204
P. Liu
Esmin
Fig. 3.31 Section specific energy curve
in the middle, called the critical particle C , The corresponding water depth
is called critical water depth, which is expressed by h C . The section specific
energy above particle C increases with the increase in water depth, while the
section specific energy below particle C decreases with the increase in water
depth. The specific energy E s along water depth h is
dE s
dh
= 1 −
q 2
gh 3 = 1 −
V 2
gh
= 1 − Fr
2
The above formula shows that the change in the specific energy of the
cross-section of the open channel with the water depth is a function of the
Froude number of the cross-section, as shown in Fig. 3.32. For Fr < 1, it is
in the subcritical flow region,
dE s
dh > 0, and is located on the upper branch
of the specific energy curve, and the specific energy of the section increases
with the increase in water depth. For Fr > 1, it is in the supercritical flow
region,
dE s
dh < 0,and is on the lower branch of the specific energy curve. The
specific energy decreases with increasing water depth. For Fr = 1, it is in a
critical state,
dE s
dh = 0, the specific energy at the section is the minimum,
and the corresponding water depth is the critical water depth h c = 0. The
calculation formula is
dE s
dh
= 0, h c =
q 2
g
1/3