Environmental Engineering Reference
In-Depth Information
energy present due to the velocity of the water. This can be expressed
mathematically as:
ez
p
w
v
2
=+ +
(2.16)
2
g
where:
e
= total energy head.
z
= height of the water above a reference plane (ft).
p
= pressure (psi)
w
= unit weight of water (62.4 lb/ft
3
).
v
= flow velocity (ft/s).
g
= acceleration due to gravity, (32.2 ft/s
2
).
Consider the constriction in the section of pipe shown in Figure
2.12. We know, based on the law of energy conservation, that the total
energy head at section A (
e
1
) must equal the total energy head at section
B (
e
2
). Using Equation 2.16, we get Bernoulli's equation:
P
w
v
2
P
w
v
2
a
a
B
B
z
++=++
z
(2.17)
a
B
2
g
2
g
The pipeline system shown in Figure 2.12 is horizontal; therefore,
we can simplify Bernoulli's equation because
z
a
=
z
B
. Because they are
equal, the elevation heads cancel out from both sides, leaving:
P
w
v
2
P
w
v
2
a
a
B
B
+=+
(2.18)
2
g
2
g
To tal energy line
2
v
2
g
v
2
g
2
Pressure
drop
E
1
P
w
P
w
E
2
A
Q
B
Constriction
z
B
z
A
Reference plane
figure 2.12 The law of conservation of energy: The velocity and kinetic
energy of the water flowing in the constricted section must increase, so
the potential energy may decrease. This is observed as a pressure drop in
the constriction. (Adapted from Nathanson, J.A.,
Basic environmental
Technology: Water Supply, Waste management, and Pollution Control
,
2nd ed., Prentice Hall, Upper Saddle River, NJ, 1997, p. 29.)
