Final answer:
The questions require applying fluid mechanics principles using Bernoulli's equation and continuity equation to calculate pressures or flow speeds in various pumping systems, taking into account the static and dynamic heads, as well as fluid properties such as density.
Step-by-step explanation:
The questions provided all relate to the calculation of pressures and speeds required for fluid mechanics problems involving pumps and piping systems. To solve these problems, principles from Bernoulli's equation and continuity equation are used, considering energy conservation in terms of pressure, kinetic, and potential energies. The complexities of fluid dynamics are approximated through these equations to understand how pumps must operate to achieve the desired fluid flow.
For example, to find out what pressure must be provided by a pump so that water can flow at 5.0 m/s at 150 m above the pump, one must account for the static head due to elevation, the dynamic head due to flow speed, and any losses such as head loss due to friction. This involves converting all terms into the same unit, which typically involves converting the head in meters of water into pressure units such as Pascals and accounting for the density of the fluid.