Pipes in series replaced by an equivalent pipe:\nWhich of the following statements about an equivalent pipe for a compound (series) pipe system is incorrect?

Introduction / Context:
Multiple pipes in series with different diameters and lengths can be replaced by one “equivalent” pipe that yields the same discharge under the same head loss. This simplification is frequently used in network calculations and preliminary sizing. Understanding what stays the same and what changes in the equivalent representation is key to correct modeling.

Given Data / Assumptions:

• All segments are in series, carrying the same discharge Q.
• Total head loss across the series is known or specified.
• Friction losses dominate; minor losses may be included by adjusting length.

Concept / Approach:
For a compound pipe in series, the total head loss h_f,total is the sum of losses over each segment. An equivalent single pipe is defined such that it carries the same Q with the same total h_f across the same overall length (often taken as the geometric length sum or an adjusted “equivalent length” including fittings). The required equivalent diameter is then computed from Darcy–Weisbach or Hazen–Williams; it generally differs from any individual segment diameter and from a simple average.

Step-by-Step Solution:

Verification / Alternative check:
Using Darcy–Weisbach with f assumed constant for a first pass: h_f ∝ (L/D^5) * Q^2 for laminar or with appropriate friction relations in turbulent range. Aggregating L/D^5 terms shows D_eq depends on a weighted combination, not equality to compound-pipe diameters.

Why Other Options Are Wrong:

• Equivalent pipe used as ordinary pipe: Correct for calculations.
• Length equal to compound pipe: Typically taken as the sum (or adjusted equivalent length), acceptable statement.
• Discharge equal: By definition, equivalence preserves Q.

Common Pitfalls:
Assuming D_eq equals arithmetic or geometric mean of component diameters; neglecting minor-loss contributions to equivalent length; mixing Darcy and Hazen–Williams forms without consistent parameters.

Final Answer:
The diameter of an equivalent pipe is equal to that of a compound pipe