Flow in Pipes: Systems & Networks

Pipes in Series

Pipes connected end-to-end.

• Discharge: Same through all pipes ($Q_1 = Q_2 = Q$).
• Head Loss: Sum of losses in individual pipes ($H_L = h_{f1} + h_{f2} + \dots$).

Pipes in Parallel

Pipes branching from a common point and rejoining.

• Discharge: Sum of discharges ($Q_{total} = Q_1 + Q_2$).
• Head Loss: Same across each parallel branch ($h_{f1} = h_{f2}$).

Branching Pipes (Three-Reservoir Problem)

Connecting three reservoirs at different elevations to a common junction. Analysis involves assuming a piezometric head at the junction and iterating until continuity ($\sum Q = 0$) at the junction is satisfied.

Pipe Networks

Complex grids of pipes (e.g., municipal water distribution). Hardy Cross Method: An iterative method to solve for flow rates.

• Correction $\Delta Q = - \frac{\sum r Q |Q|^{n-1}}{\sum n r |Q|^{n-1}}$

Solved Problems