Problem $2(40$ points$)$

The pipe network for water distribution in the town of Tolmin, shown in schematic

below, consists of $6$ pipes P$1,$ P$2,$ P$3,$ P$4,$ P$5,$ P$6$ and requires a total flowrate of $120\frac{l}{s}.$

The lengths of the pipes are $L_1=970m,L_2=600m,L_3=820m,L_4=450m,L_5=640m,$

and $L_6=470m.$ The roughness coefficient is $=1mm$ and the diameter $D=150mm$ for

all pipes. The elevation of the $5$ nodes are $z(J1)=205m,z(J2)=180m,$ and $z(J3)=190m,$

$z(J4)=200m,$ and $z(J5)=200m.$ The nodal demands are $20\frac{l}{s}$ for each of $J1,J2,J3,$ and

J$4.$ The nodal demand for J $5$ is $40\frac{l}{s}.$ The total demand for the network is $120\frac{l}{s}$ and is

provided through node J$5$ as described in Problem $1.$

a$)$ Select initial guesses for the $6$ pipe flowrates keeping in mind that continuity must be

satisfied. b$)$ Using all pertinent information calculate the friction factors and resistance

coefficients $($do not update these numbers after each iteration$).$ c$)$ Using the Hardy$-$Cross

method calculate manually the flowrate in each of the $6$ pipes. Water is flowing in all

pipes. Perform only $2_{?}$ iterations for each loop. d$)$ Node J$5$ has hydraulic head as

calculated in Problem $1.$ If for some reason you did not complete Problem $1$ assume a

head of $245$ m$.$ Calculate the pressure at node J$1$ in Pa$.$ Ignore minor losses.