Equivalent single pipe for a compound pipe Two pipes are said to be hydraulically equivalent when replacing a compound line by one new pipe. Choose the correct equivalence condition.

Introduction:
Pipeline design often replaces a series (compound) system with a single “equivalent” pipe for easier analysis. This question asks you to recall the precise criteria that define equivalence for head loss and flow rate.

Given Data / Assumptions:

• Incompressible, steady flow.
• Same fluid in both configurations.
• Minor losses may be either included in the head loss accounting or neglected consistently.

Concept / Approach:
An equivalent pipe must transport the same discharge Q under the same total head loss H between the same endpoints as the original compound system. Matching Q ensures throughput equivalence; matching H ensures the same driving energy requirement. Length and diameter individually need not match; they adjust to meet the H–Q condition via friction relations (e.g., Darcy–Weisbach or Hazen–Williams).

Step-by-Step Solution:

Verification / Alternative check:
Hydraulic-grade line across endpoints remains unchanged if H and Q match, confirming energy and capacity equivalence.

Why Other Options Are Wrong:

• Same length or diameter: not necessary individually.
• Same head loss and velocity: equal velocity does not guarantee equal Q unless diameters also match.
• Same Reynolds number: not required and may differ because D and V can change.

Common Pitfalls:
Over-focusing on geometric sameness rather than hydraulic performance (H–Q) equivalence.

Final Answer:
loss of head and discharge of both the pipes is same