Page 89 - Industrial Ventilation Design Guidebook

5 4 CHAPTER 4 PHYSICAL FUNDAMENTALS
For a parabolic velocity profile the velocity expression is

Volume flow is calculated by integrating the expression for the velocity
over the surface:

Hence

The mean velocity is

The pressure difference is

Equation (4.44) is the Hagen-Poiseuille law, which shows that the pressure
loss during laminar flow is linearly proportional to the flow velocity.
The following equations show the relationship between the pressure loss
<ir*f\ 1r\r\f* ri*ir*1"ir\n ro/"*1-/~\i*«

This connection is valid for laminar flow, as Re < 2000.

Turbulent Flow
Laminar flow after transition usually turns into turbulent flow when
Re > 2000. It has been shown that the pressure loss of a turbulent flow is
caused by a friction factor with the magnitude of

This equation is the Blasius equation.
The shearing stress T O on the surface of the flow duct and the pressure loss
can now be solved from Eq. (4.48), given below:

Thus