Problem $1$: Consider the four vessels below, each filled with the same depth of water. They are drawn to scale, and they are all a uniform depth $b$ into the page. We label each vessel from left to right as $(1),(2),(3),$ and $(4).$

a$.$ Rank the vessels in increasing order of bottom pressure.

b$.$ In which case$($s$)$ does the pressure on the bottom times the area of the base equal the weight of the fluid in the container?

c$.$ For any cases that did not make your list in part $($b$),$ explain what is going on using a sketch that shows where forces are being generated from the water onto the vessels.

Problem $2$: $2\mathrm{.}51$ Gate AB in Fig. P$2\mathrm{.}51$ is $1\mathrm{.}2m$ long and $0\mathrm{.}8m$ into the paper. Neglecting atmospheric pressure, compute the force $F$ on the gate and its center$-$of$-$pressure position $x.$