Page 206 - Modelling in Transport Phenomena A Conceptual Approach

186 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

and

7.3 CONSERVATION OF TOTAL MASS

Summation of Eq. (7.2-2) over all species gives the total mass balance in the form

(7.3-1)

Note that the term xi cvijMi is zero since mass is conserved. On the other hand,
summation of Eq. (7.2-5) over all species gives the total mole balance as

(7.3-2)

where
Ej = Ccqj (7.3-3)

i
The generation term in Q. (7.3-2) is not zero because moles are not conserved.
This term vanishes only when ?Tj = 0 for all values of j.

Example 7.2 An open cylindrical tank of height H and diameter D is initially
half full of a liquid. At time t = 0, the liquid is fed into the tank at a constant
volumetricflow rate of Qin, and at the same time it is allowed to drain out through
an orifice of diameter Do at the bottom of the tank. Express the variation of the
liquid height as a function of time.

Solution
Assumptions

1. Rate of evaporation from the liquid surface is negligible.
2. Liquid is incompressible.

3. Pressure distribution in the tad is hydrostatic.