Science of Water : Concepts and Applications

Water Hydraulics 57
FIGURE 3.6 Laminar (streamline) fl ow.
FIGURE 3.7 Turbulent fl ow.
√ Important Point: Flow may be steady or unsteady. For our purposes, we consider steady-state
fl ow only; most of the hydraulic calculations in this manual assume steady-state fl ow.
AREA/VELOCITY
The law of continuity states that the discharge at each point in a pipe or channel is the same as the
discharge at any other point (if water does not leave or enter the pipe or channel). That is, under the
assumption of steady-state fl ow, the fl ow that enters the pipe or channel is the same fl ow that exits
the pipe or channel. In equation form, this becomes
Q Q or AV AV
1 2 1 1 2 2
(3.14)
√ Note: In regard to the area/velocity relationship, Equation 3.14 also makes clear that for a given
fl ow rate, the velocity of the liquid varies indirectly with changes in cross-sectional area of the
channel or pipe. This principle provides the basis for many of the fl ow measurement devices
used in open channels (weirs, fl umes, and nozzles).
Example 3.12
Streamline Turbulent
Problem:
A pipe, 12 in. in diameter, 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?