Solution Found!
The dynamic response of a stirred-tank bioreactor can be
Chapter 5, Problem 5.4(choose chapter or problem)
The dynamic response of a stirred-tank bioreactor can be represented by the transfer function C'(s) CF(s) 4 2s + 1 where C' is the exit substrate concentration, mol/L, and C} is the feed substrate concentration, mol!L. (a) Derive an expression for c'(t) if cp(t) is a rectangular pulse (Fig. 5.2) with the following characteristics: t < 0 O:=st<2 2:=st
Questions & Answers
QUESTION:
The dynamic response of a stirred-tank bioreactor can be represented by the transfer function C'(s) CF(s) 4 2s + 1 where C' is the exit substrate concentration, mol/L, and C} is the feed substrate concentration, mol!L. (a) Derive an expression for c'(t) if cp(t) is a rectangular pulse (Fig. 5.2) with the following characteristics: t < 0 O:=st<2 2:=st
ANSWER:Problem 5.4
The dynamic response of a stirred-tank bioreactor can be represented by the transfer function
where C' is the exit substrate concentration, mol/L, and C’F is the feed substrate concentration, mol/L.
(a) Derive an expression for c'(t) if cF(t) is a rectangular pulse (Fig. 5.2) with the following characteristics:
(b) What is the maximum value of c'(t)? When does it occur? What is the final value of c'(t)?
(c) If the initial value is c(0) = 1, how long does it take for c(t) to return to a value of 1.05 after it has reached its maximum value?
Step by Step Solution
Step 1 of 5
Consider the given function.
The expression for the rectangular pulse input is given by,
