Problem $1.$ Consider the $90-$degree faucet. The hot water $(=990\frac{kg}{m^3})$ is pressurized at $P_1=$

$221,000Pa$ and enters the faucet at $v_1=4\frac{m}{s}$ through an opening of $A_1=0\mathrm{.}01m^2.$ The water

exits out at atmospheric pressure at $v_2=16\frac{m}{s}$ though an opening of $A_2=0\mathrm{.}0025m^2.$ Reaction

forces are required to hold the faucet in place. The system is at steady state.

a$)(2$ pt$.)$ Redraw the system as a schematic with a control volume around the elbow. Label

the components of the conservation of momentum equation, such as the influx$/$efflux

vectors. Draw a free body diagram for any reaction forces, pressure forces, gravity forces.

b$)(4$ pt$.)$ Determine the reaction force in the x $-$direction. Report your answer in units of $[$N$]$

c$)(4$ pt$.)$ Determine the reaction force in the $y-$direction in units of $[$N$].$ You can assume the

mass of water inside the control volume is $10$ grams.