HY8:Hydraulic Jump Calculations
Determining if a Hydraulic Jump Exists and its Location
A hydraulic jump is rapidly varied flow where supercritical flow rapidly becomes subcritical flow. As the flow performs this change, energy is lost to turbulence. However, momentum is conserved across the jump. The depth of the flow just prior and after a hydraulic jump is called sequent depths, and thus by definition conserve momentum, but not energy. Sequent depths then can be used to compare the momentum of a supercritical depth to a subcritical depth.
To determine if a hydraulic jump exists, one must determine the supercritical and subcritical water surface profiles that can form within a channel or culvert. Then at each location along the two profiles compare the sequent depth of the supercritical profile to the subcritical profile’s depth. If the sequent depth matches the depth of the subcritical profile, then a hydraulic jump is assumed to occur at that location.
First, HY-8 determines the boundary conditions for the direct step method. HY-8 then computes two flow profiles from the given boundary conditions in the culvert. One profile begins at the inlet and travels downstream and is supercritical. The second profile begins at the outlet and travels upstream and is subcritical. HY-8 uses the energy equation to determine the hydraulic grade line if the outlet is submerged. Once the hydraulic grade line falls below the crown of the culvert, HY-8 uses the direct step method to determine the remainder of the profile.
HY-8 also determines the sequent depth of the supercritical flow profile. The equations used to determine the sequent depth vary by shape and is detailed in Nathan Lowe’s thesis (Lowe, 2008).
An example of a profile set and sequent depth calculations from a box culvert is given in Table 1 and plotted in Figure 1. The subcritical depth is shown extending above the crown of the culvert to show the hydraulic grade line for comparison purposes. Once HY-8 concludes the hydraulic jump calculations, the flow profile is modified to be contained within the culvert barrel.
Table 1: Parameters of culvert used for example
| Parameter | Value | Units |
|---|---|---|
|
Culvert Shape |
Box |
|
|
Rise: |
6.0 |
ft |
|
Span: |
6.0 |
ft |
|
Length: |
100.0 |
ft |
|
Flow: |
80.0 |
cfs |
Table 2: HY-8 Water Surface Profile and Sequent Depth Calculations
| Computation Direction: Upstream to Downstream | ||
|---|---|---|
| Location (ft) | S2 Water Depth (ft) | Sequent Depth (ft) |
|
0 |
1.767423128 |
1.767423128 |
|
0.029316423 |
1.717423128 |
1.818384336 |
|
0.121221217 |
1.667423128 |
1.871344458 |
|
0.284143628 |
1.617423128 |
1.926427128 |
|
0.528025114 |
1.567423128 |
1.983769228 |
|
0.86466911 |
1.517423128 |
2.043522893 |
|
1.308192917 |
1.467423128 |
2.105857905 |
|
1.87561876 |
1.417423128 |
2.17096453 |
|
2.587657601 |
1.367423128 |
2.239056945 |
|
3.469764745 |
1.317423128 |
2.310377355 |
|
4.553586554 |
1.267423128 |
2.385201009 |
|
5.878983069 |
1.217423128 |
2.463842333 |
|
7.496921363 |
1.167423128 |
2.546662495 |
|
9.473726216 |
1.117423128 |
2.634078814 |
|
11.89752361 |
1.067423128 |
2.726576563 |
|
14.88838 |
1.017423128 |
2.824723925 |
|
18.61499626 |
0.967423128 |
2.929191151 |
|
23.32377651 |
0.917423128 |
3.040775386 |
|
29.3931714 |
0.867423128 |
3.160433253 |
|
37.44519272 |
0.817423128 |
3.289324251 |
|
48.60550709 |
0.767423128 |
3.42886946 |
|
65.23610698 |
0.717423128 |
3.580832395 |
|
93.76009585 |
0.667423128 |
3.747432593 |
|
100 |
0.663122364 |
3.762533062 |
| Computation Direction: Downstream to Upstream | |
|---|---|
| Location (ft) | S1 Water Depth (ft) |
|
100 |
7.78884205 |
|
76.62538619 |
6 |
|
76.01536408 |
5.95 |
|
75.40596369 |
5.9 |
|
74.79697048 |
5.85 |
|
74.18839865 |
5.8 |
|
73.58026305 |
5.75 |
|
72.97257915 |
5.7 |
|
72.36536314 |
5.65 |
|
71.75863195 |
5.6 |
|
71.15240324 |
5.55 |
|
70.54669552 |
5.5 |
|
69.94152813 |
5.45 |
|
69.33692135 |
5.4 |
|
68.73289638 |
5.35 |
|
68.12947544 |
5.3 |
|
67.52668185 |
5.25 |
|
66.92454003 |
5.2 |
|
66.3230756 |
5.15 |
|
65.72231547 |
5.1 |
|
65.12228788 |
5.05 |
|
64.5230225 |
5 |
|
63.92455054 |
4.95 |
|
63.32690478 |
4.9 |
|
62.73011975 |
4.85 |
|
62.13423177 |
4.8 |
|
61.5392791 |
4.75 |
|
60.94530208 |
4.7 |
|
60.35234323 |
4.65 |
|
59.76044741 |
4.6 |
|
59.16966197 |
4.55 |
|
58.58003695 |
4.5 |
|
57.9916252 |
4.45 |
|
57.40448266 |
4.4 |
|
56.81866848 |
4.35 |
|
56.23424533 |
4.3 |
|
55.6512796 |
4.25 |
|
55.06984171 |
4.2 |
|
54.49000634 |
4.15 |
|
53.91185285 |
4.1 |
|
53.33546552 |
4.05 |
|
52.76093401 |
4 |
|
52.18835372 |
3.95 |
|
51.61782627 |
3.9 |
|
51.04946001 |
3.85 |
|
50.48337049 |
3.8 |
|
49.91968113 |
3.75 |
|
49.35852381 |
3.7 |
|
48.80003962 |
3.65 |
|
48.24437962 |
3.6 |
|
47.69170569 |
3.55 |
|
47.1421915 |
3.5 |
|
46.59602356 |
3.45 |
|
46.05340235 |
3.4 |
|
45.51454362 |
3.35 |
|
44.97967983 |
3.3 |
|
44.44906168 |
3.25 |
|
43.92295991 |
3.2 |
|
43.40166723 |
3.15 |
|
42.88550053 |
3.1 |
|
42.37480328 |
3.05 |
|
41.86994835 |
3 |
|
41.37134098 |
2.95 |
|
40.87942233 |
2.9 |
|
40.39467334 |
2.85 |
|
39.91761912 |
2.8 |
|
39.44883402 |
2.75 |
|
38.98894719 |
2.7 |
|
38.53864914 |
2.65 |
|
38.09869903 |
2.6 |
|
37.66993312 |
2.55 |
|
37.25327445 |
2.5 |
|
36.84974393 |
2.45 |
|
36.46047324 |
2.4 |
|
36.08671965 |
2.35 |
|
35.72988334 |
2.3 |
|
35.39152756 |
2.25 |
|
35.07340226 |
2.2 |
|
34.77747182 |
2.15 |
|
34.50594783 |
2.1 |
|
34.26132798 |
2.05 |
|
34.04644235 |
2 |
|
33.86450893 |
1.95 |
|
33.71920038 |
1.9 |
|
33.61472501 |
1.85 |
|
33.55592549 |
1.8 |
