Problem Statement

Working in groups of up to $3$ students, solve to within $\backslash (0\mathrm{.}1\backslash \%\backslash )$ error of velocity for one of the two pipe systems listed below. Compute the volume flow rate.

$1.$ Drinking Fountain: Water is drawn from a municipal water supply, $1$ m below the ground, at $550$ kPa gauge, and $17$ C $.$ The main supply line is $7\mathrm{.}62$ cm in diameter, horizontal, and $15$ m in length, comprised of galvanized steel. The entrance to supply line is square$-$edged inlet from a reservoir. A fully$-$open globe valve is included in this line.

The water then flows through an abrupt contraction to a diameter of $3\mathrm{.}81$ cm copper piping, which has a total length of $30$ m $,$ six $90$ degree regular$-$radius flanged elbows, and a fully$-$open gate valve. The elevation in this section increases by $15$ m $.$ Just before the gate valve is an ion$-$exchange filter with $\backslash (\backslash$mathrm$\{$K$\}=14\backslash ).$

The copper piping is connected by an abrupt contraction to $1\mathrm{.}27$ cm diameter plastic tubing with a total length of $2$ m and an elevation increase of $90$ cm $.$ The tubing discharges to atmospheric pressure.

$2.$ Shower: From a water heater at ground level, water is supplied at $34$ C and $550$ kPa gauge through a re$-$entrant entrance to $2\mathrm{.}54$ cm copper pipe, four threaded $90$ degree regular$-$radius elbows, a water meter, and a swing$-$check valve. The elevation increases by $1$ m and the total length of this section is $6$ m $.$

That section connects through an abrupt contraction to copper pipe, $1\mathrm{.}76$ cm in diameter and $12$ m in length. The elevation rises by $4$ m in this section. Two $90$ degree regular$-$radius threaded elbows and a showerhead with a loss coefficient of $\backslash (\backslash$mathrm$\{$K$\}=\backslash )9$ are included in this section. This section discharges to atmospheric pressure.