Problem $2$ Consider a $5$ gallon bucket, with height $1\mathrm{.}25ft$ and diameter $0\mathrm{.}83ft.$ In this problem, you will be

filling the bucket at a constant rate, while draining it through a $10ft$ long, $\frac{1}{2}$ inch diameter tube with roughness

$lon=1\mathrm{.}5{10}^{-3}$ inches. The tube discharges as a free jet at ground level with no exit losses. There is a fish in the

bucket.

$2\mathrm{.}3$ For case $($a$)$ above $($initial water level $0\mathrm{.}25$ ft$),$ if the water in the bucket is initially dyed with a concentration

of $50$ mg$/$ft$3,$ determine and graph the concentration history c $($t $)$ of the dye in the bucket. Assume that the

dye in the bucket is $$well mixed$$ at all times, and that the water entering the bucket has no dye.

How long does it take for the concentration in the bucket to be reduced to $1$ mg$/$ft$3?\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Write out your conservation of mass equation for the dye:

As a start, populate the below spreadsheet; you$$ll need to use your values from the previous problem.

$-------------$BUCKET$------------------------------------++++++++++$FLUXES$++++++++$

Time $($s$)$ total dye volume $($ft$3)$ c $($mg$/$ft$3)$ dM$/$dt $$m$($mg$/$s$)$mout $($mg$/$s$)$

mass in $($mg$/$s$)$

bucket $($mg$)$

$0$

$1$