A vertical cylindrical container $($diameter D$)$ containing oil $($Kinematic viscosity $=2\mathrm{.}39$

$104$ m$2/$s and density $=780$ kg$/$m$3$

$)$ is rotating about its own axis at a constant angular

velocity $($anti$-$clockwise$)$ while also simultaneously translating along the horizontal direc$-$

tion with a fixed acceleration a$.$ Neglect the surface tension effects. Also, consider no spilling

of the oil out of the container is happening as the initial height of the oil Ho is much less than

the height of the cylindrical container H$.$ Take atmospheric pressure to be pa $=101$KP a

and acceleration due to gravity g $=9\mathrm{.}81$ m$/$sec$\mathrm{.}2$

$.($See Fig. $1($a$)).$

i$.$ What would be the equation for iso$-$pressure surfaces, if the fluid exhibits rigid$-$body

type motion without causing any resultant flow.

ii$.$ Will the free$-$surface be symmetric about the axis?