$1.\backslash (\backslash \{\backslash$mathbf$\{25\}\backslash$mathbf$\{$p t s$\}\backslash \}\backslash )$ Water jets are used by many types of industries and by contractors who provide specialty$-$cleaning services $($Figure $1).$ They are also widely used by the surface prep industry to remove all sorts of paints and coatings. Water jets can be easily purchased, however a supporting structure must be designed and built to keep the water jet stationary. A supporting structure needs to be attached to the flange at point $1$ in the figure.

Figure $1.$ Schematic of the water jet. Note, this is a plane view of the water jet. The viewer is looking down on the water jet, along the z $-$axis.

Problem: As the engineer for the specialty cleaning services, you are tasked with determining the forces needed to hold the water jet stationary at the flange $($point $1).$ The following requirements and constraints for the design of the structure are as follows. The water flows through the elbow of the jet and exits to the atmosphere at point $2.$ The pipe diameter is $\backslash (\backslash$mathrm$\{$D$\}\_\{1\}=1\backslash$mathrm$\{$~m$\}\backslash )$ while $\backslash (\backslash$mathrm$\{$D$\}\_\{2\}=0\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash ).$ At a flowrate of $\backslash (1\mathrm{.}0\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ),$ the pressure is $\backslash (\backslash$mathrm$\{$P$\}\_\{1\}=233\backslash$mathrm$\{$kPa$\}\backslash )($gage$).$ The weight of the empty elbow is $2$ kN $,$ and the volume of water in the bend is $\backslash (1\mathrm{.}5\backslash$mathrm$\{$~m$\}^\{3\}\backslash ).$

Your solution must be presented in Cartesian Vector Notation $(3$ components$).$