Pumping Calculations - Basic Mathematics for Water and Wastewater Operators - page 197

(c) 1 million gallons per day is 1.55 cfs, so

7.85 cfs ÷ 1.55 cfs/MGD = 5.06 MGD

Law of Continuity
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 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 (14.3)

■ Example 14.5
Problem: A pipe 12 inches 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: To use the equation A 1 × V 1 = A 2 × V 2 , we need to determine the area of
each pipe:

D 2

2

() 1ft

2

Area of 12-in.pipe =× =× = π 314 . 0.7 85 ft

4 4

D 2
4

) 2 ( 0.5 f t

0.196 ft 2 Area of 6-in.pipe =× =× π 314 . =

4

The continuity equation now becomes

AV AV ×=×

1 1 2 2

2 2

0.785 ft × 3ft/sec = 0.196 ft × V

2

Solving for V 2 ,

2 2

0.785 ft × 3ft/sec = 0.196 ft × V 2

2

0.785 ft × 3 ft/sec

= V

2

2

0.196 ft
12 ft/sec = V

2

p ipe f riCtion
The flow of water in pipes is caused by the pressure applied behind it either by grav-
ity or by hydraulic 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 size (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