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Homework Set #1:
Due date: 09/07/07 by 11:00 am
Problem #1:
Consider a spherical particle falling freely in a large fluid body. It is found experimentally that
the terminal settling velocity
u
of the particle is dependent on: (1) particle diameter D; (2) the
buoyant weight of the particle
W
(the difference between the gravity and buoyant forces acting
on the particle); (3) fluid density
ρ
, and (4) fluid viscosity
μ
.
It is assumed that the velocity
u
can be mathematically expressed as products of powers of the
above variables (i.e. similar to the example of dimensional analysis given in the previous
lectures).
abcd
uC
DW
ρµ
=
Obtain the relationship for
u
using dimensional analysis in which the set of linear equations is
solved in terms of the exponent
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 Fall '08
 dicarlo

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