Environmental Engineering Reference
In-Depth Information
assumption of steady-state flow, the flow that enters the pipe or channel
is the same flow that exits the pipe or channel. In equation form, this
becomes:
q 1 = q 2 or a 1 v 1 = a 2 v 2
(2.14)
Note: With regard to the area/velocity relationship, Equation 2.14 also
makes clear that, for a given flow rate, the velocity of the liquid var-
ies indirectly with changes in cross-sectional area of the channel or
pipe. This principle provides the basis for many of the flow measurement
devices used in open channels (weirs, flumes, and nozzles).
Example 2.12
Problem: A 12-in.-diameter pipe is connected to a 6-in.-diameter pipe.
The velocity of the water in the 12-in. pipe is 3 fps. What is the velocity
in the 6-in. pipe?
Solution: Using the equation a 1 v 1 = a 2 v 2 , we need to determine the area
of each pipe:
d
2
a
π
4
12-in. pipe
(1 ft)
4
2
2
a =
3.14
×
=
0.785 ft
6-in. pipe
(0.5)
4
2
2
a =
3.14
×
=
0.196 ft
The continuity equation now becomes:
0.785 ft 2 × 3 ft/s = 0.196 ft 2 × v 2
Solving for v 2 :
0.785ft 3ft/s
0.196ft
2
×
v 2
=
=
12 ft/s (fps)
2
2.6.2 Pressure and velocity
In a closed pipe flowing full (under pressure), the pressure is indi-
rectly related to the velocity of the liquid. This principle, when combined
with the principle discussed in the previous section, forms the basis for
several flow measurement devices (e.g., Venturi meters and rotameters)
as well as the injector used for dissolving chlorine into water and chlo-
rine, sulfur dioxide, or other chemicals into wastewater:
 
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