# 8.2: Untitled Page 191

## volume average

### area average

concentration in

concentration

the tank

in the effluent

This allows us to write Eq. 8‐10 in terms of the single unknown,  c  , in order to A

obtain

dc

A

V

  c Q   c Q

(8‐12)

A

A 1

dt

One must be very careful to understand that Eq. 8‐11 is an approximation based on the assumption that the difference between  c  and  c  is small enough so A 2

A

that it can be neglected (Whitaker, 1988).

It is convenient to divide Eq. 8‐12 by the volumetric flow rate and express the result as

dc

A

  c    c

(8‐13)

A

A 1

dt

Here  represents the average residence time that is defined explicitly by

average

V

residence 

 

(8‐14)

Q

time

In general, we are interested in processes for which the inlet concentration,

c  , is a function of time, and a classic example is illustrated in Figure 8‐2.

A 1

There we have indicated that  c  undergoes a sudden change from o c to 1

c ,

A 1

A

A

and we want to determine how the concentration in the tank,  c  , changes A

because of this change in the inlet concentration. The initial value problem associated with the sudden change in the inlet concentration is given by dc

A

1

  c   c ,

t  0

A

A

(8‐15a).

dt

IC.

o

c   c ,

t  0

A

A

(8‐15b)

Equations 8‐15 are consistent with a situation in which the inlet concentration is originally fixed at o

c and then instantaneously switched from o

c to 1

c at t  0 .

A

A

A

358