Page 72 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

46 2 Basic Properties of Gases

Assuming constant fluid density for the incompressible fluid, Eq. (2.72) becomes
1 2
P þ qv þ qgz ¼ constant ð2:73Þ
2
2
where P represents the static pressure and qv =2 the velocity pressure. The con-
1
2
sequent total pressure is P þ qv . This equation is applicable to most air emission
2
related to analysis.
When z 1 ¼ z 2 , the pressure difference between two points along a streamline is
related to the speeds at these points
1 2 2
P 1 P 2 ¼ q v v 1 ð2:74Þ
2
2
This simple equation finds important applications in air emission analysis such
as the estimation of the resistance to airflow (pressure drop) in an air cleaning
device. It is also the principle behind the design of a Pitot tube, which will be
introduced later in Chap. 15.

2.2.3 Boundary Layer and Drag

When a gas flows around outside of a body, it produces a force on the body that
tends to drag the body in the direction of the gas flow. There are two mechanisms
behind this drag effect, one is the skin friction drag and another is form drag. To
illustrate the skin drag, let us consider a flat surface with a sharp leading edge
attacked by a uniform fluid flow (Fig. 2.3).
Denote the uniform free stream speed as u 1 and set the coordinate origin at the
leading edge with x ¼ 0 and y ¼ 0 on the solid surface. The fluid is slowed down
with a layer that is close to the solid surface, which is called boundary layer. The

y Undisturbed external
flow
Boundary
layer
Subboundary layer
u(x,y)
(0,0) x
Laminar
boundary Turbulent boundary layer
layer
Transition zone
Fig. 2.3 Boundary layer concept