The magnitude of water hammer pressure rise in a pipeline depends on several factors. Which comprehensive choice correctly lists the influencing parameters?

Introduction / Context:
Water hammer is a transient pressure surge caused by rapid changes in flow velocity, such as sudden valve closures or pump trips. Correct design requires understanding all parameters that influence the peak pressure rise and wave speed.

Given Data / Assumptions:

• Rigid/elastic pipe containing a slightly compressible liquid (e.g., water).
• Valve or pump manoeuvres can be fast or slow relative to wave travel time.
• Reflections occur at boundaries (valves, reservoirs, elbows).

Concept / Approach:
The Joukowsky relation Δp = ρ * a * ΔV shows that surge magnitude depends on fluid density ρ, wave speed a, and velocity change ΔV. The wave speed a itself depends on liquid compressibility and pipe wall elasticity: a = sqrt( K / ρ / (1 + (K * D)/(E * e)) ), where K is bulk modulus, E is pipe Young’s modulus, D pipe diameter, e wall thickness.

Step-by-Step Solution:
Faster closure → larger instantaneous ΔV → larger Δp.Longer pipeline → longer wave travel time 2L/a governs whether closure is “rapid” and affects reflection interactions.Stiffer pipe (higher E) → higher wave speed a → larger Δp for the same ΔV.Less compressible liquid (higher K) → higher a → larger Δp.

Verification / Alternative check:
Method of characteristics simulations confirm that closure schedule, pipe length, and material properties all alter peak and subsequent oscillations.

Why Other Options Are Wrong:
Any single-factor answer is incomplete; all listed factors contribute materially to surge magnitude.

Common Pitfalls:

• Assuming “rigid column” without accounting for elasticity, which underestimates peak pressure.
• Ignoring reflections and timing relative to 2L/a.

Final Answer:
All of the above