Deep Tunnel
14 Feb 2002

Mesquite Trees, Anon.
Thorn Avenue
Lubbock, TX 79414

Dear Calculus Student,

Wellbuilt Design and Construction, after working primarily in the commercial sector of construction in the Fort Stockon area, has recently landed a large government contract for the construction of a "deep tunnel" for the city of Fort Stockon. This is a large (55' diameter) tunnel built well below the city, into which the city's sewer system can be voided during storms that threaten to overwhelm the system---thus preventing the release of untreated sewage into the environment. The configuration of the tunnel is shown in figure 1, and it is shown end-on in figure 2.
  plan view of tunnel
  end view of tunnel
  Figure 1: deep tunnel configuration
  Figure 2: end view of tunnel

The length of the large tunnel section will depend on the phase of the construction (which is slated to extend over 7 years). For purposes of this proposal, the length should be figured at two time points: mid-phase length of 500 ft and full-phase length of 1500 ft. The work required to pump the sewage back out of the deep tunnel is a significant concern, as it determines the nature of the pumps required to accomplish this task. We have therefore contracted with your company to find the work that it would take to empty the deep tunnel (pumping out both the main chamber and the access entrance) at mid-phase and full-phase. The top of the access entrance will be situated 85 ft below ground level. The contents in the deep tunnel would need to be pumped up to the city's sewer drainage system which lies typcially at 10 feet below ground level.

As we are good friends with one of the established gurus in Fort Stockon, Dr. Kent Pearce, we have arranged that he be available to answer any technical questions that might arise in the course of your investigation. We look forward to receiving your analysis of this problem. The final 3--5 page report should be submitted by the 19th of March.

Yours Sincerely,
William Fold
President, Wellbuilt Inc.


Technical Report Requirements

All reports submitted to Wellbuilt, Inc. should be written so that the directors receiving the report can understand and apply the information contained therein. Owing to the preeminent position of Wellbuilt, Inc. in the field, all of our directors have degrees in science, and thus have had college level mathematics, including calculus---unfortunately, however, their long experience in the field precludes a ready knowledge of the same. Therefore, the reports should assume a strong precalculus and basic calculus (about half a semester of calculus I) background, but should not expect a knowledge of much more than that.

Reports should further: