CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 319

whereis an empirical coefficient that represents the degree of turbulence.
Experimental data indicate that may vary from about 1.03 to 1.36 for pris-
matic channels. It is, however, normally taken as 1.00 for practical hydraulic work
and is evaluated only for precise investigations of energyloss.
The total energy per pound (kilogram) of water relative to the bottom of the
channel at a vertical section is called the specific energy head He. It is com-
posed of the depth of flow at any point, plus the velocity head at the point. It is
expressed in feet (meter) as

(12.79)

A longitudinal profile of the elevation of the specific energy head is called the
energy grade line, or thetotal-head line (Fig. 12.15). A longitudinal profile of the
water surface is called the hydraulic grade line.The vertical distance between these
profiles at any point equals the velocity head at that point.
Loss of head due to friction hfin channel length Lequals the drop in eleva-
tion of the channel Zin the same distance.

Normal Depth of Flow

The depth of equilibrium flow that exists in the channel of Fig. 12.15 is called
the normal depth dn. This depth is unique for specific discharge and channel
conditions. It may be computed by a trial-and-error process when the channel
shape, slope, roughness, and discharge are known. A form of the Manning equa-
tion is suggested for this calculation:

AR2/3 (12.80)

Qn

1.486S1/2

Hed

V^2

2 g

S

(^12)
hf

SW

V 2 =V 1

d 2 =d 1

S 0

Hydraulic grade line

Energy grade line

Channel bottom

V 1

d 1

Z 1

Z 2

V 2

2 g

2 g

∆Z

Datum line

L

(^2) V
1
2 g
2

V 12

FIGURE 12.15 Characteristics of uniform open-channel flow.