
Example 8.5
The concentration of a chemical in the vessel shown in Figure 8.27 is determined by the
differential equation
V
Q
dc
dt
þ c ¼ c
1
(8:180)
where
V is the constant volume of liquid in the vessel
Q is the constant flow rate of liquid in and out of the vessel
c
1
is the concentration of chemical in the liquid flowing in
c is the concentration of the chemical in the well-stirred vessel
(a) Find the analytical solution for the concentration c(t), t 0 when the input c
1
(t) ¼ c
1
, t 0.
(b) Find the difference equation for simulating the concentration response using AM-2 integra-
tion with step size T.
(c) Find an expression for the steady-state value c(n)