Environmental Engineering Reference
In-Depth Information
1
2
V 2
A 2
V 1
P 2
A 1
z 2
z 1
P 1
FIGURE 2.28
A diagram of a pipe through which an ideal fluid is flowing at a steady rate.
path. The fluid can be either a liquid or a gas, but for Bernoulli's principle to
be applicable, the fluid is assumed to have the following qualities [75]:
Fluid flows smoothly.
Fluid flows without any swirls (also known as eddies).
Fluid flows everywhere throughout the pipe (which means there is
no “flow separation”).
Fluid has the same density everywhere (it is “incompressible” like
water).
To understand how and why Bernoulli's principle works, the develop-
ment of the relationship of the static and dynamic pressures using Bernoulli's
equation has to be investigated. Bernoulli's equation along a streamline can
be summarized as follows:
1
2
1
2
v 1 +
v 2 +
P 1
+
gz 1
=
P 2
+
gz 2
=
a constant
(2.9)
where:
1isthe first point along the pipe in Figure 2.28
2isthe second point along the pipe in Figure 2.28
P is the static pressure of the fluid (Pa)
is the density of the fluid (kg/m 3 )
v is the velocity of the fluid (m/s)
g is gravitational acceleration (m/s 2 )
z is height (m)
Referring to Bernoulli's principle applied for the airfoil case shown in
Figure 2.29 , the different points that fall along the same streamline flow of
the wind (i.e., the effects due to gravity) are small compared to the effects
due to kinematics and pressure, z 1
z 2 ; hence, the
gz term in Equation 2.9
 
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