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Calculating Volume and Cost of Flowable Fill for Civil Engineering Tunnel Project, Study notes of Introduction to Business Management

Capital Community CollegeIntroduction to Business Management

Instructions and exercises for calculating the amount and cost of flowable fill needed to fill in an empty tunnel for a civil engineering project. Students are required to convert units to a common measure, calculate volumes of rectangular prisms and cylinders, and determine the cost based on the volume and price per cubic yard.

Typology: Study notes

Pre 2010

Uploaded on 08/05/2009

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FACULTY NOTES
The LTAs and Spinoffs are designed so that each professor can implement them in a way that is
consistent with his/her teaching style and course objectives. This may range from using the
materials as out-of-class projects with minimal in-class guidance to doing most of the work in
class. The LTAs and Spinoffs are amenable to small group cooperative work and typically
benefit from the use of some learning technology. Since the objective of the LTAs and Spinoffs
is to support the specific academic goals you have set for your students, the Faculty Notes are not
intended to be prescriptive. The purpose of the Faculty Notes is to provide information that
assists you to take full advantage of the LTAs and Spinoffs. This includes suggestions for
instruction as well as answers for the exercises.
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FACULTY NOTES

The LTAs and Spinoffs are designed so that each professor can implement them in a way that is consistent with his/her teaching style and course objectives. This may range from using the materials as out-of-class projects with minimal in-class guidance to doing most of the work in class. The LTAs and Spinoffs are amenable to small group cooperative work and typically benefit from the use of some learning technology. Since the objective of the LTAs and Spinoffs is to support the specific academic goals you have set for your students, the Faculty Notes are not intended to be prescriptive. The purpose of the Faculty Notes is to provide information that assists you to take full advantage of the LTAs and Spinoffs. This includes suggestions for instruction as well as answers for the exercises.

FACULTY NOTES

LTA 13

It Ain’t Heavy, It’s My Crawler Background Information Math Subject Area: Volume, Unit Conversion Math Prerequisites: Basic understanding of volume, manipulation of formulae, and unit conversion. ATE-Supported Engineering Technology Field(s): Civil Engineering. Learning Technology Suggested: Scientific Calculator Approximate Class Time required for LTA: One class period plus homework How Much Do We Need?

  1. Describe the steps you will follow to calculate the amount of Flowable Fill needed to fill in the empty space in the tunnel. The students should realize that they need to convert all units to a common unit, perhaps feet, so they can calculate volumes. They will need to find the volume of the rectangular prism tunnels and then subtract the volume of the cylindrical pipes. For example: We will need to calculate the volume of the two tunnels and then subtract the volume of the pipes. The tunnels are “boxes” with volume = lengthwidthheight. The pipes are “cylinders” with volume πr^2 h. The length of the tunnels is 379.5 ft. The width is 4.5 ft for the left tunnel and 4 ft for the right tunnel. The height of both tunnels is 6.5 ft. The “height” of the pipes is 379.5 ft. The 14 small pipes have radius (1/6) ft. One big pipe has radius (3/4) ft. The biggest pipe has radius 1 ft.

Did the contractor do the job correctly?

  1. Determine whether or not the contractor has filled the tunnel. Be sure to show work to clearly explain your answer. If a discrepancy exists, give a real-life example of something that would have approximately the same amount of volume as the discrepancy to illustrate its size (a shoebox, a house…). If we take the number of truckloads of Fill and multiply by the number of cubic yards per truckload, we will get the total cubic yards used by the contractor. 71 truckloads * 9 yd^3 /truckload = 639 yd^3 of Flowable Fill. We needed 690.402 yd^3 to fill the empty space in the tunnel. The contractor is approximately 51 yd^3 short of the required amount. One real-life example: The amount of Flowable Fill that the contractor was short would fill a small bedroom from floor to ceiling.
  2. Assume that all of the Flowable Fill from the 71 truckloads settles to the bottom so that there is an air pocket at the top. Also assume that the fill is divided between the two sides of the tunnel in such a way that the height of fill in each tunnel is the same. Approximate the amount of space left empty at the top of the tunnel. Would there be enough space for a rat to run through, a person to crawl through, …? 51 yd^3 = 51 * 27 = 1377 ft^3 379.5 ft * 8.5 ft * height of space = 1377 ft^3 So, height = 1377 ft^3 / (379.5 ft * 8.5 ft) = 0.427 ft or approximately 5 inches, and a rat would fit through this space comfortably. Note: If the space for the top four pipes is taken into account, this would add on only a little over a half inch to the depth of the air space.