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%
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