Homework Set #1:
Due date: 09/09/10 by 12:00 PM
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).
a
b
c
d
u
CD W
Obtain the relationship for
u
using dimensional analysis in which the set of linear equations is
solved in terms of the exponent
c
.
Show that the respective dimensionless groups obtained by solving the set of linear equations in
terms of the exponent
b
and
c
are correlated.
Problem #2:
The power required to rotate a drilling string is a function of string diameter D, number of
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 Spring '11
 Fisher
 Fluid Dynamics, Elementary algebra, Fundamental physics concepts

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