Answer
See answers.
Work Step by Step
a. Steady flow is assumed. If the flow rate varied with time, more terms in the equation would be necessary; energy is needed to change the flow rate.
b. Laminar flow is assumed. If this were not true, turbulence and swirling currents would be present. These would heat the fluid, resulting in energy losses that would require more terms in the equation.
c. It is assumed that the fluid is incompressible. If the fluid changed volume, work would be done on or by the fluid as it shrunk or expanded. More terms in the equation would be necessary to account for these energy changes.
d. It is assumed we have a nonviscous fluid. If we didn’t, greater pressure differences would be required to achieve certain flow rates, due to the energy lost to viscous forces. The fluid pressure and its velocity would also depend upon the distance of the fluid element from the walls of the pipe.
