Water hammer in pipelines – factors affecting magnitude The magnitude (severity) of water hammer produced by sudden valve operations in a pipeline depends primarily upon:

Introduction:
Water hammer is the rapid pressure rise or surge that occurs when flowing liquid is forced to stop or change direction suddenly. This question tests which physical factors govern the magnitude of that surge, a crucial topic in civil and mechanical pipeline design.

Given Data / Assumptions:

• Liquid initially flowing steadily in a long pipe.
• Valve operation imposes a rapid change in velocity.
• Pipe wall is elastic; liquid is slightly compressible.

Concept / Approach:
The classical Joukowsky relation gives the peak pressure rise: Δp = ρ * a * ΔV where a is the wave speed. The wave speed depends on both fluid bulk modulus and pipe-wall elasticity. Closure time relative to wave travel time sets how fully the Joukowsky rise develops.

Step-by-Step Solution:
1) Recognize that stiffer walls and less compressible liquids yield larger wave speed a.2) Larger a makes Δp greater for the same velocity change.3) Faster valve closure (small closure time) increases ΔV per wave reflection, approaching the full Joukowsky surge.4) Hence all three—pipe elasticity, fluid compressibility, and closure speed—affect magnitude.

Verification / Alternative check:
Surge analysis software and field records show that installing air vessels or using slow-closure valves reduces peak surge by altering ΔV and the effective compressibility of the system.

Why Other Options Are Wrong:

• Only one factor (a, b, or c) is incomplete; surge depends on combined properties and operation.
• Pipe diameter alone cannot explain wave speed or closure timing effects.

Common Pitfalls:
Ignoring pipe supports and entrapped air; both modify effective wave speed and observed surge.

Final Answer:
all of the above