1. A total length of 100 m of tubes must be installed in a shell and tube heat exchanger in order to provide the necessary heat transfer area. The total cost of the installation in dollars includes:

• The cost of the tubes, which is constant at $900.

• The cost of the shell = 1100D2.5L, where L is the length of the heat exchanger and D is the diameter of the shell, both in meters.

• The cost of the floor space occupied by the heat exchanger = 320DL

(a) The total cost is C = C1 + C2 + C3. Develop a function C(D) by using the following equation based on 1 m2 accommodating 200 tubes:

100 = 200 A L where A = π D2/4, Eqn. (1), also shown on Figure

(b) If the diameter D and length L vary by 10%, how does that affect the cost? Compute the new cost for the following three combinations:

• D vary by 10%, L not varying

• L vary by 10%, D not varying

• Both D and L vary by 10%

• The cost of the tubes, which is constant at $900.

• The cost of the shell = 1100D2.5L, where L is the length of the heat exchanger and D is the diameter of the shell, both in meters.

• The cost of the floor space occupied by the heat exchanger = 320DL

(a) The total cost is C = C1 + C2 + C3. Develop a function C(D) by using the following equation based on 1 m2 accommodating 200 tubes:

100 = 200 A L where A = π D2/4, Eqn. (1), also shown on Figure

(b) If the diameter D and length L vary by 10%, how does that affect the cost? Compute the new cost for the following three combinations:

• D vary by 10%, L not varying

• L vary by 10%, D not varying

• Both D and L vary by 10%