Difficulty: Medium
Correct Answer: All the above.
Explanation:
Introduction / Context:
Design and analysis of looped pipe networks require solving for unknown flows and nodal heads. Classical methods (Hardy Cross, linear theory) and modern solvers enforce mass and energy conservation with appropriate head-loss laws for each pipe segment.
Given Data / Assumptions:
Concept / Approach:
Two conservation laws govern the solution: continuity at nodes and energy around loops. Each pipe requires a constitutive relation linking discharge to head loss. Together, these equations form a solvable system for flows and heads.
Step-by-Step Solution:
Verification / Alternative check:
Compute residuals of nodal continuity and loop energy; convergence to near zero confirms a physically consistent solution.
Why Other Options Are Wrong:
Each of (a), (b), and (c) is necessary; omitting any yields an under-defined or inconsistent system. Hence “All the above” is correct.
Common Pitfalls:
Using inconsistent units; neglecting minor losses or pump curves; applying an inappropriate head-loss formula outside its range.
Final Answer:
All the above.
Discussion & Comments