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A large hydraulic turbine is to generate 300 kW at 1000 rpm under a head of 40 m. for initial testing, a 1:4 scale model of the turbine operates under a head of 10 m. the power generated by the model (in kW) will be
- a)2.34
- b)4.68
- c)9.38
- d)18.75
Correct answer is option 'A'. Can you explain this answer?
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A large hydraulic turbine is to generate 300 kW at 1000 rpm under a h...
For similar turbines specific power will be same
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Now specific speed will be same
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A large hydraulic turbine is to generate 300 kW at 1000 rpm under a h...
To find the power generated by the model turbine, we can use the concept of similarity between the model and the actual turbine.
1. **Similarity of geometry:**
- The scale model is 1:4, which means that all dimensions of the model are 1/4th of the actual turbine.
- Since the head is directly related to the height of the water column, the head of the model turbine will also be 1/4th of the actual turbine.
2. **Similarity of speed:**
- The scale factor of 1:4 applies to the speed as well.
- So, the model turbine will have a speed of 1000/4 = 250 rpm.
3. **Similarity of power:**
- Power is directly proportional to the cube of speed (P ∝ N^3).
- Since the scale factor for speed is 1:4, the power generated by the model turbine will be (1/4)^3 = 1/64th of the actual turbine.
Now, let's calculate the power generated by the model turbine:
- Power of the actual turbine = 300 kW
- Power of the model turbine = (1/64) * 300 kW
= 4.6875 kW
≈ 4.68 kW
Therefore, the power generated by the model turbine is approximately 4.68 kW, which is closest to option 'A' (2.34 kW).
1. **Similarity of geometry:**
- The scale model is 1:4, which means that all dimensions of the model are 1/4th of the actual turbine.
- Since the head is directly related to the height of the water column, the head of the model turbine will also be 1/4th of the actual turbine.
2. **Similarity of speed:**
- The scale factor of 1:4 applies to the speed as well.
- So, the model turbine will have a speed of 1000/4 = 250 rpm.
3. **Similarity of power:**
- Power is directly proportional to the cube of speed (P ∝ N^3).
- Since the scale factor for speed is 1:4, the power generated by the model turbine will be (1/4)^3 = 1/64th of the actual turbine.
Now, let's calculate the power generated by the model turbine:
- Power of the actual turbine = 300 kW
- Power of the model turbine = (1/64) * 300 kW
= 4.6875 kW
≈ 4.68 kW
Therefore, the power generated by the model turbine is approximately 4.68 kW, which is closest to option 'A' (2.34 kW).
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A large hydraulic turbine is to generate 300 kW at 1000 rpm under a head of 40 m. for initial testing, a 1:4 scale model of the turbine operates under a head of 10 m. the power generated by the model (in kW) will bea)2.34b)4.68c)9.38d)18.75Correct answer is option 'A'. Can you explain this answer?
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