Final answer:
The problem involves using Bernoulli's equation to determine the velocity of water as it exits the top of a pipe, taking into consideration factors like pressure, kinetic energy, height, and initial velocity.
Step-by-step explanation:
The question pertains to the applications of Bernoulli's principle and the principles of fluid dynamics as it asks about the speed of water leaving a pipe. To solve for the speed of water exiting the pipe, we need to consider the energy conservation in the flow of the fluid and apply Bernoulli's equation, which is given by:
P + ½ρv² + ρgh = constant
Here, P is the pressure, ρ is the fluid density, v is the fluid velocity, g is the acceleration due to gravity, and h is the height relative to a reference point.
We assume that the diameters of the input and the output of the pipe are the same, therefore, the velocity at the lower end (input) and at the upper end (output) can be related by Bernoulli's equation, taking into account the height to which the water is raised and the initial velocity of the water. While we don't have all the information to calculate it in this case, the pressure provided by the pump and the kinetic energy at the bottom of the pipe will be converted into potential energy and kinetic energy at the top, giving us an equation that would allow for solving the exit speed should the pressure provided by the pump be known.