Consider the pipe fitting shown in the figure below. 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 b 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$)$