Question $2[$MEENIA$,$ CLO $2\mathrm{.}4][8$ marks$]$ A reducing elbow in a horizontal pipe is used to deflect mater flow by an angle $\backslash (\backslash$theta$=45^\{\backslash$circ$\}\backslash )$ from the flow direction while accelerating it$.$ The elbow discharges water into the atmosphere. The cross$-$sectional area of the elbow is $\backslash (150\backslash$mathrm$\{$~cm$\}^\{2\}\backslash )$ at the inlet and $\backslash (25\backslash$mathrm$\{$~cm$\}^\{2\}\backslash )$ at the exit. The elevation difference between the centers of the exit and the inlet is $40$ cm $.$ The mass of the elbow and the water in it is $30$ kg $.($a$)$ Calculate the velocities at inlet and outlet of the pipe $[2$ marks$].($b$)$ Use the Bernoulli Equation for any gauge pressure calculations and the Momentum Equation $[2$ marks$]$ to $($c$)$ determine $\backslash ($ F$\_\{\backslash$text $\{$Rx $\}\}\backslash )$ and $\backslash ($ F$\_\{$R z$\}\backslash )[3$ marks$]$ and calculate the final anchoring force needed to hold the elbow in place $[1$ mark$].$ Take the momentum flisx correction factor to be $1\mathrm{.}03$ at both the inlet and outlet. Take the density of water to be $\backslash (1000\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$