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A model of a hydraulic turbine is tested at a head of 1/4th of that under which the full scale turbine works. The diameter of the model is half of that of the full scale turbine, if N is the RPM of the full scale turbine, then RPM of the model will be
- a)N/4
- b)N/2
- c)N
- d)2N
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A model of a hydraulic turbine is tested at a head of 1/4th of that un...
Given:
- The head of the model turbine is 1/4th of the head of the full-scale turbine.
- The diameter of the model turbine is half of the diameter of the full-scale turbine.
- The RPM of the full-scale turbine is N.
To find:
- The RPM of the model turbine.
Explanation:
To understand the relationship between the RPM of the model and full-scale turbine, we need to consider the principle of similitude. Similitude is a scaling technique used in engineering to design and test models that accurately represent the behavior of larger systems.
Geometric Similarity:
- The diameter of the model turbine is half of the diameter of the full-scale turbine. This implies that the linear dimensions (such as length, width, and height) of the model turbine are also half of those of the full-scale turbine.
- Geometric similarity states that if two objects are geometrically similar, their corresponding linear dimensions are proportional.
Dynamic Similarity:
- The head of the model turbine is 1/4th of the head of the full-scale turbine. This implies that the pressure drop across the model turbine is 1/4th of the pressure drop across the full-scale turbine.
- Dynamic similarity states that if two systems are dynamically similar, the forces acting on corresponding parts of the systems are proportional.
Applying Similarity Principles:
- Since the linear dimensions of the model turbine are half of those of the full-scale turbine, the rotational speed (RPM) of the model turbine should be adjusted to maintain dynamic similarity.
- According to the principle of geometric similarity, if the diameter is halved, the RPM should be doubled to maintain dynamic similarity.
- Therefore, the RPM of the model turbine will be 2N (twice the RPM of the full-scale turbine).
Conclusion:
The RPM of the model turbine is 2N. Therefore, option 'C' is the correct answer.
- The head of the model turbine is 1/4th of the head of the full-scale turbine.
- The diameter of the model turbine is half of the diameter of the full-scale turbine.
- The RPM of the full-scale turbine is N.
To find:
- The RPM of the model turbine.
Explanation:
To understand the relationship between the RPM of the model and full-scale turbine, we need to consider the principle of similitude. Similitude is a scaling technique used in engineering to design and test models that accurately represent the behavior of larger systems.
Geometric Similarity:
- The diameter of the model turbine is half of the diameter of the full-scale turbine. This implies that the linear dimensions (such as length, width, and height) of the model turbine are also half of those of the full-scale turbine.
- Geometric similarity states that if two objects are geometrically similar, their corresponding linear dimensions are proportional.
Dynamic Similarity:
- The head of the model turbine is 1/4th of the head of the full-scale turbine. This implies that the pressure drop across the model turbine is 1/4th of the pressure drop across the full-scale turbine.
- Dynamic similarity states that if two systems are dynamically similar, the forces acting on corresponding parts of the systems are proportional.
Applying Similarity Principles:
- Since the linear dimensions of the model turbine are half of those of the full-scale turbine, the rotational speed (RPM) of the model turbine should be adjusted to maintain dynamic similarity.
- According to the principle of geometric similarity, if the diameter is halved, the RPM should be doubled to maintain dynamic similarity.
- Therefore, the RPM of the model turbine will be 2N (twice the RPM of the full-scale turbine).
Conclusion:
The RPM of the model turbine is 2N. Therefore, option 'C' is the correct answer.
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A model of a hydraulic turbine is tested at a head of 1/4th of that un...
The relation between rpm (N), diameter (D) and head (H) is, 
Calculation:
Given:
Calculation:
Given:
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A model of a hydraulic turbine is tested at a head of 1/4th of that under which the full scale turbine works. The diameter of the model is half of that of the full scale turbine, if N is the RPM of the full scale turbine, then RPM of the model will bea)N/4b)N/2c)Nd)2NCorrect answer is option 'C'. Can you explain this answer?
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