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A Newtonian fluid is filled in the clearance between a shaft and a concentric sleeve. The sleeve attains a speed of 80 cm/s, when a force of 40 N is applied to the sleeve parallel to the shaft. Determine the speed if a force of 300N is applied.
- a)600 cm/s
- b)200 cm/s
- c)250 cm/s
- d)300 cm/s
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A Newtonian fluid is filled in the clearance between a shaft and a con...
Concept:
Newtonian fluids always follow Newton's law of Viscosity. Mathematically Newton's law of viscosity is represented as
Force equation from the above equation can be obtained as
where, μ = Coefficient of Viscosity, τ = Shear Stress
From the given question we can observe that Area(A), Viscosity(μ) and clearance(dy) is constant, hence Force is directly proportional to velocity.
Newtonian fluids always follow Newton's law of Viscosity. Mathematically Newton's law of viscosity is represented as
Force equation from the above equation can be obtained as
where, μ = Coefficient of Viscosity, τ = Shear Stress
From the given question we can observe that Area(A), Viscosity(μ) and clearance(dy) is constant, hence Force is directly proportional to velocity.
Calculation:
Given:
F1 = 40 N, F2 = 300 N, V1 = 80 cm/s
40/300 = 80/V2
V2 = 600 cm/s
Given:
F1 = 40 N, F2 = 300 N, V1 = 80 cm/s
40/300 = 80/V2
V2 = 600 cm/s
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Community Answer
A Newtonian fluid is filled in the clearance between a shaft and a con...
Given Data:
- Initial speed of the sleeve, \(v_1 = 80 \, cm/s\)
- Force applied on the sleeve, \(F_1 = 40 \, N\)
- Force to be determined, \(F_2 = 300 \, N\)
Explanation:
Newton's Law of Viscosity:
The relationship between the force applied to a Newtonian fluid and the resulting velocity is given by Newton's Law of Viscosity:
\[ F = \mu \frac{A(v)}{\Delta x} \]
Where:
- \(F\) = Force applied
- \(\mu\) = Viscosity of the fluid
- \(A\) = Area of contact between the fluid layers
- \(v\) = Velocity of the fluid layers
- \(\Delta x\) = Distance between the two layers
Using Newton's Law of Viscosity:
- For the initial condition:
\[ F_1 = \mu \frac{A(v_1)}{\Delta x} \]
- For the second condition:
\[ F_2 = \mu \frac{A(v_2)}{\Delta x} \]
Calculating the New Speed:
- Dividing the equations:
\[ \frac{F_2}{F_1} = \frac{v_2}{v_1} \]
- Substituting the given values:
\[ \frac{300}{40} = \frac{v_2}{80} \]
\[ v_2 = 600 \, cm/s \]
Therefore, the speed of the sleeve when a force of 300N is applied is 600 cm/s. Hence, option 'A' is correct.
- Initial speed of the sleeve, \(v_1 = 80 \, cm/s\)
- Force applied on the sleeve, \(F_1 = 40 \, N\)
- Force to be determined, \(F_2 = 300 \, N\)
Explanation:
Newton's Law of Viscosity:
The relationship between the force applied to a Newtonian fluid and the resulting velocity is given by Newton's Law of Viscosity:
\[ F = \mu \frac{A(v)}{\Delta x} \]
Where:
- \(F\) = Force applied
- \(\mu\) = Viscosity of the fluid
- \(A\) = Area of contact between the fluid layers
- \(v\) = Velocity of the fluid layers
- \(\Delta x\) = Distance between the two layers
Using Newton's Law of Viscosity:
- For the initial condition:
\[ F_1 = \mu \frac{A(v_1)}{\Delta x} \]
- For the second condition:
\[ F_2 = \mu \frac{A(v_2)}{\Delta x} \]
Calculating the New Speed:
- Dividing the equations:
\[ \frac{F_2}{F_1} = \frac{v_2}{v_1} \]
- Substituting the given values:
\[ \frac{300}{40} = \frac{v_2}{80} \]
\[ v_2 = 600 \, cm/s \]
Therefore, the speed of the sleeve when a force of 300N is applied is 600 cm/s. Hence, option 'A' is correct.
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A Newtonian fluid is filled in the clearance between a shaft and a concentric sleeve. The sleeve attains a speed of 80 cm/s, when a force of 40 N is applied to the sleeve parallel to the shaft. Determine the speed if a force of 300N is applied.a)600 cm/sb)200 cm/sc)250 cm/sd)300 cm/sCorrect answer is option 'A'. Can you explain this answer?
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