A t$-$joint is another common piping component, typically used to combine or separate flows of fluid. This t$-$joint has two inlets and one outlet. We want to find the flow rate through the outlet and the force to hold the t$-$joint in place. The working fluid is water. One inlet, open to the left, is $6$ cm diameter and receives water at a velocity of $4$ m$/$s$.$ The other inlet, open to the right, has a volume flow rate of $1$ L$/$sand a diameter of $4$ cm $.$ If the outlet has a diameter of $12$ cm and faces upwards with regard to gravity, determine:

$($a$)$ the velocity through the second inlet. $[$Answer is $0\mathrm{.}80]$

$($b$)$ the velocity through the outlet. $[$Answer is $1\mathrm{.}09$ m$/$s$]$

$($c$)$ the reaction forces $($x$,$y$,$z directions$)[$Answer is $$: $181\mathrm{.}7$ N$,$: $1156$ N$]$

Losses due to viscosity are assumed negligible. The outlet discharges to atmosphere. The weight of the t$-$joint and the fluid within it are negligible.