Final answer:
Yes, the density difference of sea water at different depths affects the power required by a pump because the water's density increases with depth, leading to a higher pressure that the pump must overcome, requiring more power.
Step-by-step explanation:
The question relates to the effect of density differences of sea water at different depths on the power required by a pump. The density of a fluid, like sea water, increases at greater depths due to the weight of the water above causing a compression effect, though this is usually minimal for liquids like water. Therefore, when a pump operates at greater depths, it must work against higher pressure to move the same volume of water, as the pressure can be calculated using the formula for hydrostatic pressure, which is the product of depth, gravitational acceleration, and density (pgh). This increase in pressure requires the pump to exert more power to overcome the increased resistance to flow, leading to a higher energy demand.
Looking at energy considerations, a pump's role is to increase the pressure of the water, which does require more power when the density of the water is greater at increased depths. Since the input and output diameters and heights are constant, the increase in power supplied is primarily used to boost the pressure, rather than changing the water's kinetic or potential energies.