Page 242 - Modelling in Transport Phenomena A Conceptual Approach

222 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

Figure 7.5 Schematic diagram for Problem 7.4

(Answer: a) 0.2m3/min b) 0.17m5I2/min)

7.5 Time required to empty a vessel is given for four common tank geometries
by Foster (1981) as shown in Table 7.1. In each case, the liquid leaves the tank
through an orifice of cross-sectional area A,,. The orifice coefficient is C,. Assume
that the pressure in each tank is atmospheric. Verify the formulas in Table 7.1.

7.6 For steady flow of an incompressible fluid through a control volume whose
boundaries are stationary in space, show that Eq. (6.3-9) reduces to

-++++Ah+(AU-Qin,) =Ws
AP
A(v)~
P 2
where A represents a difference between the outlet and inlet values.

a) Using the thermodynamic relations

and
dQint
&= -
+ dsgen
T (3)
show that
dEv = T dS'gen = do - dQirst (4)

where fiv, the friction loss per unit mass, represents the irreversible degradation
of mechanical energy into thermal energy, and S'gen is the entropy generation per
unit mass.