CIVIL ENGINEERING FORMULAS

322 CHAPTER TWELVE

The pressure force Fdeveloped in hydraulic jump is

(12.86)

whered 1 depth before jump, ft (m)
d 2 depth after jump, ft (m)
wunit weight of water, lb/ft^3 (kg/m^3 )

The rate of change of momentum at the jump per foot width of channel equals

(12.87)

whereMmass of water, lbs^2 /ft (kgs^2 /m)
V 1 velocity at depth d 1 , ft/s (m/s)
V 2 velocity at depth d 2 , ft/s (m/s)
q discharge per foot width of rectangular channel, ft^3 /s (m^3 /s)
tunit of time, s
gacceleration due to gravity, 32.2 ft/s^2 (9.81 kg/s^2 )

Then (12.88)

(12.89)

(12.90)

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

(12.91)

whereHe 1 specific-energy head of stream before jump, ft (m); and He 2 
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

(12.92)

whereqdischarge, ft^3 /s (m^3 /s) per ft (m) of channel width; and dccritical
depth for the channel, ft (m).
It may be seen from this equation that if d 1 dc,d 2 must also equal dc.
Figure 12.18 shows how the length of hydraulic jump may be computed using
the Froude number and the L/d 2 ratio.

d 1 d 2

d 1 d 2

2



q^2

g

d^3 c

HeHe 1 He 2 

(d 2 d 1 )^3

4 d 1 d 2

d 1 

d 2

2



B

2 V^22 d 2

g



d^22

4

d 2 

d 1

2



B

2 V^21 d 1

g



d^21

4

V^21 

gd 2

2 d 1

(d 2 d 1 )

F

MV 1 MV 2

t



qw

g

(V 1 V 2 )

F

d^22 w

2



d 12 w

2