Problem $4$

$(6$ points$)$ :

A $10$ m long seawall separates a freshwater body from a saltwater body as shown in the figure. The wall is a total of $6$ m $(h_{\text{f}\text{r}\text{e}\text{s}\text{h}})$ high, with the top half of the wall being semicircular $(R=2m).$ Under design conditions, the surface of the freshwater body $($on the left$)$ is at the top of the wall and the surface of the saltwater body $($on the right$)$ is at $3\mathrm{.}90$ m $)$ of the wall. Determine the magnitude of resultant hydrostatic force $($FR in N $)$ on the wall under the design condition. Assume that the fresh water has density of $975k\frac{g}{m^3}$ and salt water has a specific gravity of $1\mathrm{.}25.$ Take the specific weight of water at $4^{0}C$ as $9810\frac{N}{m^3}$ and acceleration due to gravity as $9\mathrm{.}81\frac{m}{s^2}.$

Hint: The volume of water causes a force that acts vertically downwards on the upper left side of the seawall and this volume can be calculated by deducting quarter of cylinder from a square with side R$.$