$3.(30$ pts total$)$ The water jet, exposed to atmospheric pressure, strikes a plate containing a hole $($shown in figure$).$ Part of the jet passes through the hole, and part is deflected.

Assume the flow is symmetric with respect to the horizontal centerline.

a$.$ Determine the mass flow rate of water at stations $\backslash (1,2,3,4\backslash ).(8$ pts $)$

b$.$ Determine the magnitudo and direction of horizontal force and vertical force required to hold the plate in place. $(20$ pts$)$

c$.$ How would you adjust your analysis in Part b if the plate was moving horizontally at a constant velocity $\backslash (\backslash$mathrm$\{$V$\}\_\{\backslash$mathrm$\{$c$\}\}\backslash )?(2$ pts$)($Note: Provide equation or explanation, no calculations needed$)$