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Feb 6, 2023 at 2:10 history edited Jeffrey J Weimer CC BY-SA 4.0
answered op's question
Feb 6, 2023 at 2:08 comment added Jeffrey J Weimer I've added an explanation for the integrals and an explanation for the $p/\rho$ term. Do not consider that energy density in the fluid packet being changed because it pushes (or pulls) other fluid packets. Consider only what happens to energy density terms for internal energy (temperature), kinetic energy (velocity), potential energy (height), and capacity to expand/contract ($p/\rho$) as you sit on the fluid packet while it is moving through the control volume.
Feb 6, 2023 at 2:04 history edited Jeffrey J Weimer CC BY-SA 4.0
answered op's question
Feb 5, 2023 at 20:31 comment added Jan F. S Appreciate the detailed answer although I can't really follow the integrals. So this means that there is no flow work for a fluid that does not leave a system boundary? So in your open system example, if the fluid pushes something while moving a certain distance, that would result in a higher energy density and therefore higher pressure? Due to bernoulli's equation?
Feb 5, 2023 at 16:18 history answered Jeffrey J Weimer CC BY-SA 4.0