H1 = H2 + ∆z

(2.135)

where

V2

H=

+y

(2.136)

2g

The term H is called the specific head, and is the height of the total head above the channel

bed.

For simplicity, the following specific energy (often referred to as specific head) analysis is done

on a unit width of channel so that Equation 2.136 becomes:

q2

H=

+y

(2.137)

2

2gy

For a given q, Equation 2.137 can be solved for various values of H and y. When y is plotted as

a function of H, Figure 2.20 is obtained (Rouse 1946). There are two possible depths called

alternate depths for any H larger than a specific minimum. Thus, for specific energy larger than

the minimum, the flow may have a large depth with small velocity or small depth with large

velocity. Flow cannot occur with specific energy less than the minimum. The single depth of flow

at the minimum specific energy is called the critical depth yc and the corresponding velocity, the

critical velocity Vc = q/yc. To determine yc the derivative of H with respect to y is set equal to 0.

Figure 2.20. Specific energy diagram.

q2

dH

= 1- 3 = 0

(2.138)

dy

gy

2.39

Integrated Publishing, Inc. |