MECH $342$ Assignment $2$: Hydrostatic Pressure

Q$1$: A curved gate with radius $R=1\mathrm{.}6m$ is located in the side of a reservoir containing two fluids.

a$)$ Derive an expression for the horizontal $F_H$ and vertical $F_v$ hydrostatic forces acting on the gate.

$4$

b$)$ Given the fluid densities: ${}_1=700k\frac{g}{m^3}($oil$)$ and ${}_2=1000k\frac{g}{m^3}($water$),$ calculate the resultant hydrostatic force acting on the gate. $[2]$

c$)$ Assuming a uniform fluid $)={}_2=({}_{\text{w}\text{a}\text{t}\text{e}\text{r}},$ determine the force $F$ required to keep the gate from opening. $[4]$

Depth into page: $b=1\mathrm{.}8m$