Problem $1(30$ points$)$

You are designing a water storage system for the town of Tolmin, Slovenla that comprises three reservoirs as shown in schematic bird's eve vew below. The water elevations of the three reservoirs are as follows: $z(R1)=250m,z(R2)=230m,$ and $z(R3)$ elerations The elevation of node $15,$ where the $3$ pipes converge is $2(15)=200m.$

Node $15$ is supposed to store$/$pass enough water to provide for the water demands of the town network; this network will be analyzed in Problem $2.$ The flowrate that needs to be available at node $15$ is $120\frac{V}{s}.$ This means that at $J5,Q=120\frac{V}{s}.$

Ignore minor losses and do not update friction factors after each iteration.

The characteristics of the three plpes are in the table below:

$\backslash$table$[[$The characteristics of the three ploses.are,R$1.$J$5,$R$2\mathrm{.}15,$R$3-15],[$Diameter $(mm),350,200,200],[$Length $(m),500,900,1675],[$Rouphess$,c(mm),1,1,1]]$

a$)$ Perform a maximum of $3$ iterations and calculate the flowrates going through this system and the head at node $15.$ You will need this head for Problem $2.$

b$)$ Perform all appropriate calculat

Problem $2(40$ points$)$

The pipe network for water distribution in the town of Tolmin, shown in schema below, consists of $6$ pipes P$1,$ P$2,$ P$3,$ P$4,$ P$5,$ P$6$ and requires a total flowrate of $120$ The lengths of the pipes are $L_1=970m,L_2=600m,L_3=820m,L_4=450m,L_5=640$ and $L_6=470m.$ The roughness coefficient is $=1mm$ and the diameter $D=150mm$ all pipes. The elevation of the $5$ nodes are $z(J1)=205m,z(J2)=180m,$ and $z(J3)=190z(J4)=200m,$ and $z(J5)=200m.$ The nodal demands are $20\frac{\text{I}}{s}$ for each of $J1,J2,J3,$ J$4.$ The nodal demand for $J5$ is $40\frac{\text{I}}{s}.$ The total demand for the network is $120\frac{\text{I}}{s}$ an provided through node $J5$ as described in Problem $1.$

a$)$ Select initial guesses for the $6$ pipe flowrates keeping in mind that continuity mus 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 ir pipes. Perform only $2$ iterations for each loop. d$)$ Node $J5$ has hydraulic head calculated in Problem $1.$ If for some reason you did not complete Problem $1$ assum head of $245$ m$.$ Calculate the pressure at node J$1$ in Pa$.$ Ignore minor losses.ions manually and draw the HGL and EGL curves for pipe R$1-$I$5.$

show all steps and use Darcy$-$W equation