Page 36 - Modelling in Transport Phenomena A Conceptual Approach

2.1. MOLECULAR TRANSPORT 17

In SI units, shear stress is expressed in N/ m2( Pa) and velocity gradient in
( m/ s)/ m. Thus, the examination of Eq. (2.1-1) indicates that the units of viscosity
in SI units are
N/ m2 = pa.~= - kg
N.s (kg.m/s2).s
P= = =-
(m/s)/m m2 m2 m. s
Most viscosity data in the cgs system are usually reported in g/( cm. s), known as
a poise (P), or in centipoise (1 CP = 0.01 P) where

1Pa.s = 10 P = io3 CP
Viscosity varies with temperature. While liquid viscosity decreases with in-
creasing temperature, gas viscosity increases with increasing temperature. Con-
centration also affects viscosity for solutions or suspensions. Viscosity values of
various substances are given in Table D.l in Appendix D.

Example 2.1 A Newtonian fluid with a viscosity of 10 cP is placed between two
large parallel plates. The distance between the plates is 4mm. The lower plate is
pulled in the positive x-dimtion with a force of 0.5N, while the upper plate is
pulled in the negative x-direction with a force of 2N. Each plate hm an area of
If
2.5m2. the velocity of the lower plate is 0.1 m/s, calculate:
a) The steady-state momentum flux,
b) The velocity of the upper plate,
c) Parts (a) and (b) for a Newtonian fluid with p = 1 cP.

Solution

F=-2N-

Y=4mm

't, __* F = 0.5 N

v, = 0.1 m/s

a) The momenturn flux (or, force per unit area) is

F
ryz = -
A
0.5 + 2
=-- - 1Pa
2.5