A cylindrical vessel with vertical axis is closed top and bottom with flat ends. Its diameter is $0\mathrm{.}5$ m and the height is $0\mathrm{.}67$ m $.$ It is filled with water to a depth of $0\mathrm{.}6$ m $,$ the remainder with air at atmospheric pressure. It is then revolved about its axis at a speed of $200$ rpm $.$ Calculate the force on the bottom and top covers.

$($Force on top $\backslash (=629\backslash$mathrm$\{$~N$\}\backslash ),$ force on bottom $\backslash (=1784\backslash$mathrm$\{$~N$\}\backslash ))$