Thermodynamics

To push the entire fluid element into the control volume, this force must actthrough a distance L. Thus, the work done in pushing the fluid elementacross the boundary (i.e., the flow work) isW flow FL PAL PV1kJ2(5–23)The flow work per unit mass is obtained by dividing both sides of this equationby the mass of the fluid element:w flow Pv1kJ>kg2(5–24)The flow work relation is the same whether the fluid is pushed into or outof the control volume (Fig. 5–13).It is interesting that unlike other work quantities, flow work is expressed interms of properties. In fact, it is the product of two properties of the fluid. Forthat reason, some people view it as a combination property (like enthalpy) andrefer to it as flow energy, convected energy, or transport energy instead offlow work. Others, however, argue rightfully that the product Pv representsenergy for flowing fluids only and does not represent any form of energy fornonflow (closed) systems. Therefore, it should be treated as work. This controversyis not likely to end, but it is comforting to know that both argumentsyield the same result for the energy balance equation. In the discussions thatfollow, we consider the flow energy to be part of the energy of a flowingfluid, since this greatly simplifies the energy analysis of control volumes.Total Energy of a Flowing FluidAs we discussed in Chap. 2, the total energy of a simple compressible systemconsists of three parts: internal, kinetic, and potential energies (Fig. 5–14). Ona unit-mass basis, it is expressed ase u ke pe u V 22 gz1kJ>kg2(5–25)where V is the velocity and z is the elevation of the system relative to someexternal reference point.FChapter 5 | 227FIGURE 5–12In the absence of acceleration, theforce applied on a fluid by a piston isequal to the force applied on the pistonby the fluid.w flowPvAP(a) Before enteringw flowPv(b) After enteringCVCVFIGURE 5–13Flow work is the energy needed topush a fluid into or out of a controlvolume, and it is equal to Pv.KineticenergyFlowenergyKineticenergyNonflowingfluidVe = u + 2+ gz2Flowingfluidθ = Pv + u + + gz2V 2 FIGURE 5–14InternalenergyPotentialenergyInternalenergyPotentialenergyThe total energy consists of three partsfor a nonflowing fluid and four partsfor a flowing fluid.