1. CE 356 Elements of Hydraulic Engineering
Specific Energy
(Alternate Depths)
Hydraulic Jump
(Sequent Depths)

2. Energy in Open Channels
Specific Energy
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3. Specific Energy, E
E = energy (head) measured with respect to the channel bottom
E = V2/2g + y = q2/(2gy2) + y
Multiply through by y2 and arrange to find
y3 – E y2 + q2/2g = 0
What kind of equation is this? How many roots? Significance of roots?
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4. Specific Energy Diagram
Rectangular channel:
B = 20 ft
Q = 600 ft3/s.
E = y
Fr = 1
Fr = 2
Fr = V/(gy)0.5
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5. Example: Sluice Gate
q = 30 ft2/s
y = 5.6 ft
y = 1.8 ft
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6. Note that there is head loss in an hydraulic jump
figure 1
Hydraulic jump
Note that there is head loss in an hydraulic jump
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7. Hydraulic jump on Rattan Creek, TX. July 2, 2002
strong jump: Fr > 9.0, rough wavy surface downstream
steady jump: 4.5<Fr < 9.0, stable and well-balanced
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8. classification
Classification
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9. picture
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10. figure 2
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11. Now let’s consider an hydraulic jump
jump cv
Now let’s consider an hydraulic jump
We know that or
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12. rearranging and dividing by g:
momentum balance
Our momentum balance
can be written as
rearranging and dividing by g:
Using A=By for a rectangular channel
Let’s go back to our hydraulic jump…
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13. solvable set
If we have an open channel where we know Q, B, and y1, we can solve for y2
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14. Recalling the definition of the flow rate per unit width
rectangular
Starting from
Recalling the definition of the flow rate per unit width
we can obtain
Solving for y2
y1 solution is similar (see text)
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15. Now, what are the limitations of this equation?
limits
Now, what are the limitations of this equation?
shear forces are neglected
shear causes smaller head loss than turbulence in the jump
requires jump occurs over a short distance
rectangular channel
effect of gravity downslope is neglected
again requires jump to occur over a short distance
neglect non-hydrostatic pressure
uniform density fluid
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16. …and what is the fundamental principle for this equation?
conservation of momentum
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17. E–M graphs
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18. The more general head loss formula is
Valid for any cross section
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