CHEMICAL ENGINEERING

MOMENTUM, HEAT AND MASS TRANSFER 313

the surface. Obtain the relation betweenuCandyCin the laminar sub-layer. Outside the
laminar sub-layer, the relation takes the form:

uCD 2 .5lnyCC 5. 5

At what value ofyCdoes the transition from the laminar sub-layer to the turbulent zone
occur?
In theUniversal Velocity Profile, the laminar sub-layer extends to values ofyCD5, the
turbulent zone starts atyCD30 and the range 5<yC<30, the buffer layer, is covered by
a second linear relation betweenuCand lnyC. What is themaximumdifference between
the values ofuC, in the range 5<yC<30, using the two methods of representation of
the velocity profile?
Definitions:

uCD

ux

uŁ

yCD

yuŁ



uŁ^2 DR/

whereuxis velocity at distanceyfrom surface
Ris wall shear stress
, are the density and viscosity of the fluid respectively.

Solution

Laminar sub-layer
If the velocity gradient approaches constant value in the laminar sub-layer, then
d^2 ux/dy^2 !0 and:

RD

ux

y

uŁ^2 D

ux

y

and:

ux

uŁ

D

uŁy



or:uCDyC, by definition

The point of interaction ofuCDyC

and: uCD 2 .5lnyCC 5. 5

is given by: yCD 2 .5lnyCC 5. 5