Sample input, Calculation of total sediment discharge by the Modified Einstein Procedure (USBR method), Victor Miguel Ponce, San Diego State University

online_modified_einstein: Total sediment discharge by the Modified Einstein Procedure

References

Einstein, H. A., 1950. The bed-load function for sediment transportation in open channel flows. USDA Soil Conservation Service, Technical Bulletin No. 1026, Washington, D.C., September.

Colby, B. R. and C. H. Hembree, 1955. Computations of total sediment discharge, Niobrara river, near Cody, Nebraska. U.S. Geological Survey Water Supply Paper 1357, Washington, D.C.

U.S. Bureau of Reclamation, 1955. Step method for computing total sediment load by the Modified Einstein Procedure. Sedimentation Section, Hydrology Branch, Project Investigations Division, July.

U.S. Bureau of Reclamation, 1966. Computation of "Z's" for use in the Modified Einstein Procedure. Sedimentation Section, Hydrology Branch, Project Investigations Division, June.

SAMPLE INPUT

[Rationale]     [Procedure]     [Features]     [Main Page]
Stream or river: Niobrara river, near Cody, Nebraska
U.S. Customary Units.

1. Discharge Q [cfs]:      230
2. Mean velocity u [fps]:      2.08
3. Average depth d [ft]:      0.98
4. Width w [ft]:      113
5. Flow area A [ft²]:      111
6. Water temperature t [^oF]:      64

7. Kinematic viscosity ν [ft²/s]:      0.00001153

8. Diameter D₆₅ [ft]:      0.00105
9. Diameter D₃₅ [ft]:      0.00075
10. Measured concentration C [ppm]:      262
11. Sampled suspended load Q_sm [tons/day]:      163
12. Vertical distance not sampled d_n [ft]:      0.3
13. Mean water depth at sampled verticals d_s [ft]:      1.22

14. Number of size fractions:     Normal
15. Fraction of bed material in each size range i_b (9 values):      0.,0.,0.38,0.50,0.05,0.01,0.01,0.,0.
16. Percentage of suspended material in each size range Q'_s (9 values):      22.,25.,42.,11.,0.,0.,0.,0.,0.
17. Z' mode of computation:     USBR (1955).

SAMPLE OUTPUT:

Stream or river: Niobrara river, near Cody, Nebraska
•   U.S. Customary Units.   •   Number of size fractions: Normal (9)   •   USBR (1955) Z' mode of computation   •   Computed load (Column 24) in T/D units (tons/day)   •
•   RS = 0.000226   •   u'_* = 0.0853   •   δ = 0.00157   •   k_s/δ = 0.67   •   x = 1.53   •   P = 10.7   •   A' = 0.246   •
•   Percentage of flow in sampled zone = 80%   •   Sediment discharge through the sampled zone Q'_s = 130 tons/day   •
•   Reference size fraction D = 0.00058 ft   •   Reference size fraction Z' = 0.76   •
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Size
fraction
(mm) D
(mm) D
(ft) ψ φ_*/2 1200 D^3/2 i_b i_bq_b 43.2 w i_BQ_B
(T/D)
% Size
Q'_s Q'_s
(T/D)
Mult. Z' A" J'₁ -J'₂ J"₁ -J"₂ PJ"₁+J"₂
________
PJ'₁+J'₂
I"₁ -I"₂ PI"₁+I"₂
+1
Computed
load
(T/D)
0.002-0.0625 0.0112 0.000037 5.49 0.2571 0.00027 0. 0.000000 4,882 0.00 22.0 28.6 0.025 0.019 0.000075 0.74 0.40 1.01 1.04 1.23 35.3
0.0625-0.125 0.0884 0.00029 5.49 0.2571 0.00593 0. 0.000000 4,882 0.00 25.0 32.5 0.438 0.33 0.00059 0.63 0.43 1.22 2.02 1.62 52.5
0.125-0.25 0.177 0.00058 5.49 0.2571 0.0168 0.38 0.001637 4,882 7.99 42.0 54.6 1.000 0.76 0.00118 2.93 8.50 23.78 190.0
0.25-0.5 0.354 0.00116 5.49 0.2571 0.0474 0.50 0.006093 4,882 29.75 11.0 14.3 1.77 1.34 0.00237 0.50 2.07 4.31 128.2
0.5-1 0.707 0.00232 6.79 0.1467 0.1341 0.05 0.000984 4,882 4.80 0.0 0.0 2.57 1.95 0.00473 0.22 0.87 2.45 11.8
1-2 1.41 0.00464 13.58 0.0127 0.3793 0.01 0.00048 4,882 0.24 0.0 0.0 3.43 2.61 0.00947 0.14 0.55 1.94 0.5
2-4 2.83 0.00928 27.15 0.0000 1.0727 0.01 0.000000 4,882 0.00 0.0 0.0 4.45 3.38 0.01894 0.09 0.31 1.64 0.0
4-8 5.66 0.01856 54.30 0.0000 3.0340 0. 0.000000 4,882 0.00 0.0 0.0 5.70 4.33 0.03788 0.06 0.18 1.46 0.0
8-16 11.31 0.03712 108.60 0.0000 8.5816 0. 0.000000 4,882 0.00 0.0 0.0 7.28 5.53 0.07575 0.04 0.10 1.35 0.0
Total 100 130 418.3

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