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PART - 2 CH - 9 Mechanical Properties of Fluids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 9 Mechanical Properties of Fluids3 Marks
Question
A liquid is kept in a cylindrical container which is being rotated around its axis. The support of the walls will rise higher. If the radius of the container is 0.05 m and speed of rotation is 2 revolutions per second then find the difference in height of the container between the center and the side of the container.
✓

Answer

According to the Bernoulli's theorem
$P+\frac{1}{2} \rho v^2=\text { Constant }$
The velocity is greater along the wall. Hence, the pressure will be less. But the pressure should be equal in the same horizontal surface. Hence liquid rises on the edges.
$\therefore \frac{1}{2} \rho v^2=\rho g h$
or $h=\frac{ v ^2}{2 g}$
But $v =r \omega=2 \pi nr$
$\begin{aligned}v & =2 \times \pi \times 2 \times 0.05 \\v & =0.2 \pi m / sec \\\therefore \quad h & =\frac{(0.2 \pi)^2}{2 \times 9.8}=\frac{0.04 \pi^2}{19.6}\end{aligned}$
But $\pi^2=9.86$
$\begin{aligned}\therefore \quad h & =\frac{0.04 \times 9.86}{19.6}=\frac{0.3944}{19.6}=0.02 m \\& =2 cm\end{aligned}$
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