Problem 1: Two Pipes in Series

Pipe 1 has $L_1=100\text{ m}$, $D_1=0.20\text{ m}$, and $f_1=0.020$. Pipe 2 has $L_2=200\text{ m}$, $D_2=0.30\text{ m}$, and $f_2=0.015$. Both carry $Q=0.100\text{ m}^3/\text{s}$. Determine total friction head loss.

Problem 2: Equivalent Diameter for Series Pipes

Replace the series system in Problem 1 with one $300\text{ m}$ long pipe carrying the same discharge with $f=0.020$ and the same $6.184\text{ m}$ head loss. Estimate the equivalent diameter.

Problem 3: Flow Split between Parallel Pipes

Two pipes connect the same nodes and carry a total of $0.100\text{ m}^3/\text{s}$. Pipe 1: $L=200\text{ m}$, $D=0.20\text{ m}$, $f=0.020$. Pipe 2: $L=300\text{ m}$, $D=0.25\text{ m}$, $f=0.022$. Determine branch flows.

Problem 4: Three-Reservoir Junction

Reservoir heads are $H_1=100\text{ m}$, $H_2=80\text{ m}$, and $H_3=60\text{ m}$. Their pipes connect to one junction and have resistance coefficients $R_1=2000$, $R_2=1000$, and $R_3=3000$ in $h=RQ^2$. Determine junction head and flow directions.

Problem 5: One Hardy Cross Loop Correction

For one loop, take clockwise flow as positive. Three pipe terms have $(r,Q)$ values $(500,0.040)$, $(800,0.020)$, and $(300,-0.010)$, with head loss $h=rQ|Q|$. Determine the first Hardy Cross correction.

Problem 6: Equivalent Resistance of Parallel Pipes

Two parallel branches obey $h=RQ^2$ with $R_1=1000$ and $R_2=4000$. Determine the equivalent resistance and branch flows when total flow is $0.090\text{ m}^3/\text{s}$.

Problem 7: Rapid and Slow Valve Closure

A $500\text{ m}$ pipeline carries water at $2.0\text{ m/s}$. Wave celerity is $1000\text{ m/s}$. Compare pressure rise for valve closure in (a) $0.60\text{ s}$ and (b) $2.0\text{ s}$. Use $\rho=1000\text{ kg/m}^3$.

Problem 8: Pump and System Operating Point

A pump curve and system curve use discharge $Q$ in $\text{L/s}$:

Determine operating discharge and head.