7/29/2019 L34 OpenChannel PartV
1/12
7/29/2019 L34 OpenChannel PartV
2/12
M1 curve example dam across non-symmetric trapezoidal channel
Calculation proceed upstream, thus, the values ofx are negative.
7/29/2019 L34 OpenChannel PartV
3/12
Gradually Varied Flow - Non-symmetric trapezoidal Channel
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
-10000.0
0
-9000.00 -8000.00-7000.00 -6000.00 -5000.00 -4000.00 -3000.00-2000.00 -1000.00 0.00
Position along channel (x)
z,W
Bed ElevationWS elevation
Usingys= 6.88 ft,ye = 2.88 ft, y = -0.25 ft,ye/yo = 1.04, we findx = -1.68 mi.
Gradually Varied Flow - Non-symmetric trapezoidal Channel
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
-12000.00 -10000.00 -8000.00 -6000.00 -4000.00 -2000.00 0.00
Position along channel (x)
z,W
Bed ElevationWS elevation
Usingys= 6.88 ft,ye = 2.78 ft, y = -0.25 ft,ye/yo = 1.01, we findx = -1.95 mi.
7/29/2019 L34 OpenChannel PartV
4/12
7/29/2019 L34 OpenChannel PartV
5/12
M2 curve example free fall at the end of a circular channel
Calculation proceeds downstream, thus values ofx are positive.
7/29/2019 L34 OpenChannel PartV
6/12
Gradually Varied Flow - Circular Channel
1244.6
1244.8
1245
1245.2
1245.4
1245.6
1245.8
1246
1246.2
1246.4
1246.6
0.00 1000.00 2000.00 3000.00 4000.00 5000.00 6000.00 7000.00 8000.00 9000.00
Position along channel (x)
z,W
Bed Elevation
WS elevation
Notice how, at the downstream end, the profile approaches the critical depth line almost perpendicular to it.
M3 curve example flow downstream of a sluice gate in a wide-rectangular channel
As in the M2 profile shown above, the M3 profile in this example approaches the critical depth almost
perpendicular.
7/29/2019 L34 OpenChannel PartV
7/12
Calculation proceeds downstream, thus values ofx are positive.
S1 curve example Flow upstream of a dam in a rectangular channel
Calculation proceeds upstream, thus values ofx are negative.
7/29/2019 L34 OpenChannel PartV
8/12
Gradually Varied Flow - Rectangular Channel
1234.5
1235
1235.5
1236
1236.5
1237
1237.5
1238
1238.5
-300.00 -250.00 -200.00 -150.00 -100.00 -50.00 0.00
Position along channel (x)
z,W
Bed ElevationWS elevation
S2 curve example flow over a hump in a steep channel of circular cross-section
Calculations proceed downstream, , thus values ofx are positive.
7/29/2019 L34 OpenChannel PartV
9/12
Gradually Varied Flow - Circular Channel
1243
1243.5
1244
1244.5
1245
1245.5
1246
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00
Position along channel (x)
z,W
Bed Elevation
WS elevation
S3 curve example flow under a gate in a parabolic channel
Calculation proceeds downstream, thus values ofx are positive.
7/29/2019 L34 OpenChannel PartV
10/12
Gradually Varied Flow - Parabolic Channel
1559.5
1560
1560.5
1561
1561.5
1562
-100.00 -80.00 -60.00 -40.00 -20.00 0.00
Position along channel (x)
z,W
Bed ElevationWS elevation
C1 Flow upstream of a dam in a critical slope, rectangular channel
Calculation proceeds upstream, thus values ofx are negative.
7/29/2019 L34 OpenChannel PartV
11/12
Gradually Varied Flow - Rectangular Channel
1234.5
1235
1235.5
1236
1236.5
1237
1237.5
1238
-300.00 -250.00 -200.00 -150.00 -100.00 -50.00 0.00
Position along channel (x)
z,W
Bed ElevationWS elevation
C3 Flow under a gate in critical slope, rectangular channelThe depth calculations are the same as in the previous example. The GVF table is shown
next.
Calculations proceed downstream.
Gradually Varied Flow - Rectangular Channel
1233.5
1234
1234.5
1235
1235.5
1236
0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00
Position along channel (x)
z,W
Bed ElevationWS elevation
7/29/2019 L34 OpenChannel PartV
12/12
H1 free fall in horizontal-bed, rectangular channel
Gradually Varied Flow - Rectangular Channel
1234.5
1235
1235.5
1236
1236.5
1237
1237.5
1238
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00
Position along channel (x)
z
,W
Bed ElevationWS elevation