In an impulse reaction turbine, the enthalpy drop in fixed and moving blades are 20 kJ/Kg and 40 kJ/Kg respectively. Then the degree of reaction of stage is.
0.66
This problem asks us to determine the degree of reaction for an impulse reaction turbine stage. Understanding the degree of reaction is crucial in the study of turbines, especially in the fields of thermodynamics and power plant engineering.
Reaction Turbine Degree of Reaction Defined
The degree of reaction, often represented by \(R\), is a fundamental concept in turbine design. It quantifies the proportion of the total enthalpy drop (or pressure drop) that occurs within the moving blades of a turbine stage, relative to the total enthalpy drop across the entire stage (both fixed and moving blades).
The general formula for the degree of reaction in terms of enthalpy drops is:
\[R = \frac{\text{Enthalpy drop in moving blades}}{\text{Total enthalpy drop in the stage}}\]The total enthalpy drop in the stage is the sum of the enthalpy drop that occurs in the fixed blades (nozzles or stationary cascade) and the enthalpy drop that occurs in the moving blades (rotor blades).
\[\text{Total enthalpy drop in stage} = \text{Enthalpy drop in fixed blades} + \text{Enthalpy drop in moving blades}\]Enthalpy Drop Data Provided
The question provides us with the following specific values for the enthalpy drops within this particular turbine stage:
- Enthalpy drop in fixed blades: \(20 \text{ kJ/Kg}\)
- Enthalpy drop in moving blades: \(40 \text{ kJ/Kg}\)
Total Enthalpy Drop Calculation
To use the degree of reaction formula, we first need to calculate the total enthalpy drop across the entire turbine stage. This is simply the sum of the enthalpy drops in the fixed and moving blades.
Let \(\Delta H_{fixed}\) be the enthalpy drop in fixed blades and \(\Delta H_{moving}\) be the enthalpy drop in moving blades.
\[\text{Total enthalpy drop in stage} = \Delta H_{fixed} + \Delta H_{moving}\]Substituting the given values:
\[\text{Total enthalpy drop in stage} = 20 \text{ kJ/Kg} + 40 \text{ kJ/Kg}\] \[\text{Total enthalpy drop in stage} = 60 \text{ kJ/Kg}\]Reaction Degree Calculation Steps
Now that we have both the enthalpy drop in the moving blades and the total enthalpy drop in the stage, we can proceed to calculate the degree of reaction \(R\).
\[R = \frac{\text{Enthalpy drop in moving blades}}{\text{Total enthalpy drop in the stage}}\]Substitute the values:
\[R = \frac{40 \text{ kJ/Kg}}{60 \text{ kJ/Kg}}\] \[R = \frac{4}{6}\] \[R = \frac{2}{3}\]Converting this fraction to a decimal value:
\[R \approx 0.6666...\]Rounding this value to two decimal places, the degree of reaction is approximately \(0.66\).
This result indicates that in this impulse reaction turbine stage, approximately 66% of the total enthalpy drop (and thus, energy conversion) occurs within the moving blades, while the remaining 34% occurs in the fixed blades.
Important Questions from Reaction Turbine
A draft tube is used with _____.
Reaction turbines are used for _____
When a hydraulic turbine is operated, it is found that it has a high design efficiency and this efficiency remains constant over a wide range of regulations from the design condition. What is the type of this turbine?
For a non-dimensional specific speed value of 1, for maximum efficiency, which of the following turbines is preferred?
- Which is the wrong statement about hydraulic turbine?
