Page 353 - Modelling in Transport Phenomena A Conceptual Approach

9.1. MOMENTUM TRANSPORT 333

Note that Eq. (9.1-55) is a consequence of the jump condition given by Eq. (9.1-
48). Application of the boundary conditions results in

(9.1-57)

The maximum velocity takes place at the liquid-air interface, i.e., at x = 0, as

(9.1-58)

The use of the velocity distribution, Eq. (9.1-57), in Eq. (9.1-37) gives the
shear stress distribution as
(9.1-59)
Integration of the velocity profile across the flow area gives the volumetric flow
rate, i.e.,
Q = 1" i6 dxdy (9.1-60)
v,

Substitution of Eq. (9.1-57) into Eq. (9.1-60) yields

(9.1-61)

Dividing the volumetric flow rate by the flow area gives the average velocity as

(9.1-62)

9.1.2.1 Macroscopic balance

Integration of the governing equation, Eq. (9.1-53), over the volume of the system
gives the macroscopic equation as

PS
- JdL Jd" I" p 2 dxdydz = I" Jd" l6 hdydz (9.1-63)

(9.1-64)