There is a 1, mm thick layer of glycerine between a flat plate of area 100, cm^2 and a big plate. If

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9-1.Fluid Mechanics

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There is a $1\, mm$ thick layer of glycerine between a flat plate of area $100\, cm^2$ and a big plate. If the coefficient of viscosity of glycerine is $1.0\, kg\, (m-s)$, then ....... $N$ force is required to move the plate with a velocity of $7\, cm/s$ .

A

$0.7$

B

$0.1$

C

$0.2$

D

$0.6$

Solution

To move the plate with a constant velocity, the necessary force will be equal to the viscosity force

$\mathrm{F}(\text { say }) .$ Now $\mathrm{F}=\eta \mathrm{A} \frac{\Delta \mathrm{V}_{\mathrm{x}}}{\Delta \mathrm{z}}$

Here $\eta=1.0 \mathrm{kg} /(\mathrm{m}-\mathrm{s}) , \mathrm{A}=100 \mathrm{cm}^{2}=10^{-2} \mathrm{m}^{2}$

$\Delta v_{x}=7 \times 10^{-2} \mathrm{m} / \mathrm{sec}$ and $\Delta z=1 \mathrm{mm}=10^{-3} \mathrm{m}$

$\mathrm{F}=\frac{1.0 \times 10^{-2} \times\left(7 \times 10^{-2}\right)}{10^{-3}}=0.7 \mathrm{N}$

Standard 11

Physics

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