Science of Water : Concepts and Applications

74 The Science of Water: Concepts and Applications
FIGURE 3.18 Pipe in parallel.
In making calculations involving pipes in series, remember these two important basic operational
tenets:
1. The same fl ow passes through all pipes connected in series.
2. The total head loss is the sum of the head losses of all of the component pipes.
In some operations involving series networks where the fl ow is given and the total head loss is
unknown, we can use the Hazen–Williams formula to solve for the slope and the head loss of each
pipe as if they were separate pipes. Adding up the head losses to get the total head loss is then a
simple matter.
Other series network calculations may not be as simple to solve using the Hazen–Williams
equation. For example, one problem we may be faced with is what diameter to use with varying
sized pipes connected together in a series combination. Moreover, head loss is applied to both pipes
(or other multiples), and it is not known how much loss originates from each one; thus, determining
slope would be diffi cult—but not impossible.
In such cases the equivalent pipe theory, as mentioned earlier, can be used. Again, one single
“equivalent pipe” is created which will carry the correct fl ow. This is practical because the head
loss through it is the same as that in the actual system. The equivalent pipe can have any C factor
and diameter, just as long as those same dimensions are maintained all the way through to the end.
Keep in mind that the equivalent pipe must have the correct length, so that it will allow the correct
fl ow through, which yields the correct head loss (the given head loss).
PIPES IN PARALLEL
Two or more pipes connected (as in Figure 3.18) so that fl ow is fi rst divided among the pipes and is then
rejoined comprise a parallel pipe system. A parallel pipe system is a common method for increasing the
capacity of an existing line. Determining fl ows in pipes arranged in parallel are also made by application
of energy conservation principles—specifi cally, energy losses through all pipes connecting common
junction points must be equal. Each leg of the parallel network is treated as a series piping system
and converted to a single equivalent length pipe. The friction losses through the equivalent length parallel
pipes are then considered equal and the respective fl ows determined by proportional distribution.
√ Note: Computations used to determine friction losses in parallel combinations may be accomplished
using a simultaneous solution approach for a parallel system that has only two branches.
However, if the parallel system has three or more branches, a modifi ed procedure using the
Hazen–Williams loss formula is easier.
OPEN-CHANNEL FLOW
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Water is transported over long distances through aqueducts to locations where it is to be used and/or
treated. Selection of an aqueduct type rests on such factors as topography, head availability, climate,
construction practices, economics, and water quality protection. Along with pipes and tunnels, aqueducts
may also include or be solely composed of open channels.
—W. Viessman, Jr. and M.J. Hammer (1998)