A drinking fountain shoots water about 12 cm up in the air from a nozzle of diameter 0.60 cm (Fig. 13–67). The pump at the base of the unit (1.1 m below the nozzle) pushes water into a 1.2-cm-diameter supply pipe that goes up to the nozzle. What gauge pressure does the pump have to provide? Ignore the viscosity; your answer will therefore be an underestimate.
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Key Concepts

Bernoulli's Principle

Bernoulli's Principle states that in a flowing fluid, an increase in the fluid's speed occurs simultaneously with a decrease in pressure or potential energy. This principle is essential for understanding how the water is propelled upward from the nozzle, as it relates the pressure at the pump to the kinetic energy of the water exiting the nozzle.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. In this scenario, the pressure at the pump must overcome the hydrostatic pressure created by the height difference (1.1 m) between the pump and the nozzle, which is crucial for determining the required gauge pressure.

Continuity Equation

The Continuity Equation states that for an incompressible fluid, the mass flow rate must remain constant from one cross-section of a pipe to another. This concept helps in understanding how the change in diameter from the supply pipe to the nozzle affects the velocity of the water, which is necessary for calculating the pressure needed at the pump.