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While water passes through a given pipe at mean velocity V the flow isfound to change from laminar to turbulent. If another fluid of specificgravity 0.8 and coefficient of viscosity 20% of that of water, is passed through the same pipe, the transition of flow from laminar to turbulentis 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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While water passes through a given pipe at mean velocity V the flow is...
Ans. (d) Rew =
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While water passes through a given pipe at mean velocity V the flow is...
Explanation:
Fluid Flow:
Fluid flow can be classified into two types: laminar flow and turbulent flow. In laminar flow, the fluid particles move in parallel layers with minimal mixing between them. In turbulent flow, the fluid particles move in irregular patterns with high mixing.
Transition from Laminar to Turbulent Flow:
The transition from laminar to turbulent flow depends on the Reynolds number (Re), which is a dimensionless quantity. It is given by the formula:
Re = (ρ * V * L) / μ
Where,
ρ = density of the fluid
V = velocity of the fluid
L = characteristic length (diameter of the pipe in this case)
μ = coefficient of viscosity of the fluid
Given Data:
For water:
Re = V * D / μ
For another fluid:
Re' = V' * D / μ'
Where,
V = velocity of water
D = diameter of the pipe
μ = coefficient of viscosity of water
V' = velocity of the other fluid
μ' = coefficient of viscosity of the other fluid
Specific Gravity:
Specific gravity (SG) is the ratio of the density of a substance to the density of a reference substance (usually water). In this case, the specific gravity of the other fluid is given as 0.8.
SG = ρ' / ρ
ρ' = density of the other fluid
ρ = density of water
Since the density of water is constant, we can write:
ρ' = SG * ρ
Coefficient of Viscosity:
The coefficient of viscosity of the other fluid is given as 20% of the coefficient of viscosity of water.
μ' = 0.2 * μ
Reynolds Number for the Other Fluid:
Substituting the given values, we can write the Reynolds number for the other fluid as:
Re' = V' * D / μ'
= V' * D / (0.2 * μ)
Since the densities of water and the other fluid are proportional, the Reynolds number for the other fluid can be simplified as:
Re' = V' * D / (0.2 * μ)
= (V' * D) / (0.2 * V * D)
= V' / (0.2 * V)
Transition from Laminar to Turbulent Flow:
The transition from laminar to turbulent flow occurs when the Reynolds number exceeds a critical value, which is typically around 2000. So, we can write:
Re' > 2000
V' / (0.2 * V) > 2000
V' > 2000 * 0.2 * V
V' > 400 * V
Therefore, the flow velocity (V') for the other fluid should be greater than 400 times the flow velocity (V) of water in order to transition from laminar to turbulent flow.
Answer:
Hence, the correct answer is option 'd) V/4'.
Fluid Flow:
Fluid flow can be classified into two types: laminar flow and turbulent flow. In laminar flow, the fluid particles move in parallel layers with minimal mixing between them. In turbulent flow, the fluid particles move in irregular patterns with high mixing.
Transition from Laminar to Turbulent Flow:
The transition from laminar to turbulent flow depends on the Reynolds number (Re), which is a dimensionless quantity. It is given by the formula:
Re = (ρ * V * L) / μ
Where,
ρ = density of the fluid
V = velocity of the fluid
L = characteristic length (diameter of the pipe in this case)
μ = coefficient of viscosity of the fluid
Given Data:
For water:
Re = V * D / μ
For another fluid:
Re' = V' * D / μ'
Where,
V = velocity of water
D = diameter of the pipe
μ = coefficient of viscosity of water
V' = velocity of the other fluid
μ' = coefficient of viscosity of the other fluid
Specific Gravity:
Specific gravity (SG) is the ratio of the density of a substance to the density of a reference substance (usually water). In this case, the specific gravity of the other fluid is given as 0.8.
SG = ρ' / ρ
ρ' = density of the other fluid
ρ = density of water
Since the density of water is constant, we can write:
ρ' = SG * ρ
Coefficient of Viscosity:
The coefficient of viscosity of the other fluid is given as 20% of the coefficient of viscosity of water.
μ' = 0.2 * μ
Reynolds Number for the Other Fluid:
Substituting the given values, we can write the Reynolds number for the other fluid as:
Re' = V' * D / μ'
= V' * D / (0.2 * μ)
Since the densities of water and the other fluid are proportional, the Reynolds number for the other fluid can be simplified as:
Re' = V' * D / (0.2 * μ)
= (V' * D) / (0.2 * V * D)
= V' / (0.2 * V)
Transition from Laminar to Turbulent Flow:
The transition from laminar to turbulent flow occurs when the Reynolds number exceeds a critical value, which is typically around 2000. So, we can write:
Re' > 2000
V' / (0.2 * V) > 2000
V' > 2000 * 0.2 * V
V' > 400 * V
Therefore, the flow velocity (V') for the other fluid should be greater than 400 times the flow velocity (V) of water in order to transition from laminar to turbulent flow.
Answer:
Hence, the correct answer is option 'd) V/4'.
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While water passes through a given pipe at mean velocity V the flow isfound to change from laminar to turbulent. If another fluid of specificgravity 0.8 and coefficient of viscosity 20% of that of water, is passed through the same pipe, the transition of flow from laminar to turbulentis 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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