Transient hydraulics in pipelines: The “critical time” for development of water hammer corresponds to which travel time of the pressure wave?

Introduction / Context:Water hammer (surge) arises when flow is suddenly altered, sending a pressure wave that travels at acoustic velocity in the liquid–pipe system. The concept of “critical time” is crucial for evaluating whether a given valve-closure schedule will cause maximum surge.

Given Data / Assumptions:

• Single pipeline between valve and reservoir/tank.
• Wave speed a; pipeline length L.
• Elastic water and pipe wall properties define a.

Concept / Approach:

The reflection of the wave at a reservoir boundary and its return to the valve controls transient magnitude. The critical time equals the round-trip travel time 2L/a. Closure faster than this is “sudden,” producing near-Joukowsky surge; slower closure spreads acceleration and reduces peak pressure.

Step-by-Step Solution:

Verification / Alternative check:

Transient analysis software and classical water-hammer charts confirm that the most severe pressure rise occurs when closure completes within the round-trip time.

Why Other Options Are Wrong:

• “Closing the valve” is an action, not the definition of critical time.
• One-way travel underestimates the condition that sets peak surge.
• “Entire network once” is irrelevant in a single-pipe context.

Common Pitfalls:

• Ignoring elastic wave speed reduction due to pipe wall flexibility.
• Overlooking boundary conditions (air vessel, surge tank) that change reflections.

Final Answer:

the wave to travel from the valve to the reservoir and back.