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While water passes through a given pipe at mean velocity V, the flow is found to change from laminar to turbulent. If another fluid of specific gravity 0.8 and coefficient of viscosity 20% of that of water, is passed through the same pipe, the transition of flow from laminar to turbulent is expected if the flow velocity is :
  • a)
    2V
  • b)
    V
  • c)
    V/2
  • d)
    V/4
Correct answer is option 'D'. Can you explain this answer?
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Explanation:
The transition from laminar to turbulent flow depends on the Reynolds number (Re) of the fluid flowing through the pipe. Reynolds number is given by:

Re = (ρVD)/μ

where ρ is the density of the fluid, V is the velocity of the fluid, D is the diameter of the pipe, and μ is the coefficient of viscosity of the fluid.

When the Reynolds number is less than 2000, the flow is laminar, and when it is greater than 4000, the flow is turbulent. The transition from laminar to turbulent occurs in the range of 2000 to 4000.

Given that the specific gravity of the new fluid is 0.8 and the coefficient of viscosity is 20% of that of water, the density of the new fluid can be calculated as:

ρ_new = 0.8ρ_water

The coefficient of viscosity of the new fluid can be calculated as:

μ_new = 0.2μ_water

Substituting these values in the Reynolds number equation, we get:

Re_new = (0.8ρ_water VD)/(0.2μ_water)

Re_new = 16ρ_waterVD/μ_water

The Reynolds number for the new fluid is 16 times less than that of water.

To maintain the laminar flow for the new fluid, the velocity of the new fluid should be 16 times less than that of water. Therefore, the velocity of the new fluid should be:

V_new = V/16

To find the velocity at which the flow transitions from laminar to turbulent for the new fluid, we need to calculate the Reynolds number for the new fluid at this velocity.

Re_new = (0.8ρ_water (V/4)D)/(0.2μ_water)

Re_new = 4ρ_waterVD/μ_water

Substituting the values of ρ_water and μ_water, we get:

Re_new = 80VD/μ_new

Re_new = 80VD/(0.2μ_water)

Re_new = 400VD/μ_water

Since the Reynolds number for the new fluid at this velocity is greater than 4000, the flow transitions from laminar to turbulent.

Therefore, the correct answer is option D, i.e., the transition of flow from laminar to turbulent is expected at a velocity of V/4.
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While water passes through a given pipe at mean velocity V, the flow is found to change from laminar to turbulent. If another fluid of specific gravity 0.8 and coefficient of viscosity 20% of that of water, is passed through the same pipe, the transition of flow from laminar to turbulent is expected if the flow velocity is :a)2Vb)Vc)V/2d)V/4Correct answer is option 'D'. Can you explain this answer?
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While water passes through a given pipe at mean velocity V, the flow is found to change from laminar to turbulent. If another fluid of specific gravity 0.8 and coefficient of viscosity 20% of that of water, is passed through the same pipe, the transition of flow from laminar to turbulent is expected if the flow velocity is :a)2Vb)Vc)V/2d)V/4Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about While water passes through a given pipe at mean velocity V, the flow is found to change from laminar to turbulent. If another fluid of specific gravity 0.8 and coefficient of viscosity 20% of that of water, is passed through the same pipe, the transition of flow from laminar to turbulent is expected if the flow velocity is :a)2Vb)Vc)V/2d)V/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for While water passes through a given pipe at mean velocity V, the flow is found to change from laminar to turbulent. If another fluid of specific gravity 0.8 and coefficient of viscosity 20% of that of water, is passed through the same pipe, the transition of flow from laminar to turbulent is expected if the flow velocity is :a)2Vb)Vc)V/2d)V/4Correct answer is option 'D'. Can you explain this answer?.
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