3.7.3 PROBLEM 3 Resistance to Flow in Alluvial Channels
Manning's n in Sand Bed Streams
(a) Plane bed
Considering only the bed of the stream determine the following:
What is the range of Manning's n values for a plane bed sand channel stream?
Manning's n ranges from 0.010 to 0.013.
What is the Manning's n for a plane bed stream with a D50 of 0.32 mm.
Using the Strickler equation as an approximation:
n = 0.0482 D1/6 with D in m n = 0.0482 (0.00032 m)1/6 = 0.013
(b) Antidune Flow
A sandbed channel is observed to have an undulating water surface, a discharge of 24.07
m3/s, an average velocity of 1.06 m/s, a channel width of 32.00 m, and a bed slope of 0.003.
The stream bed has a D50 of 0.35 mm. An estimate of the bed form and n-value of the channel
is desired.
Assuming the sieve diameter equals the fall diameter, and the bed slope equals the friction
slope. Determine the stream power.
Stream power equals Vγyo So = (1.06) (9800) (24.07/32.00 x 1.06) (0.003) = 22.126 N/sec-m.
Figure 3.13 is in English units. Therefore convert velocity and stream power to English units.
V = 1.06 x 3.281 = 3.48 ft/sec
1m
0.225 lb
lb
N
Stream Power = 22.126
= 152
x
x
sec - N
sec - ft
3.281ft
N
Figure 3.13 for this stream power indicates that upper flow regime is expected. The bed
configuration should be antidunes with standing waves.
Based upon the bedform the n-value is estimated to be 0.013.
Manning's n in Gravel Bed Streams
Use the following gravel bed material size analysis to estimate the Manning's n-value of the
stream.
D16 = 1.8 mm D75 = 4.0 mm D90 = 4.9 mm
D50 = 3.1 mm D84 = 4.4 mm
3.57