Engineers compare two pipes that carry the same incompressible fluid from a wide region into a much narrower region at the same volume flow rate. Pipe X lies entirely horizontal, while pipe Y rises vertically so that the narrow region is 6 m above the wide region. Apart from their orientation, the two pipes are identical and frictional effects can be neglected.
(a) Describe qualitatively how the pressure changes between the wide and narrow regions for pipe X. Identify the forms of mechanical energy whose changes account for this pressure difference.
(b) For pipe Y, explain how the additional vertical displacement modifies the pressure change required to maintain the same flow rate compared with pipe X.
(c) Based on your explanations, state which pipe requires a larger pressure increase at the entrance to achieve the specified flow and justify your answer with appropriate reasoning.