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A Newtonian fluid fills the clearance between a shaft and a sl

Question

A Newtonian fluid fills the clearance between a shaft and a sleeve. When a force of $800 N$ is applied to the shaft, parallel to the sleeve, the shaft speed of $1.5 c m / sec$ . If a force of $2.4 k N$ is applied instead, the shaft would move with a speed of

1.5 c m / sec

13.5 c m / sec

4.5 c m / sec

None

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A Newtonian fluid fills the clearance between a shaft and a sleeve. When a force of

800 N

is applied to the shaft, parallel to the sleeve, the shaft speed of

1.5 c m / sec

. If a force of

2.4 k N

is applied instead, the shaft would move with a speed of

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Text solutionVerified

Using the relation

τ = μ \frac{d u}{d y}

. Here

τ

is the shear stress between the layers of the liquid which is equal to

\frac{F}{A}

d u

is the change of velocity=

u - 0 = u

and

d y

is the clearance which is equal to

y

.
Thus we get

\frac{F}{A} = μ \frac{u}{y}

F = \frac{A μu}{y} \propto u

Thus we get

\frac{F _{1}}{u _{1}} = \frac{F _{2}}{u _{2}}

Substituting the values we get

\frac{800}{1.5} = \frac{2400}{u _{2}}

Thus we get

u_{2} = 4.5 c m / s

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Question Text	A Newtonian fluid fills the clearance between a shaft and a sleeve. When a force of $800 N$ is applied to the shaft, parallel to the sleeve, the shaft speed of $1.5 c m / sec$ . If a force of $2.4 k N$ is applied instead, the shaft would move with a speed of
Answer Type	Text solution:1
Upvotes	150