Page 394 - Civil Engineering Formulas

322 CHAPTER TWELVE

The pressure force F developed in hydraulic jump is
2
2
d 2 w d 1 w
F (12.86)
2 2
where d depth before jump, ft (m)
1
d depth after jump, ft (m)
2
3
3
w unit weight of water, lb/ft (kg/m )
The rate of change of momentum at the jump per foot width of channel equals
qw
MV 1 MV 2
F (V 1 V 2 ) (12.87)
t g
2
2
where M mass of water, lb s /ft (kg s /m)
V velocity at depth d , ft/s (m/s)
1
1
V velocity at depth d , ft/s (m/s)
2
2
3
3
q discharge per foot width of rectangular channel, ft /s (m /s)
t unit of time, s
2
2
g acceleration due to gravity, 32.2 ft/s (9.81 kg/s )
2
Then V 1 gd 2 (d 2 d 1 ) (12.88)
2d 1
2 2
d 1 2V 1 d 1 d 1
d 2 (12.89)
2 B g 4
2 2
d 1 d 2 2V 2 d 2 d 2 (12.90)
2 B g 4
The head loss in a jump equals the difference in specific-energy head before
and after the jump. This difference (Fig. 12.17) is given by
(d 2 d 1 ) 3
H e H e1 H e2 (12.91)
4d 1 d 2
where H e1 specific-energy head of stream before jump, ft (m); and H e2
specific-energy head of stream after jump, ft (m).
The depths before and after a hydraulic jump may be related to the critical
depth by
q 2
d 1 d 2 3
d 1 d 2 d c (12.92)
2 g
3
3
where q discharge, ft /s (m /s) per ft (m) of channel width; and d critical
c
depth for the channel, ft (m).
It may be seen from this equation that if d d , d must also equal d .
1 c 2 c
Figure 12.18 shows how the length of hydraulic jump may be computed using
the Froude number and the L/d ratio.
2