A piping system for a pump contains a tee as shown below to permit the pressure at the outlet of the pump to be measured. Assuming friction losses in the short section of pipe is negligible, determine:

a$)$ The head loss through the tee if $\backslash (60\backslash$mathrm$\{$~L$\}/\backslash$mathrm$\{$s$\}\backslash )$ of water flows through the system.

b$)$ The change in pressure $($from pump inlet to downstream end of tee$)$ if the upstream pipe is a $8-$in Schedule $80$ pipe and the power added to the water by the pump is $3\mathrm{.}2$ KW $.$