$4.$ Consider the pipe fitting shown in the figure below.

Water is flowing through the fitting, and pressure measurements indicate that the pressure at point $1$ is $234\mathrm{.}36$ kPa $,$ the pressure at point $2$ is $241\mathrm{.}25$ kPa $,$ and the pressure at point $3$ is $230\mathrm{.}91$ kPa $.$ The flow rate at point $2$ is $\backslash (\backslash$mathrm$\{$Q$\}\_\{2\}=0\mathrm{.}02832\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ),$ and the flow rate at point $1$ is $\backslash (\backslash$mathrm$\{$Q$\}\_\{1\}=0\mathrm{.}04616\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$

a$.$ Draw a control volume suitable for determining the forces requested in part $\backslash ($ b $\backslash )$ and show the appropriate flow parameters on the control volume. $(5$ points$)$

b$.$ Determine the horizontal and vertical force components necessary to keep the fitting stationary $(10$ points$)$

c$.$ What is the momentum of the flow exiting the surface of a control volume boundary located at point $3?(5$ points$)$

d$.$ What is the momentum of the flow entering a control volume boundary passing through point $1?(5$ points$)$