$1.$a$)$ What is the difference between dynamic viscosity and kinematic

viscosity? State their unit of measurements. Determine the

viscosity of a liquid having kinematic viscosity $6$ stokes and

specific gravity $1\mathrm{.}9.$

b$)$ The right limb of a simple U$-$tube manometer containing mercury

is open to the atmosphere while the left limb is connected to a

pipe in which a fluid of sp$.$ gr$.0\mathrm{.}9$ is flowing. The centre of the

pipe is $12$ cm below the level of mercury in the right limb$.$ Find

the pressure of fluid in the pipe if the difference of mercury level

in the two limbs is $20$ cm $.$

$2.$a$)$ A rectangular plane surface $2$ m wide and $3$ m deep lies in water

in such a way that its plane makes an angle of $30$ degree with the

free surface of water. Determine the

i$)$ Total pressure and

ii$)$ Position of centre of pressure when the upper edge is $1\mathrm{.}5$ m

below the free water surface.

b$)$ A solid cylinder of diameter $5\mathrm{.}0$ m has a height of $5\mathrm{.}0$ m $.$ Find the

meta$-$centric height of the cylinder if the specific gravity of the

material of cylinder is $0\mathrm{.}7$ and it is floating in water with its axis

vertical. State whether the equilibrium is stable or unstable.

A rectangular tank is moving horizontally in the direction of its

length with a constant acceleration of $2\mathrm{.}4\frac{m}{s^2}.$ The length, width

and depth of the tank are $6m,2\mathrm{.}5m$ and $2$ m respectively. If the

depth of water in the tank is $1$ m and tank is open at the top then

calculate:

a$)$ The angle of the water surface to the horizontal.

b$)$ The maximum and minimum pressure intensities at the

bottom.

c$)$ The total force due to water acting on each end of the tank.