If a valve in a pipe is suddenly closed, a large pressure surge may develop. For example, when the electrically operated shutoff valve in a dishwasher closes quickly, the pipes supplying the dishwasher may rattle or "bang" because of this large pressure pulse. Explain the physical mechanism for this "water hammer" phenomenon. How could this phenomenon be analyzed?

The water hammer effect occurs when a fluid in motion is suddenly forced to stop, such as when a valve closes quickly. The kinetic energy of the moving fluid doesn't disappear, but instead manifests as a sudden increase in pressure, much like how a moving car that hits a wall doesn't stop instantly but imparts force onto the wall.

In the case of pipe and valve, when the valve is suddenly shut, the flow of water, which was once smooth, gets interrupted. The water's momentum changes quickly, and since fluids are nearly incompressible, this rapid change in momentum results in a large pressure pulse or wave. This surge of pressure moves through the pipe, causing it to rattle or 'bang', an effect commonly known as 'water hammer'.

The water hammer phenomenon can be analyzed using physics and engineering principles. One can use concepts such as the conservation of momentum, fluid dynamics, and the bulk modulus of incompressibility. The principle essentially involved here is Newton's second law - when the momentum of an object (in this case, the fluid) changes but its time of interaction is very short (due to rapid valve closure), a large force is generated. However, as the fluid volume is incompressible, the force manifests as an increased pressure. One could theoretically calculate this pressure surge using these principles, and practical measures can be taken to prevent or mitigate its negative effects, such as gradual door closure or using pressure relief valves.