05-07-2012, 02:33 PM
CHEMICAL ENGINEERING
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It is found experimentally that the terminal settling velocity u0 of a spherical particle in
a fluid is a function of the following quantities:
particle diameter, d; buoyant weight of particle (weight of particle weight of displaced
fluid), W; fluid density,
, and fluid viscosity, .
Obtain a relationship for u0 using dimensional analysis.
Stokes established, from theoretical considerations, that for small particles which settle
at very low velocities, the settling velocity is independent of the density of the fluid
except in so far as this affects the buoyancy. Show that the settling velocity must then be
inversely proportional to the viscosity of the fluid.
A drop of liquid spreads over a horizontal surface. What are the factors which will
influence:
(a) the rate at which the liquid spreads, and
(b) the final shape of the drop?
Obtain dimensionless groups involving the physical variables in the two cases.
(b) The final shape of the drop as indicated by its diameter, d, may be obtained by
using the argument in (a) and putting R D 0. An alternative approach is to assume the
final shape of the drop, that is the final diameter attained when the force due to surface
tension is equal to that attributable to gravitational force. The variables involved here will
be: volume of the drop, V; density of the liquid,
; acceleration due to gravity, g, and the
surface tension of the liquid, . In this case:
Taking the heat transfer coefficient, h, as a function of the fluid velocity, density, viscosity,
specific heat and thermal conductivity, u,
, , Cp and k, respectively, and of the inside
and outside diameters of the annulus, di and d0 respectively, then: