Example $6\mathrm{.}5.$ A gasoline storage tank drains by gravity to a tank truck; see Fig. $6\mathrm{.}11.$ The pipeline between the tank and the truck is $100m$ of $0\mathrm{.}1m$ diameter commercial steel pipe. The properties of gasoline are given in the Common Units and Values for Problems and Examples $($App$.$ E$).$ Both tank and truck are open to the atmosphere, and the level in the tank is $10m$ above the level in the truck. What is the volumetric flow rate of the gasoline?

Applying B$.$E$.$ between the free surface in the tank, point $1,$ and the free surface in the truck, point $2,$ we see that all terms cancel except

$(gz)=-F=-4f(\frac{x}{D})*\frac{V^2}{2}$

IGURE $6\mathrm{.}11$

A gravity$-$driven fluid transfer from one tank to another, used in Example $6\mathrm{.}5.$ The air from the headspace displaced by the liquid flow into the ruck exits by the vent on the tank roof. In the United States such tank vent emissions are controlled to prevent air pollutant emissions.

a Type $2$ problem. The equation contains two unknowns, $V$ and $f,$ therefore, to solve it$,$ we need an additional equation or $\frac{?}{\text{b}\text{a}\text{r}}($ Page $193)$ ship among the variables listed. The second relationship is provided by Fig. $6\mathrm{.}10,$ which relates $f$ and $V.$ We could use Eq$.$replace either $f$ or $V$ in terms of the other; some computer programs do that. Others follow the trial$-$and$-$error procedure shown here,

Excel Assignment

Solve Examples $6\mathrm{.}4,6\mathrm{.}5$ and $6\mathrm{.}6$ in Excel. You should use the Goal seek method for Examples $6\mathrm{.}5$ and $6\mathrm{.}6.$ After submission, you should arrange a $10$min meeting to discuss your solutions.