Page 178 - Modelling in Transport Phenomena A Conceptual Approach

158 CHAPTER 6. STEADY-STATE MACROSCOPIC BALANCES

The rate of work done on the system by the surroundings is given by
w = ws + (P?m)jn-(P?m),t (6.3-8)
* P
Shaft work Flow work
In Figure 6.2, when the stream enters the system, work is done on the system by
the surroundings. When the stream leaves the system, however, work is done by
the system on the surroundings. Note that the boundaries of the system are fixed
in the case of a steady-state flow system. Therefore, work associated with volume
change is not included in Eq. (6.3-8).
Substitution of Eq. (6.3-8) into Eq. (6.3-7) and the use of the definition of
enthalpy, i.e., H = + PP, gives

which is known as the steady-state energy equation.
Kinetic and potential energy terms in Eq. (6.3-9) are expressed in the form
..
EK=-v 2 (6.3-10)
1
2
and
Ep=gh (6.3-11)
where g is the acceleration of gravity and h is the elevation with respect to a
reference plane.
Enthalpy, on the other hand, depends on temperature and pressure. Change in
enthalpy is expressed by
dfi = CpdT + C(1- 8T)dP (6.3-12)
where is the coeficient of volume expansion and is defined by

(6.3-13)

Note that
0 for an incompressible fluid
8={ 1/T for an ideal gas (6.3-14)
When the changes in the kinetic and potential energies between the inlet and
outlet of the system are negligible, Eq. (6.3-9) reduces to

In terms of molar quantities, Eqs. (6.3-9) and (6.3-15) are written as