Depth of Flow for No Bed Material Movement as Function of Q and D. The velocity V in
Equation 3.51 can be replaced with the discharge Q using the continuity equation (Q = W y
V). From continuity V = Q/(W y) The relation between y, Q and D for the condition of no bed
material transport is very useful in determining clear-water contraction scour as explained in
Chapter 7.
Replacing V with Q in Equation 3.51 to determine the depth (y) when there is no bed material
movement of size D, gives the following equation:
Q6 / 7
y = Ku
(3.52)
D2 / 7 W 6 / 7
K u = K 1/u7 = 0.210
(SI)
y
K u = K 1/u7 = 0.126
(English)
y
3.5.6 Tables for Determining Critical Velocities
Table 3.4 gives the permissible velocity recommended by Fortier and Scobey (1926). for
channels at small slope for bed material ranging from fine sand to cobbles. Table 3.5 gives
non-scour velocities for noncohesive and compact cohesive soils suggested by Keown et al.
(1977) for bed material ranging from loess soils to boulders.
Table 3.4. Maximum Permissible Velocities Proposed by Fortier and Scobey (1926).
Mean velocity, after aging of canals [y ≤ 0.9 m (3 ft)]
Water transporting
Original
noncolloidal silts,
Material excavated for
Clear water, no
Water transporting
sands, gravels or rock
n
canals
detritus
colloidal silt
fragments
ft/sec
M/sec
ft/sec
m/sec
ft/sec
m/sec
Fine sand (colloidal)
0.02
1.50
0.46
2.50
0.76
1.50
0.46
Sandy loam (noncolloidal)
0.02
1.75
0.53
2.50
0.76
2.00
0.61
Silt loam (noncolloidal)
0.02
2.00
0.61
3.00
0.91
2.00
0.61
Alluvial silt
(noncolloidal)
0.02
2.00
0.61
3.50
1.07
2.00
0.61
Ordinary firm loam
0.02
2.50
0.76
3.50
1.07
2.25
0.69
Volcanic ash
0.02
2.50
0.76
3.50
1.07
2.00
0.61
Fine gravel
0.02
2.50
0.76
5.00
1.52
3.75
1.14
Stiff clay
0.025
3.75
1.14
5.00
1.52
3.00
0.91
Graded loam to
Cobbles (noncolloidal)
0.03
3.75
1.14
5.00
1.52
5.00
1.52
Alluvial silt (colloidal)
0.025
3.75
1.14
5.00
1.52
3.00
0.91
Graded, silt to cobbles
(colloidal)
0.03
4.00
1.22
5.50
1.68
5.00
1.52
Coarse gravel
(noncolloidal)
0.025
4.00
1.22
6.00
1.83
6.50
1.98
Cobbles and shingles
0.035
5.00
1.52
5.50
1.68
6.50
1.98
Shales and hard pans
0.025
6.00
1.83
6.00
1.83
5.00
1.52
3.43
Previous Page
