Page 88 - Industrial Ventilation Design Guidebook

4,1 FLUID FLOW 53

Viscosity is defined by means of the equation

where dv/dy is the velocity gradient, T is the shearing stress between two flow
layers, and 17 is the dynamic viscosity.

4.1.5.3 Laminar and Turbulent Flow

Flow phenomena can be divided into three main types:
• Laminar (streamline)
• Transitional
• Turbulent
In laminar flow there are no disturbances, and therefore all flow particles move
in the same direction. Transitional flow is the flow regime that takes place dur-
ing the change from streamline to turbulent flow. In the case of turbulent flow
the particles move in a given flow direction, but the flow is erratic and random.
Laminar Tube Flow
When the Reynolds number is under 2000, it is shown empirically that
the flow in a smooth tube is laminar. This flow has a parabolic velocity pro-
file, as shown in Fig. 4.3.
Now consider a cylindrical volume element in a flow stream. The radius
of the element is r and its length is L. The force produced by the flow in this
volume is due to the viscosity, which is

t»4> i \* t
The pressure difference (drop) between the ends of the element produces
2
force A/771T , and considering the force balance,

Simplifying this gives

Denoting w as v ml at r = 0 and noting that v m = 0 at r = R, the integration gives

FIGURE 4.3 Cylindrical volume element.