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For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE?
  • a)
    It increases until the flow is fully developed.
  • b)
    It is constant and is equal to the average velocity in the fully developed region.
  • c)
    It decreases until the flow is fully developed.
  • d)
    It is constant but always lower than the average velocity in the fully developed region.
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
For steady flow of a viscous incompressible fluid through a circular p...
The average velocity in pipe flow always be same either for developing flow or fully developed flow. OPTION (B) IS CORRECT.

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For steady flow of a viscous incompressible fluid through a circular p...
Statement:
For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant.

Explanation:
In fluid mechanics, the fully developed region refers to the portion of a pipe or channel where the flow velocity profile becomes fully developed and remains constant along the length of the pipe. This region is typically located far away from any disturbances or entry/exit effects.

Developing Region:
The developing region, on the other hand, refers to the portion of the pipe where the flow velocity profile is still changing and has not yet reached the fully developed state. It is the region closer to the entry section of the pipe.

Statement Analysis:
The given statement states that the average velocity in the fully developed region is constant. This is true because in the fully developed region, the flow velocity profile becomes fully developed and remains constant along the length of the pipe.

Answer Explanation:
The question asks about the average velocity in the developing region.

Option A: It increases until the flow is fully developed.
This option is incorrect because the velocity in the developing region does not necessarily increase. It depends on the flow conditions and the specific pipe geometry.

Option B: It is constant and is equal to the average velocity in the fully developed region.
This option is correct. In the fully developed region, the average velocity is constant. As the flow progresses from the developing region to the fully developed region, the velocity profile becomes fully developed and remains constant. Therefore, the average velocity in the developing region is equal to the average velocity in the fully developed region.

Option C: It decreases until the flow is fully developed.
This option is incorrect because the velocity in the developing region does not necessarily decrease. It depends on the flow conditions and the specific pipe geometry.

Option D: It is constant but always lower than the average velocity in the fully developed region.
This option is incorrect because the average velocity in the developing region can be equal to the average velocity in the fully developed region. It depends on the flow conditions and the specific pipe geometry.

Conclusion:
The correct answer is option B. The average velocity in the developing region is constant and is equal to the average velocity in the fully developed region.
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For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE?a)It increases until the flow is fully developed.b)It is constant and is equal to the average velocity in the fully developed region.c)It decreases until the flow is fully developed.d)It is constant but always lower than the average velocity in the fully developed region.Correct answer is option 'B'. Can you explain this answer?
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