Concept reference
Water hammer is the system’s transient response when flow changes faster than pressure information can travel and reflect through the pipeline. A pump trip, check-valve closure or control action launches waves; high pressure can burst components, while low pressure can collapse pipe, admit contamination or separate the liquid column.
The ideal instantaneous velocity-change bound is Δp = ρaΔV or ΔH = aΔV/g, where wave speed a is m/s (ft/s). A characteristic pipeline period is related to 2L/a or 4L/a depending on the event and boundary reflection being judged. Real analysis includes pipe restraint/elasticity, pump inertia, valve law, profile and vapour effects.
Using Joukowsky as the entire analysis can miss column separation and later cavity collapse, which may govern. Assuming a “slow-closing” check valve is always safer can increase reverse velocity before closure and make slam worse.
§8.5 develops the transient mechanisms; §8.4 connects check-valve closure.
Physics sets the relationships; the owner, manufacturer and governing local standard set the project criteria.