What causes hydraulic transients (water hammer) and how are they analyzed?

Water hammer is pressure surge from rapid flow velocity change in pipelines. Causes: pump trip, valve closure, demand changes. Joukowsky equation: delta_P = rho*a*delta_V, where a = wave speed (typically 900-1200 m/s). Analysis methods: (1) Arithmetic - hand calculation for simple systems, (2) Method of characteristics - solving hyperbolic PDEs numerically (standard approach), (3) Commercial software (HAMMER, Surge, WANDA). Protection devices: surge tanks, air chambers, pressure relief valves, slow-closing valves, flywheels on pumps. Design must prevent negative pressures (column separation) and overpressure.