Figure 1 provides a diagram and Table 1 the steady-state operating data for a vapor power plant using water as the working fluid. The mass flow rate of the water is 12.4 kg/s. The turbine and pump operate have thermal losses and inefficiencies. Determine the thermal efficiency, work net output, rate of heat transfer during steam generation in kW, and the back work ratio. What is the thermal efficiency if you remove the pipe losses (hs and hi change so that hs = ha and hi =hs)? Steam generator Turbine

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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This problem must be presented in a logical order showing the necessary steps used to arrive at an answer. Each homework problem should have the following items unless otherwise stated in the problem:

a. Known: State briefly what is known about the problem.


b. Schematic: Draw a schematic of the physical system or control volume.


c. Assumptions: List all necessary assumptions used to complete the problem.


d. Properties: Identify the source of property values not given to you in the problem. Most sources will be from a table in the textbook (i.e. Table A-4).


e. Find: State what must be found.


f. Analysis: Start your analysis with any necessary equations. Develop your analysis as completely as possible before inserting values and performing the calculations. Draw a box around your answers and include units and follow an appropriate number of significant figures.

**Understanding the Rankine Cycle in Vapor Power Plants**

The diagram in Figure 1 and Table 1 provide essential information on the steady-state operating data for a vapor power plant using water as the working fluid. The mass flow rate of the water is specified to be 12.4 kg/s. Both the turbine and pump possess thermal losses and inefficiencies which impact the performance of the plant.

**Figure Description:**

**Figure 1 – Possible Rankine Cycle**

Figure 1 illustrates a possible Rankine Cycle for a vapor power plant. In this cycle:

- **Heat ( \( \dot{Q}_{in} \) )** is added in the steam generator.
- The high-pressure steam then moves to the **turbine** where work is extracted, denoted as \( \dot{W}_{t} \).
- The steam then flows to the condenser where heat ( \( \dot{Q}_{out} \) ) is rejected.
- Condensed water moves to the **pump** wherein work is supplied to the fluid, denoted as \( \dot{W}_{p} \).
- The process repeats as the pumped fluid returns to the steam generator.

**Table 1 – Steady-State Operating Data:**

The enthalpy values at various points in the cycle are provided in Table 1.

| State | h (kJ/kg) |
|-------|-----------|
| 1     | 2766.2    |
| 2     | 2024.4    |
| 3     | 190.3     |
| 4     | 206.9     |
| 5     | 198.6     |
| 6     | 2788.0    |

**Understanding the Data:**

- **State 1**: Represents the high-pressure steam entering the turbine.
- **State 2**: Represents the steam after expanding through the turbine.
- **State 3**: Represents the steam after condensation.
- **State 4**: Represents the liquid water after pumping.
- **State 5**: Represents the liquid water before entering the steam generator.
- **State 6**: Represents the final state after the heat is added to the steam generator.

**Key Questions:**

1. **Thermal Efficiency**: 
   - The thermal efficiency needs to be calculated taking into account thermal losses and inefficiencies.
   - Additionally, an ideal scenario is considered where pipe losses are
Transcribed Image Text:**Understanding the Rankine Cycle in Vapor Power Plants** The diagram in Figure 1 and Table 1 provide essential information on the steady-state operating data for a vapor power plant using water as the working fluid. The mass flow rate of the water is specified to be 12.4 kg/s. Both the turbine and pump possess thermal losses and inefficiencies which impact the performance of the plant. **Figure Description:** **Figure 1 – Possible Rankine Cycle** Figure 1 illustrates a possible Rankine Cycle for a vapor power plant. In this cycle: - **Heat ( \( \dot{Q}_{in} \) )** is added in the steam generator. - The high-pressure steam then moves to the **turbine** where work is extracted, denoted as \( \dot{W}_{t} \). - The steam then flows to the condenser where heat ( \( \dot{Q}_{out} \) ) is rejected. - Condensed water moves to the **pump** wherein work is supplied to the fluid, denoted as \( \dot{W}_{p} \). - The process repeats as the pumped fluid returns to the steam generator. **Table 1 – Steady-State Operating Data:** The enthalpy values at various points in the cycle are provided in Table 1. | State | h (kJ/kg) | |-------|-----------| | 1 | 2766.2 | | 2 | 2024.4 | | 3 | 190.3 | | 4 | 206.9 | | 5 | 198.6 | | 6 | 2788.0 | **Understanding the Data:** - **State 1**: Represents the high-pressure steam entering the turbine. - **State 2**: Represents the steam after expanding through the turbine. - **State 3**: Represents the steam after condensation. - **State 4**: Represents the liquid water after pumping. - **State 5**: Represents the liquid water before entering the steam generator. - **State 6**: Represents the final state after the heat is added to the steam generator. **Key Questions:** 1. **Thermal Efficiency**: - The thermal efficiency needs to be calculated taking into account thermal losses and inefficiencies. - Additionally, an ideal scenario is considered where pipe losses are
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