Page 249 - Modelling in Transport Phenomena A Conceptual Approach

PROBLEMS 229

7.13 When Newton’s law is applicable, the friction factor is constant and is given
by Eq. (4.3-9).
a) Substitute Eq. (4.3-9) into Eq. (7.4-7) and show that
v l-exp(-yt)
-=
wt 1 + exp( - yt)
where the terminal velocity, vt, and y are given by

b) Show that the distance travelled is

7.14 Consider twedimensional motion of a spherical particle in a fluid. When
the horizontal component of velocity is very large compared to the vertical camp+
nent, the process can be modelled as a one-dimensional motion in the absence of a
gravitational field. Using unsteady-state momentum balance show that

4ppD;
t=- dRep
3~ Lep fRe$
where Rep, is the value of the Reynolds number at t = 0.
a) When Stokes’ law is applicable, show that the distance travelled by the particle
is given by
[
s=- WO~PD; - exp (- X)] (2)
1
18 P PPD;
where v, is the value of velocity at t = 0.
b) When Newton’s law is applicable, show that the distance travelled by the particle
is given by
3.03ppDp In (I +
S= (3)
P 3.03 pp Dp

7.15 Coming home with a friend to have a cold beer after work, you find out that
you had left the beer on the kitchen counter. As a result of the sunlight coming
from the kitchen window, it was too warm to drink.