24
CHAPTER 2. DIMENSIONAL ANALYSIS
Note that the conversion factor is composed of ratios of values that are equivalent
(i.e , 1 hour = 3600 seconds) placed in such a way that all but the desired dimensions
The student’s committee chairman decides that the student should publish the
findings in the Journal of Weird Research (a popular publication!); however, the
chairman insists that the result be given in units of furlongs per fortnight. Noting
that 1 furlong = 660 ft and 1 fortnight = 14 days, the student (against his better
judgment) makes the following conversion.
13.9 —
3
r ip i
10.3048 mJ
1 furl (3600 si
24 À
660 ft L 1 h J 1 day
conversion factor
14 days
1 fort
= 83,580
furlongs
fortnight
Example 2.2. Equilibrium Beach Profile
The equilibrium beach profile for a beach with mean grain size of 0.2 mm is given
approximately by the equation
h = 0.15 x2/3
where h and x have dimensions of feet, and 0.15 [=] ft1/3. This equation can be
converted so that it can be used with the preferred SI units of meters by providing
an equivalent value for the coefficient, 0.15, having units of m1/3, i.e.,
0-15 ft1'3
7 = 0.1 m1/3
And the equivalent equilibrium beach profile equation in SI units is
h = 0.112/3
where x and h now have units of meters.