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M1 curve example dam across non-symmetric trapezoidal channel

Calculation proceed upstream, thus, the values ofx are negative.

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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.

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M2 curve example free fall at the end of a circular channel

Calculation proceeds downstream, thus values ofx are positive.

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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.

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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.

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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.

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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.

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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.

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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

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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