Book contents
- Frontmatter
- Dedication
- Contents
- The Purpose of This Book
- An Overview of the Projects
- Detailed Mathematical Requirements
- The Projects
- The Solutions
- 1 The Case of the Parabolic Pool Table—Solution
- 2 Calculus for Climatologists—Solution
- 3 The Case of the Swiveling Spotlight—Solution
- 4 Finding the Salami Curve—Solution
- 5 Saving Lunar Station Alpha—Solution
- 6 An Income Policy for Mediocria—Solution
- 7 The Case of the Cooling Cadaver—Solution
- 8 Designing Dipsticks—Solution
- 9 The Case of the Gilded Goose-egg—Solution
- 10 Sunken Treasure—Solution
8 - Designing Dipsticks—Solution
from The Solutions
- Frontmatter
- Dedication
- Contents
- The Purpose of This Book
- An Overview of the Projects
- Detailed Mathematical Requirements
- The Projects
- The Solutions
- 1 The Case of the Parabolic Pool Table—Solution
- 2 Calculus for Climatologists—Solution
- 3 The Case of the Swiveling Spotlight—Solution
- 4 Finding the Salami Curve—Solution
- 5 Saving Lunar Station Alpha—Solution
- 6 An Income Policy for Mediocria—Solution
- 7 The Case of the Cooling Cadaver—Solution
- 8 Designing Dipsticks—Solution
- 9 The Case of the Gilded Goose-egg—Solution
- 10 Sunken Treasure—Solution
Summary
To: Joe Moosemess
From: Anne G. Gables
Subject: Dipstick Calibration
Here is my report on how to calibrate the dipsticks for the cylindrical and spherical fuel tanks. In each case I have worked out an algebraic expression giving the fraction F(d) of the tank capacity that is filled with fuel as a function of the length d of dipstick that is wetted by the fuel. I have also provided a table of values for F(d) for values of d ranging from 0 to D (the value of d when the tank is full) in increments of D/32. For the cylindrical tank I have derived the algebraic expression in two ways. (You will be reassured to note that they agree!)
Cylindrical Tanks
Consider a right circular cylindrical fuel tank whose circular ends are vertical. Let the radius of its ends be R, and let its length be h (all distances will be measured in meters). Suppose that a dipstick inserted in the slot at the top is wetted to a length d. This means that the surface of the fuel in the tank intersects the circular ends of the tank along a line that is a distance d above the bottom of the end of the tank (see Figure A).
- Type
- Chapter
- Information
- Calculus Mysteries and Thrillers , pp. 107 - 112Publisher: Mathematical Association of AmericaPrint publication year: 1998