27. In the textile industry, filament and yarn sizes are reported in denier which is defined as the
mass in grams of a length of 9000 meters.
If a synthetic fiber has an average specific gravity of
1.32 and a filament of this material has a denier of 5.0, what is the mass per unit length in pounds
mass per yard?
What is the cross sectional area of this fiber in square inches?
The specific
gravity is defined as
density
specific gravity
=
density of water
27. To begin this problem, we note that there is a conversion factor
hidden
in the
problem statement, i.e.,
1 denier
1 g 9000 m
=
(1)
or
4
1 denier
1.11 10
g m
−
=×
(2)
The answer to the first question is given by
4
mass per
5 denier
5.55 10
g m
unit length
−
==
×
(3)
and in order to obtain the desired units we make use of the proper conversion factors to
express Eq. 3 in the form
42
m
6
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 Winter '10
 B.G.Higgins
 Conversion of units, Square yard, ΓL

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