Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

The fluid entering or leaving a control volume possesses an additional

form of energy—the flow energy Pv, as already discussed. Then the total

energy of a flowing fluidon a unit-mass basis (denoted by u) becomes

(5–26)

But the combination Pvuhas been previously defined as the enthalpy h.

So the relation in Eq. 5–26 reduces to

(5–27)

By using the enthalpy instead of the internal energy to represent the

energy of a flowing fluid, one does not need to be concerned about the flow

work. The energy associated with pushing the fluid into or out of the con-

trol volume is automatically taken care of by enthalpy. In fact, this is the

main reason for defining the property enthalpy. From now on, the energy of

a 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.

Energy Transport by Mass

Noting that uis total energy per unit mass, the total energy of a flowing fluid

of mass mis simply mu, provided that the properties of the mass mare uni-

form. Also, when a fluid stream with uniform properties is flowing at a mass

flow rate of m

.

, the rate of energy flow with that stream is m

.

u(Fig. 5–15).

That is,

Amount of energy transport: (5–28)

Rate of energy transport: (5–29)

When the kinetic and potential energies of a fluid stream are negligible, as

is often the case, these relations simplify to Emassmhand E

.

massm

.

h.

In general, the total energy transported by mass into or out of the control

volume is not easy to determine since the properties of the mass at each

inlet 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 as

a result of mass flow is to consider sufficiently small differential masses dm

that have uniform properties and to add their total energies during flow.

Again noting that uis total energy per unit mass, the total energy of a

flowing fluid of mass dmis udm. Then the total energy transported by mass

through an inlet or exit (miuiand meue) is obtained by integration. At an

inlet, for example, it becomes

(5–30)

Most flows encountered in practice can be approximated as being steady

and one-dimensional, and thus the simple relations in Eqs. 5–28 and 5–29

can be used to represent the energy transported by a fluid stream.

Ein,mass


mi

ui dmi


mi

ahi

Vi^2

2

gzib dmi

E

#

massm

#um#ahV^2

2

gzb¬¬ 1 kW 2

Emassmumah

V^2

2

gzb¬¬ 1 kJ 2

uhkepeh

V^2

2

gz¬¬ 1 kJ>kg 2

uPvePv 1 ukepe 2

228 | Thermodynamics

m ̇i,kg/s

CV

θi,kJ/kg

θi

(kW)

m ̇i

FIGURE 5–15

The product m

.

iuiis the energy

transported into control volume

by mass per unit time.