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8 - Designing Dipsticks—Solution

from The Solutions

R. Grant Woods
R. Grant Woods
Affiliation:
The University of Manitoba
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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).

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Calculus Mysteries and Thrillers , pp. 107 - 112
Publisher: Mathematical Association of America
Print publication year: 1998

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