Problem $4(25$ points$)$

Concepts: Fundamental equation of hydrostatics. Gage pressure. Pascal$$s Principle.

a$)$ Water of density $$ occupies the bottom $1$ cm of a cylindrical tank. On top of the water of a depth of $2$

meter of kerosene with density $.$ The tank is open to the atmosphere.

$($i$)$ Determine the gage pressure at the bottom of the tank, stating your answer in terms of the variables given.

$($ii$)$ Assuming $1=90,2=10,$ and $=80/3,$ compute the gage pressure at the bottom

of the tank.

b$)$ Consider the hydraulic lift shown on the right, filled with oil with

specific gravity $.$

$($i$)$ If a force $1$ is applied to the piston with the small diameter

$1,$ what is the magnitude of the force $2$ that can be

resisted by the piston with the large diameter $2?$ Pistons

are vertically $$ meter apart. You may neglect the weights of

the pistons. State your answer in terms of the variable given.

$($ii$)$ Assuming $1=100,1=4,2=10,=2$ and

$=0\mathrm{.}85,$ compute $2.$

$($iii$)$ This is an application of what principle?