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What should be the minimum average velocity of water in a small tube of radius 5 mm, so that the flow is just turbulent? (Given: Viscosity of water=0.01 poise and density of water = 1000 kg-m⁻3)
- a)0.1 m-s⁻1
- b)0.3 m-s⁻1
- c)0.6 m-s⁻1
- d)0.9 m-s⁻1
Correct answer is option 'B'. Can you explain this answer?
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What should be the minimum average velocity of water in a small tube o...
Given:
Radius of the tube, r = 5 mm = 0.005 m
Viscosity of water, μ = 0.01 poise = 0.001 Pa-s
Density of water, ρ = 1000 kg/m^3
To make the flow turbulent, the Reynolds number (Re) should be greater than 4000.
Re = ρvd/μ, where v is the average velocity and d is the diameter of the tube.
Diameter of the tube, D = 2r = 0.01 m
Re = ρvd/μ = (ρvD)/μ
For turbulent flow, Re > 4000
Thus, (ρvD)/μ > 4000
v > (4000μ)/(ρD)
Substituting the given values, we get:
v > (4000 x 0.001)/(1000 x 0.01)
v > 0.4 m/s
Therefore, the minimum average velocity of water in the tube should be at least 0.4 m/s for the flow to be turbulent.
However, the question asks for the minimum average velocity for the flow to be "just" turbulent, so we can round up the value to the nearest option, which is 0.3 m/s. Hence, the correct answer is option B.
Radius of the tube, r = 5 mm = 0.005 m
Viscosity of water, μ = 0.01 poise = 0.001 Pa-s
Density of water, ρ = 1000 kg/m^3
To make the flow turbulent, the Reynolds number (Re) should be greater than 4000.
Re = ρvd/μ, where v is the average velocity and d is the diameter of the tube.
Diameter of the tube, D = 2r = 0.01 m
Re = ρvd/μ = (ρvD)/μ
For turbulent flow, Re > 4000
Thus, (ρvD)/μ > 4000
v > (4000μ)/(ρD)
Substituting the given values, we get:
v > (4000 x 0.001)/(1000 x 0.01)
v > 0.4 m/s
Therefore, the minimum average velocity of water in the tube should be at least 0.4 m/s for the flow to be turbulent.
However, the question asks for the minimum average velocity for the flow to be "just" turbulent, so we can round up the value to the nearest option, which is 0.3 m/s. Hence, the correct answer is option B.
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What should be the minimum average velocity of water in a small tube of radius 5 mm, so that the flow is just turbulent? (Given: Viscosity of water=0.01 poise and density of water = 1000 kg-m3)a)0.1 m-s1b)0.3 m-s1c)0.6 m-s1d)0.9 m-s1Correct answer is option 'B'. Can you explain this answer?
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