Page 107 - Modelling in Transport Phenomena A Conceptual Approach

4.4. FLOW NOW TO A SINGLE CYLllVDER 87

The rate of transfer of benzoic acid (species A) to water is calculated by wing Eq.
(4.3-37):

mA = (XD;) (k) - CAW) MA = (TD;) (Ic,) (PA, - PA,)
= [~(12 (5.46 x 10-5)(3.412 - 0) = 8.43 x lO-’kg/s
x
The amount of benzoic acid dissolved in 10s is

MA ‘hAt
= (8.43 x 10-8)(10) = 8.43 x lO-’kg

Verification of assumption # 2

The initial mass of the benzoic acid sphere, M,, is
Mo = [ T(12 xi0-3)3]
(1267)
x
1.146
=
kg
The percent decrease in the mass of the sphere is given by
( 18;4q36~~~3) 100 = 0.074%
x

Therefore, the assumed constancy of Dp and ut is justified.

4.4 FLOW NORMAL TO A SINGLE
CYLINDER

4.4.1 Friction Factor Correlations

For cross flow over an infinitely long circular cylinder, Lapple and Shepherd (1940)
presented their experimental data in the form off versus Reo, the Reynolds num-
ber based on the diameter of the cylinder. Their data can be approximated as

(4.4-1)

f = 1.2 lo4 5 Reo 5 1.5 x lo5 (4.4-2)

The friction factor f in Eqs. (4.4-1) and (4.42) is based on the projected area of
a cylinder, i.e., diameter times length, and Reo is defined by

(4.43)