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Which of the following statement is true? 
  • a)
    For an ideal fluid μ = 0, ρ = constant, K = 0
  • b)
    A floating body is in stable, unstable or neutral equilibrium accordingto as the metacentric height zero, positive or negative.
  • c)
    The exact analysis of viscous flow problems can be made by Euler'sequation
  • d)
    The most economical diameter of a pipe is the one for which theannual fixed cost and annual power cost (to overcome friction) areminimum.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which of the following statement is true?a)For an ideal fluid μ =...
Ans. (d) Here (a) is wrong: For an ideal fluid μ= 0, ρ = constant, K = const.
(b) is wrong: A floating body is in stable, unstable or neutral equilibrium according to as the metacentric height positive or negative or zero respectively. (c) is wrong: The exact analysis of viscous flow problems can be made by Navier stroke equations. Euler's equation is valid for nonviscous fluid.
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Most Upvoted Answer
Which of the following statement is true?a)For an ideal fluid μ =...
The correct answer is option 'D': The most economical diameter of a pipe is the one for which the annual fixed cost and annual power cost (to overcome friction) are minimum.

Explanation:

To determine the most economical diameter of a pipe, we need to consider the costs associated with the pipe's construction and operation. These costs typically include the annual fixed cost and the annual power cost.

1. Annual fixed cost:
The annual fixed cost includes expenses such as the initial cost of the pipe, installation costs, and maintenance costs. It is a fixed expense that does not vary with the flow rate or diameter of the pipe.

2. Annual power cost:
The annual power cost is the energy cost required to overcome the frictional losses in the pipe. It depends on the flow rate and the pipe diameter. As the flow rate increases, the power cost increases due to higher frictional losses. Similarly, as the diameter of the pipe increases, the power cost decreases as the flow has a larger cross-sectional area and encounters less friction.

To find the most economical diameter, we need to find the diameter at which the sum of the annual fixed cost and the annual power cost is minimum. This is because we want to minimize both the initial and operational costs.

By performing cost analysis and optimization calculations, we can determine the diameter that minimizes the total cost. This diameter will be the most economical choice for the given pipe system.

In practice, engineers and designers use cost optimization techniques, such as the concept of "life cycle cost analysis," to consider the total cost over the lifespan of the pipe system. This approach takes into account factors such as material costs, installation costs, maintenance costs, and energy costs.

In conclusion, the most economical diameter of a pipe is determined by minimizing the annual fixed cost and the annual power cost associated with the pipe's construction and operation. This optimization process ensures that the pipe system is cost-effective and efficient.
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Which of the following statement is true?a)For an ideal fluid μ = 0, ρ = constant, K = 0b)A floating body is in stable, unstable or neutral equilibrium accordingto as the metacentric height zero, positive or negative.c)The exact analysis of viscous flow problems can be made by Euler'sequationd)The most economical diameter of a pipe is the one for which theannual fixed cost and annual power cost (to overcome friction) areminimum.Correct answer is option 'D'. Can you explain this answer?
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