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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