$1.$ There is an L$-$shaped pipe $($Figure a$),$ with a horizontal section length of $\backslash ($ L$=2\backslash$mathrm$\{$~m$\}\backslash )$ and a vertical section length of $\backslash ($ L$=3\backslash$mathrm$\{$~m$\}\backslash ).$ The horizontal section is fixed at section $\backslash ($ A $\backslash )$ with a flange, and the end of the vertical section is a nozzle. The pipe diameter $\backslash ($ D$=16\backslash$mathrm$\{$~cm$\}\backslash ),$ nozzle diameter $\backslash (\backslash$mathrm$\{$d$\}=8\backslash$mathrm$\{$~cm$\}\backslash ),$ and the vertical section is powered by a pump that provides a head of $2\mathrm{.}5$ m $.$ Water flows out at a speed of $\backslash ($ V$=4\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ),$ at an angle $\backslash (\backslash$theta$=40^\{\backslash$circ$\}\backslash )$ to the horizontal. The weight of the horizontal section $($pipe $+$ water$)$ is $400$ N $,$ and the weight of the vertical section $($pipe $+$ water $+$ pump$)$ is $680$ N$.$ Find:

$($a$)$ The force F exerted by the flange. What is the value of F in N $,$ and what is the direction?

$($b$)$ The torque T exerted by the flange. What is the value of T in $\backslash (\backslash$mathrm$\{$N$\}\backslash$cdot $\backslash$mathrm$\{$m$\}\backslash ),$ and what is the direction?