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Two reservoirs at different levels are connected by two parallel pipes of diameter '2d' and 'd'. The ratio of the flows in the two pipes (larger: smaller) is
  • a)
  • b)
     2 : 1
  • c)
    4 : 1
  • d)
Correct answer is option 'C'. Can you explain this answer?
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Two reservoirs at different levels are connected by two parallel pipes...

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Two reservoirs at different levels are connected by two parallel pipes...
Analysis:
- Let the flow rates in the pipes of diameter 2d and d be Q1 and Q2 respectively.
- The flow rate is directly proportional to the fourth power of the diameter of the pipe.
- Therefore, the flow rate in the pipe of diameter 2d is proportional to (2d)^4 = 16d^4
- Similarly, the flow rate in the pipe of diameter d is proportional to d^4

Solution:
- Since the pipes are connected in parallel, the total flow rate into both reservoirs must be the same.
- Therefore, Q1 = Q2
- This gives us 16d^4 = d^4
- Simplifying, we get 16 = 1
- Hence, the ratio of the flows in the two pipes (larger: smaller) is 16:1 = 4:1.
Therefore, the correct answer is option C) 4 : 1.
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Two reservoirs at different levels are connected by two parallel pipes of diameter '2d' and 'd'. The ratio of the flows in the two pipes (larger: smaller) isa)b)2 : 1c)4 : 1d)Correct answer is option 'C'. Can you explain this answer?
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