$7\mathrm{.}5$ A$5)$ In a precision fluid metering system, water is flowing in a $6$ inch "Type L$"$ copper tube prior to transitioning to a $3$ inch "Type L$"$ copper tube, as shown. At point A$,$ the pressure and temperature of the water are $\backslash (200\backslash$mathrm$\{$kPa$\}(\backslash$mathrm$\{$g$\})\backslash )$ and $\backslash (80^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ respectively. The water is required to be kept to a maximum $($average$)$ velocity of $\backslash (5\mathrm{.}000\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ at any point in the piping system between points A and B $.$ It is also known that the water temperature drops by $\backslash (65^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ as it flows from A to B $.$ What is the average velocity $[\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash )]$ a flow sensor placed at $"$A$"$ should read, so that the velocity limit condition is not exceeded? Also, state the flow rate at $"$A$"$ in terms of $[$L$/$s$]$ and $[$gpm$].$