Problem $2(25$ points$)$

Concepts: fluid pressure gradients balance the weight of gravity, which itself can vary with $$depth$.$

a$)$ Treating air as an ideal gas and assuming that the temperature of the Earth$$s atmosphere varies linearly with

height above the Earth,

$()=0$

Where $$ is constant, derive an expression for atmosphere pressure as a function of altitude $,$ where $=0$ at

the Earth$$s surface. You may neglect fluid motion in the atmosphere as well as the earth$$s rotation.

b$)$ The gage pressure at a depth of $5$ in an open tank of liquid is $73\mathrm{.}6.$ Determine the specific weight and

specific gravity of the liquid