Question $1(25\%)$

A rectangular water reservoir has a cylindrical cone sealed at an opening in its wall with air pressure

above it $($see Figure $1).$ The cone has a radius of $R=0\mathrm{.}6m$ and extends to a depth of $5$ meters into

the reservoir.

a$.$ Calculate the total horizontal force acting on the cone $($magnitude and direction$).(10$ points$)$

b$.$ Calculate the vertical force acting on the cone $($magnitude and direction$).(5$ points$)$

c$.$ Calculate the force due to water acting on the left wall of the reservoir $($magnitude only$).$

points$)$

Data:

$=1000\frac{kg}{m^3}$

$=0\mathrm{.}001\frac{kg}{m*s}$

Volume of the cone:

$V=\frac{R^{2}H}{3}$

Where $H$ is the height of the cone and $R$ is the radius.

Figure $1$: A water reservoir with air pressure above it$.$