Optimal Insulation Thickness for Steam Piping

by Broderick Williams

Submitted : Spring 2010

As the title of this project implies, we are informed that a plant uses a pipe that is 1000 ft in length and 8 inches in width to transport steam. Without insulation, heat is lost from the pipe, which requires additional generation of steam to make up the required difference, costing more money. Insulation also costs money, so there is a trade off that must be made. The task at hand requires finding the most cost efficient width of insulation in order to save on steam transport. This goal can be obtained primarily through derivation and algebra. A summary of steps to solve this problem includes the following:

1. Set Equations (1) and (2) equal to each other and solve for T_s.
2. Obtain cost of insulation and steam.
3. Formulate the equation of net cost.
4. Take the derivative with respect to (R) for equations T_s and C(R).
5. Now, plug ?T'?_s into C’(R) to obtain a cubic function in the form of AR³+BR²+CR+D.
6. Use maple computer system to solve the cubic function in order to find the value of (R).
7. Subtract R - R₀ to attain the optimal radius of insulation. Once the aforementioned sequences are complete, the optimal width of insulation will be found, allowing the plant to transport steam in a cost-effective manner.

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