Topic II: Hydrostatics and Buovancy $(15$ points$)$

Problem $(4)$: A water tank is kept barely closed by an inclined square gate of

weight $(W),$ as shown in the figure. The depth of water in the tank is $(h)$ and

the gate is inclined at an angle $().$

Given the values of $h[cm]$ and $[$degrees$],$ calculate $W[N].$

Problem $(5)$: A tank of depth $($h$)$ containing two different

liquids with specific gravities $(S_1)$ and $(S_2),$ respectively, is

to be designed so that its side walls are inclined at an angle

$().$

Given the values of $S_1[-],$ and $S_2[-],$ calculate the

percentage ratio between the hydrostatic pressure forces on

the part of the side wall in contact with liquid $1$ to that in

contact with liquid $2(\frac{F_1}{F_2})[\%].$

Hint: you don't need to know $(h)$ and $()$ to solve the

problem for the shown case $($since the interface is at $\frac{h}{2}).$

Problem $(6)$: A spring scale is used to measure the weight of an object of specific gravity $(S)$ and volume $(V).$

While fully immersed in water, the object is found to weigh $(W_w).$

Given the values of $S[-]$ and $V$ in $c{m}^3,$ calculate $W_w[N].$

Givens:

$S=1\mathrm{.}611$

$V=14501\mathrm{.}981c{m}^3$

answers:

$86\mathrm{.}835N$

$61\mathrm{.}317N$

$103\mathrm{.}018N$

$119\mathrm{.}906N$