Problem $3$ Bucket Problem

A bucket system has the following properties

Item Units Value

Q$($in$)[$GPM$]440$

Dh$/$dt $[$in$/$s$]+\mathrm{.}01$

V$($out$)[$fps$]5$

A $[$ft$^2]\mathrm{.}1$

Find the diameter of the outlet in inches.

This problem is solved using conservation of mass

$($Equation $7)$

m $\_$sys$=$m $\_$in$-$m $\_$out

And

$($Equation $8)$

A dh$/$dt$=$Q$\_$in$-$Q$\_$out$=$V$\_$in A$\_$in$-$V$\_$out A$\_$out