Qs = 518 x 60.96 = 31,580 metric-tons/day
Note Qs = 31,580 metric-tons/day = 31,580 x 2204.62/2000 = 34,800 tons/day
4.12.8 Problem 7 Calculate Total Bed-Material Discharge Using Yang's Sand Equation
Yang's sand equation (Equation 4.51) is as follows
V*
VS
Vcr S
ωD50
ωD50
V*
log
+ 1.799 - 0.409 log
log C t = 5.435 - 0.286 log
- 0.457 log
- 0.314 log
-
ω
ω
ν
ω
ν
ω
Vcr
2.5
VD
=
+ 0.66 for 1.2 < * 50 < 70
VD
ω
ν
log * 50 - 0.06
ν
and
Vcr
VD
= 2.05 for * 50 ≥ 70
ω
ν
Compute the bed-material transport in metric-tons/day.
Given:
Q = 221.39 m3/sec
ν = 1.16 x 10-6 m2/s
W = 103.95 m
ω = 0.043 m/sec
y = 2.31 m
D50 = 0.32 mm
V = 0.922 m/sec
S = 0.00022 m/m
Calculate:
τo = 9800 x 2.31 x 0.00022 = 4.98 N/m2
V* = (4.98/ 1000)0.5 = 0.0706 m/s
V* D50
= 0.0706 x 0.00032 / 1.16 x 10 -6 = 19.5
ν
Vcr
2.5
=
+ 0.66 = 2.69
ω
log19.5 - 0.06
Vcr S
= 2.69 x 0.00022 = 0.00059
ω
VS
= 0.922 x 0.00022 / 0.043 = 0.00472
ω
4.41
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