Thermodynamics

228 | ThermodynamicsThe fluid entering or leaving a control volume possesses an additionalform of energy—the flow energy Pv, as already discussed. Then the totalenergy of a flowing fluid on a unit-mass basis (denoted by u) becomesu Pv e Pv 1u ke pe2(5–26)But the combination Pv u has been previously defined as the enthalpy h.So the relation in Eq. 5–26 reduces tou h ke pe h V 22 gz1kJ>kg2(5–27)By using the enthalpy instead of the internal energy to represent theenergy of a flowing fluid, one does not need to be concerned about the flowwork. The energy associated with pushing the fluid into or out of the controlvolume is automatically taken care of by enthalpy. In fact, this is themain reason for defining the property enthalpy. From now on, the energy ofa fluid stream flowing into or out of a control volume is represented by Eq.5–27, and no reference will be made to flow work or flow energy.ṁ i ,kg/sθ i ,kJ/kg˙CVm iθ i(kW)Energy Transport by MassNoting that u is total energy per unit mass, the total energy of a flowing fluidof mass m is simply mu, provided that the properties of the mass m are uniform.Also, when a fluid stream with uniform properties is flowing at a massflow rate of ṁ, the rate of energy flow with that stream is ṁu (Fig. 5–15).That is,Amount of energy transport: E mass mu m a h V 2 gz b1kJ2 (5–28)2FIGURE 5–15The product m . iu i is the energytransported into control volumeby mass per unit time.Rate of energy transport: E # mass m # u m # a h V 2 gz b1kW2 (5–29)2When the kinetic and potential energies of a fluid stream are negligible, asis often the case, these relations simplify to E mass mh and E . mass ṁh.In general, the total energy transported by mass into or out of the controlvolume is not easy to determine since the properties of the mass at eachinlet or exit may be changing with time as well as over the cross section.Thus, the only way to determine the energy transport through an opening asa result of mass flow is to consider sufficiently small differential masses dmthat have uniform properties and to add their total energies during flow.Again noting that u is total energy per unit mass, the total energy of aflowing fluid of mass dm is u dm. Then the total energy transported by massthrough an inlet or exit (m i u i and m e u e ) is obtained by integration. At aninlet, for example, it becomesE in,mass m iu i dm i m ia h i V i 22 gz i b dm i(5–30)Most flows encountered in practice can be approximated as being steadyand one-dimensional, and thus the simple relations in Eqs. 5–28 and 5–29can be used to represent the energy transported by a fluid stream.