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
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
Stream Power = 22.126
sec - N
sec - ft
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
D16 = 1.8 mm D75 = 4.0 mm D90 = 4.9 mm
D50 = 3.1 mm D84 = 4.4 mm