Determining the Characteristic Dimension of an Object
TABLE 7.5. Calculation of characteristic dimension for
various shapes.
Object
Diagram
Explanation
Rectangular
plate or cylinder
with axis
parallel to wind
Circular disk
Intersecting
parabolas (leaf
shape)
Sphere or
cylinder (axis
perpendicular to
wind)
Animal shape
wind >
0 I w l
wind
d is the length
of the plate or
cylinder in the
direction of flow
d = 0.81w,
where w is the
disk diameter.
d = 0.72w,
where w is the
maximum leaf
width in the
direction of
wind flow.
d is the diameter
of the cylinder
or sphere.
d = V ' f 3 , V is
animal volume.
the leaf. For forced convection the characteristic dimension is computed
from:
where 1 is the length of the leaf perpendicular to the wind and d(y) indicates the variation of the leaf width with distance along the length of the
leaf. Table 7.5 gives values for a circular disk and a leaf shape (intersecting parabolas) from Eq. (7.37). Leaves, of course, have many different
shapes, and none of them exactly matches the overlapping parabolas in
Table 7.5. Typically, however, a factor around 0.7 converts maximum dimension in the direction of wind flow to characteristic dimension. This
is also a typical ratio of the area of a leaf to the product of its length and
width.