Problem $4-$ The horizontal piping restraints in the basement of DeMoss Hall need to be redesigned to handle an increased water pressure from the Lynchburg city water lines. The water entering the piping system at C $($see drawing$)$ is $\backslash (4\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$sec$\}\backslash ).$ The pipe inside diameters are as follows: $25$ mm at $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$; and $50$ mm at $\backslash ($ C $\backslash ).$ Determine the $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ components required to restrain the piping system. Neglect any head losses due to friction or pipe fittings, elbows, etc. The outlet pressures at $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ are atmospheric. The density of water is assumed to be $\backslash (1000\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$ This problem requires the simultaneous solution of several equations. Full credit is earned by completely defining the simultaneous equations and the solution process. Extra credit is provided for the correct numerical solution. The coordinate directions are x is the horizontal direction on the page and y is the vertical direction on the page. The system is horizontal in the DeMoss Hall basement. The problem description is shown below along with the free$-$body diagram.

Free$-$body diagram in the horizontal plane