Page 451 - Modelling in Transport Phenomena A Conceptual Approach

10.1. MOMENTUM TRANSPORT 431

Substitution of Eqs. (10.1-1) and (10.1-3) into Eq. (10.1-7) and noting that
dv,/az = 0 yields
av, 6221%
Pz=P- 8x2 (10.1-8)
The initial and the boundary conditions associated with Eq. (10.1-8) are

at t=O v,=O (10.1-9)

at x=O v,=V (10.1-10)
at x=B v,=O ( 10.1- 11)
The physical significance and the order of magnitude of the terms in Eq. (10.1-8)
are given in Table 10.1.

able 10.1 The physical significance and the order of magnitude of the terms in
Eq. (10.1-8).
Term Physical Significance Order of Magnitude

a2v,
Pds2 Viscous force
av, Rate of momentum -
PV
Pdt accumulation t

Therefore, the ratio of the viscous force to the rate of momentum accumulation is
given by

Viscous force =-=- ut
pV/B2
Rate of momentum accumulation p V/t B2 (10.1-12)
Introduction of the dimensionless quantities
e=- V% (10.1-13)
V

X
(=- (10.1-14)
B
ut
r=- (10.1- 15)
B2
reduces Eqs. (10.1-8)-(10.1-11) to

(10.1-16)

( 10.1- 17)