226
P. Liu
coefficient α 2 is larger than 1. The total head of the downstream section is
E 3 = h 3 +
α 3 V 2
3
2g
≈ h 2 +
α 3 V 2
2
2g
where the section 3-3 is a gradually varied flow section and the velocity distribution tends to normal distribution, in which we can take α 3 ≈ 1.0. The
head loss of the hydraulic jump section is
E j = (h 1 +
V 2
1
2g
) − (h 2 +
α 2 V 2
2
2g
)
The head loss of the post jump section is defined as
E j j = (h 2 +
α 2 V 2
2
2g
) − (h 3 +
V 2
3
2g
)
For the rectangular section, the kinetic energy correction coefficient of the
section after the jump is calculated by empirical formula, namely
α 2 = 0.85Fr
2/3
1 + 0.25
In the rectangular channel, the head loss of hydraulic jump section is
E j =
h 1
4η
[(η − 1)
3
− (α 2 − 1)(η + 1)]
The head loss of the post jump section is
E j j = (α 2 − 1)
V 2
2
2g
=
h 1
4η
(α 2 − 1)(η + 1)
The total head loss is
E = E j + E j j =
h 1
4η
(η − 1)
3
The ratio of head loss of hydraulic jump section to total head loss is
E j
E
= 1 − (α 2 − 1)
η + 1
(η − 1) 3