Fundamental Chemistry and Hydraulics - Mathematics and Statistics for the Environment - page 371

■ EXAMPLE 14. 30
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?

Solution: Using the equation A 1 V 1 = A 2 V 2 , we need to determine the area of each pipe:

2 2

D
=× =

1ft

2

12-inch pipe: A π 3 14159 . × = 0.785 f t

4 4

2 2

D
=× =

0.5 ft

96 ft 2 6-inch pipe: A π 3 14159 . × = 0.1

4 4

The continuity equation now becomes

2 2

0.785 ft × 3ft/sec = 0.196 ft × V 2

Solving for V 2 ,

2

0.785 ft 3ft/sec
0.196 ft

×

V 2 = = 12 ft/sec or fps

2

14.2.1.9 Pipe Friction
The flow of water in pipes is caused by the pressure applied behind it either by gravity or by hydrau-
lic machines (pumps). The flow is retarded by the friction of the water against the inside of the pipe.
The resistance of flow offered by this friction depends on the diameter of the pipe, the roughness of
the pipe wall, and the number and type of fittings (bends, valves, etc.) along the pipe. It also depends
on the speed of the water through the pipe—the more water you try to pump through a pipe, the
more pressure it will take to overcome the friction. The resistance can be expressed in terms of the
additional pressure needed to push the water through the pipe, in either pounds per square inch or
feet of head. Because it is a reduction in pressure, it is often referred to as friction loss or head loss.
Friction loss increases as

• Flow rate increases.
• Pipe diameter decreases.
• Pipe interior becomes rougher.
• Pipe length increases.
• Pipe is constricted.
• Bends, ittings, and valves are added.

The actual calculation of friction loss is beyond the scope of this text. Many published tables give
the friction loss in different types and diameters of pipe and standard fittings. What is more impor-
tant here is recognition of the loss of pressure or head due to the friction of water flowing through
a pipe.
One of the factors in friction loss is the roughness of the pipe wall. A number called the C factor
indicates pipe wall roughness; the higher the C factor, the smoother the pipe.

Note: C factor is derived from the letter C in the Hazen-Williams equation for calculating water
flow through a pipe.

Some of the roughness in the pipe will be due to the material; cast iron pipe will be rougher than
plastic, for example. Additionally, the roughness will increase with corrosion of the pipe material and
deposits sediments in the pipe. New water pipes should have a C factor of 100 or more; older pipes