Sch$$ma du r$$seau de canalisation multiples Problem Formulation $1.$ Knowing that the pipes are semi$-$rough, with pipe roughness k$=0\mathrm{.}00002$m $,$ and water's kinematic viscosity v$=1\mathrm{.}13106$m$2/$s o Calculate the Ki coefficients and ni exponents. o The Ki coefficients are calculated based on the expected flow rate plus or minus $10\%$ of their values, according to the methodology used in class. o Express the formula for linear head losses for each pipe in power format $($h$=$KiQi$^$ni$)$ by determining the value of Ki and ni for each pipe. o Present your reasoning and methodology for the calculation and summarize the results in a table. $2.$ Using the law of mass conservation at the nodes and the law of energy conservation in loops $($real and fictitious, if necessary$),$ along with the pump characteristic curve hp$=$H$0+$BQ$+$AQ$^2$ o Formulate the system of equations necessary to solve the flow in the network. o Clearly detail your reasoning and methodology, respecting the norms and sign conventions presented in class. $3.$ Solve the problem! o You can use the method presented in class $($Excel spreadsheet$)$ or solve the system of equations using your own approach. o Clearly describe the steps, the results obtained, and the convergence criteria adopted. Network Modeling and Discussion of Results $4.$ Model the network in question using the EPANET $2\mathrm{.}2$ software with the provided and calculated data from part $1$ as needed. $5.$ Solve the problem $($Run$)$ and synthesize the results in tables, presenting the results for: o Pipes $($flows$,$ velocities, head losses, etc.$)$ o Pressures$/$heads at the nodes o Pump head $6.$ Discuss the results obtained using both methods and report all your observations regarding: o Changes in flow direction and why? o Velocities? o Heads at the nodes? Point Distribution Total points: $10010$ points for language: Grammar, spelling, syntax $10$ points for presentation: Proper pagination, title page, justified text, etc. $30$ points for problem formulation: $($Calculations of head loss coefficients, system of equations, etc.$)25$ points for correct network modeling $($Attach your EPANET project to the report$)25$ points for discussion Formatting Requirements: $$ Line spacing: $1\mathrm{.}15$ Font size: $12$ Normal margins $$ Single$-$line paragraph spacing