Head losses in pipes arranged in series Select the correct statement about the total head loss when pipes are connected in series.

Introduction:
This question targets network hydraulics. When several pipe segments are connected in series carrying the same flow, their frictional and local losses accumulate. Understanding this additive nature is essential for sizing pumps and predicting pressures at nodes.

Given Data / Assumptions:

• Steady, incompressible flow.
• Same discharge through each series segment.
• Head losses include friction and, if accounted, minor losses at fittings and entries/exits.

Concept / Approach:
Energy equation between inlet and outlet across a series of segments: H_total loss = Σ(H_f,i + H_m,i). Because the discharge is the same through each segment, each segment’s loss can be computed (e.g., via Darcy–Weisbach) and then summed. Therefore, the total head loss equals the sum of head losses in individual pipes.

Step-by-Step Solution:

Verification / Alternative check:
Equivalent single-pipe calculations reproduce the same overall head drop if the summed loss is used as the design constraint, confirming additivity.

Why Other Options Are Wrong:

• No: contradicts the energy balance.
• Only if diameters are equal: additivity holds regardless of diameter differences.
• Only for laminar flow: valid for any regime; the formula for each segment changes but losses still add.
• Only if minor losses are neglected: minor losses also add when included.

Common Pitfalls:
Forgetting to include local (minor) losses or misapplying the friction factor regime; the summation principle remains valid either way.

Final Answer:
Yes