Question $2$: $(30$ points$)$

A horizontal circular jet of water exposed to atmospheric conditions hits a $90$ deflector that deflects the horizontal jet into a vertical jet as shown in the schematic.

$($a$)$ What are the dimensionless parameters for this flow $($conduct dimensional analysis using the parameters shown next to the schematic$)?$

$($b$)$ What is the horizontal force $F$ exerted on the deflector in terms of the given parameters. $($use conservation of momentum equation and neglect vertical elevation changes$).$

$($c$)$ Determine the value of the dimensionless parameter from $($a$)$ by comparing your solutions from $($a$)$ and $($b$).$