$6.)$ The tank shown below is pressurized at the top so that the pressure acting on the water

surface is always constant. The depth of the tank is $2$ m $,$ and the tank has a cross$-$

sectional area of $1\mathrm{.}7m^2,$ while the exit pipe at the bottom has an area of $9c{m}^2.$ The

constant pressure at the top of the tank is maintained at $10$ kPa $,$ while the exit pipe

opens to the atmosphere.

a$)$ Derive an equation for the exit velocity $v_e,$ in terms of the variables for the

constant pressure at the top of the tank $(p),$ the constant density of water $(),$ the

acceleration due to gravity $(g),$ and the variable height of water in the tank $(h).$

Hint: Assume the assumptions of Bernoulli's Equation are valid for this problem,

and assume the water surface falls at a velocity much lower than the exit velocity

at the outlet.

b$)$ Find the initial exit velocity of the water through the outlet at the starting height of

$2$ meters.

c$)$ Find the time required to empty the tank. Hint: Our exit velocity will be defined by

the equation derived in part a$.$ Note that your variable $h$ will be changing with

time, starting at its initial value of $2$ meters and ending at $0$ meters, meaning that

the exit velocity will be changing. So$,$ you will need to integrate the continuity

equation.