Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts. Mays, Water Resources Engineering, 3rd ed. (pipe networks, valves, pumps); Chow, Open-Channel Hydraulics (Manning uniform flow, hydraulic jump, gutter flow); Crowe, Elger & Roberson, Engineering Fluid Mechanics (pipe force balance, wall shear). Exam-supplied relations used throughout: Hazen–Williams $Q=0.278\,C\,D^{2.63}\,S^{0.54}$ with $S=h_f/L$ (SI), Manning $Q=\tfrac{1}{n}A\,R^{2/3}\,S^{1/2}$, Darcy–Weisbach $\Delta h=0.0826\,\tfrac{fL}{D^5}Q^2$, and $\text{TDH}=H_s+H_f$. Unless stated, local losses and velocity head are neglected and water has $\rho=1000\ \text{kg/m}^3$, $\nu=1.31\times10^{-6}\ \text{m}^2/\text{s}$.