 bar, with a velocity of 150 m/s and a volumetric flow rate of 9.48 m³/s. Find the power developed by the turbine, in kW.

2) Water vapor enters a turbine operating at steady state at 500°C, 40 bar, with a velocity of 200 m/s, and expands adiabatically to the exit, where it is saturated vapor at 0.8 bar, with a velocity of 150 m/s and a volumetric flow rate of 9.48 m³/s. Find the power developed by the turbine, in kW.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

### Problem Statement

Water vapor enters a turbine operating at steady state at 500°C and 40 bar, with a velocity of 200 m/s, and expands adiabatically to the exit, where it is saturated vapor at 0.8 bar, with a velocity of 150 m/s and a volumetric flow rate of 9.48 m³/s. Find the power developed by the turbine, in kW.

### Explanation

This problem involves calculating the power generated by a steam turbine under specified conditions. The process is adiabatic, meaning no heat is transferred to or from the surroundings. The power output is determined by the change in enthalpy and kinetic energy of the steam as it passes through the turbine.

---

Here are the steps to solving the problem:

1. **Determine Initial and Final Conditions:**
- Initial: 500°C, 40 bar, 200 m/s
- Final: 0.8 bar, 150 m/s, 9.48 m³/s

2. **Apply the Energy Balance Equation for Adiabatic Process:**
The power developed (Ẇ) can be calculated using:

\[
Ẇ = \dot{m} \times (\Delta h + \frac{\Delta (v^2)}{2})
\]

where:
- \(\dot{m}\) is the mass flow rate.
- \(\Delta h\) is the change in specific enthalpy.
- \(\Delta (v^2)\) is the change in specific kinetic energy.

3. **Calculate Mass Flow Rate:**
Mass flow rate \(\dot{m}\) can be derived from the volumetric flow rate using the final specific volume:
\[
\dot{m} = \frac{\text{Volumetric flow rate}}{\text{Specific Volume}}
\]

4. **Use Steam Tables or Mollier Chart:**
- Find specific enthalpies at initial and final conditions using steam tables.

5. **Compute Change in Enthalpy and Kinetic Energy:**
Substitute into the energy equation to find power developed.

This method provides an understanding of how turbines harness the energy from steam to produce power, emphasizing thermodynamics and fluid dynamics principles.

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