Parallel Pipes – Governing Conditions for Head Loss and Discharge In a pipeline system where multiple branches run in parallel between the same two junctions, the head loss (energy drop) across each branch is identical, and the total discharge equals the algebraic sum of the discharges through the individual parallel pipes.

Introduction:
Parallel pipe networks are common in water distribution and process plants. Correctly identifying how head loss and discharge partition among branches is essential for sizing lines, selecting pumps, and predicting system behavior.

Given Data / Assumptions:

• Pipes connect the same upstream and downstream nodes (parallel configuration).
• Steady, incompressible flow; elevation difference between nodes is fixed.
• Losses are represented by standard head-loss formulas (e.g., Darcy–Weisbach).

Concept / Approach:

Between two common nodes, energy grade lines must meet the same boundary conditions. Therefore, each branch experiences the same head loss. Continuity at the junctions requires that the total inflow equals total outflow, so total discharge splits among branches and sums to the supply/exit flow.

Step-by-Step Solution:

Verification / Alternative check:

Solving a two-branch example using Darcy–Weisbach with different diameters shows different velocities and individual Q values, yet identical head losses; adding the Q values gives the total system discharge.

Why Other Options Are Wrong:

Total head loss is the sum...: This applies to series, not parallel. None of the above: Incorrect because (A) and (B) are established principles.

Common Pitfalls:

Confusing series vs parallel rules; forgetting that minor losses per branch must also match the same overall drop between nodes.

Final Answer:

Both (A) and (B)