How do you calculate the change in water pressure as the diameter of the hose changes? – JH
When water flows through a hose, it has three main forms for its energy: kinetic energy, gravitational potential energy, and an energy associated with its pressure—which I’ll call pressure potential energy. Since energy is conserved, the water’s energy can’t change as it flows through the hose (we’ll ignore frictional forces here, although they really are pretty important in a hose). Let’s assume that the hose is horizontal, so that the water’s gravitational potential energy can’t change. When the water enters a narrowing in the hose, the water must speed up to avoid delaying the water behind it. This increase in speed is associated with an increase in kinetic energy. Since the water’s energy can’t change, the increase in kinetic energy must be accompanied by a decrease in pressure. If the water then enters a widening in the hose, it slows down, its kinetic energy drops, and its pressure rises to conserve energy! If the hose then rises upward, so that the water’s gravitational potential energy rises, the water’s pressure must drop to conserve energy. In general, one form of energy can become another but the sum of those three forms can’t change.