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  •  A thin horizontal disc of radius is located within a cylindrical cavity filled with oil whose v

 A thin horizontal disc of radius \mathrm{R} is located within a cylindrical cavity filled with oil whose viscosity is\mathrm{ ' \eta '.} The distance between the disc and horizontal planes of cavity is \mathrm{ ' h '. }The power developed by the viscous forces acting on the disc when it rotates with angular velocity \mathrm{ \omega} (The end effects are to be neglected)

Option: 1

\mathrm{\frac{4 \pi \eta \omega^2 R^4}{h}}


Option: 2

\mathrm{\frac{\pi \eta \omega^2 R^4}{4 h}}


Option: 3

\mathrm{\frac{\pi \eta \omega^2 R^4}{2 h}}


Option: 4

\mathrm{\frac{\pi \eta \omega^2 \mathrm{R}^4}{\mathrm{~h}}}


Answers (1)

best_answer

Area at radius \mathrm{r, d A=2 \pi r d r} (one side)

\mathrm{ v=\omega r }

\mathrm{ \begin{aligned} d F & =\eta \frac{v}{h} d A \\\\ d z & =d F r \\\\ z & =\eta \frac{\pi r 4 \omega}{2 h} \end{aligned} }
for both side \mathrm{P=2 \times \eta \frac{\pi r 4 \omega}{2 h} \times \omega}

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HARSH KANKARIA

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