$=26\mathrm{.}3$ slug $\frac{?}{f{t}^3}$; see notes at the end of the exam$)$

Question Is$.(28$ points$)$

A $10$ cm diameter pipe feeds a cylindrical water storage tank with a constant water flow speed of $1\frac{m}{s}.$ The tank has a diameter of $0\mathrm{.}5$ m and has a $5$ cm diameter circular outlet at $10$ cm above the tank bottom. Considering atmospheric conditions outside the tank and using the density of water, ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1000k\frac{g}{m^3},$ calculate the maximum water depth $($ h $)$ in the tank? $[$The direction of gravity is in the negative $z$ direction in the schematic. Hint: maximum water depth occurs when the water level in the tank stops changing$].$

Free$-$body diagrams

Control$-$volume diagrams

Bernoulli's Equation points of interest

Work$-$Energy Equation points of interest

Units for all answers

Work for all calculations used in equations

Boxing$-$in$/$circling answers

Reference$/$Datum lines