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

Onestion $3$: $(40$ points$)$

As shown in the schematic, water from a horizontal pipe flows into a two$-$outlet connector piece at point $1,$ and exits the connector through Outlets $2$ and $3$ as free jets with a speed of $15\frac{m}{s}$ from each outlet. Cross$-$sectional areas of the constant$-$diameter pipe, Outlets $2$ and $3$ are given in the schematic. Water exits Outlet $3$ in the horizontal direction $($i$.$e$.+x$ direction$)$ and Outlet $2$ in the vertical direction $($i$.$e$.+z$ direction$).$

What are the horizontal $($ x $)$ and vertical $($ z $)$ components of the force exerted on the connector?

$[$Hint: Assume negligible viscous and gravity effects. The density of water, ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1000k\frac{g}{m^3}$; atmospheric pressure outside the pipe and connector throughout$].$

Free$-$body diagrams

Control$-$volume diagrams

Bemoulli'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