1. For a moving fluid the system possesses not only internal energy, but kinetic and potential energy (i.e. effect of gr

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1 For A Moving Fluid The System Possesses Not Only Internal Energy But Kinetic And Potential Energy I E Effect Of Gr 1 (348.07 KiB) Viewed 57 times

1. For a moving fluid the system possesses not only internal energy, but kinetic and potential energy (i.e. effect of gravity). A second difference is that we must consider any word done as a result of motion of the system boundaries. (a) Since the First Law of thermodynamics applies to closed systems, select a system which moves and deforms with the fluid. Apply the First Law of thermodynamics to a mov- ing fluid considering pressure forces but neglecting viscous forces. HINT: Generally, the work done by displacing an object a distance dr against a force, Ē, is dW = F. dr. The rate of doing work is dW dr = F. = F. dt dt (1) The pressure force on some small element of surface is: dĒ = -pñdA (2) Dotting this with ū and integrating over the entire closed surface yields the net pV-work by the universe outside on the system (sinde dF in the equation above is the force exerted on the system by the fluid outside). Thus, dW dt - [ plū•ü)dA (3) A ANSWER: a [(u +*+ o)) + .[(u + + )"]+= ] + U р + 02 + р 2 Фа Du +1.q=0 (4) at (b) Repeat part (a) using a macroscopic but stationary system. You will need to consider convection of energy across the boundaries. Show that, to get the same answer as in (a), the mass flowrate across the boundary must be multiplied by the Enthalpy per unit mass (H = U + p/p) rather than internal energy. HINT: Let the energy flux (rate per area) by convection e denoted as pXū, where X is the energy content of the fluid per unit mass. Comparing your result to that in (a) conclude that v2 X =U + P + + og р 2 (5) which includes a term containt the pressure (the term represents the pV-work done on teh fluid). After the kinetic energy and potential energy terms are accounted for, we see the remaining energy content of the entering fluid is the enthalpy rather than just the internal energy.