A low dam $($also called as a cylindrical weir$)$ of cross$-$sectional diameter $D$ stores fluid $1$ of depth $D$ and

separates it with another fluid $2$ of depth $\frac{D}{2},$ as shown in the figure below. The width of the dam is $W$ into

the page.

$($a$)$ Obtain expressions for the net horizontal and vertical hydrostatic forces applied to the low dam. Indicate

the direction of each force in the free body diagram.

$($b$)$ If both fluids are water, compute the minimum mass of the dam so that it does not float over the water.

If you are an engineer designing this dam, which concrete among those listed in Table $1$ would you choose

to use? It is assumed that the dam has an uniform density ${}_{\text{d}\text{a}\text{m}}.$ The density of water is $1000k\frac{g}{m^3},$

the gravitational acceleration $g=9\mathrm{.}81\frac{m}{s^2},$ the diameter $D=5m$ and the width $W=10m.$

Table $1$: Density of commonly$-$used concrete.