vm = v0 − 25.4 √ (mi).

But

vm = c √ (mi),

where c is a coefficient, the values of which have been already given in the table in § 98. Hence

vm = cv0 / (c + 25.4).

Values of Coefficient c/(c + 25.4) in the Formula vm = cv0/(c + 25.4).

Hydraulic
Mean Depth
= m.		Very
Smooth
Channels.
Cement.		Smooth
Channels.
Ashlar or
Brickwork.		Rough
Channels.
Rubble
Masonry.		Very Rough
Channels.
Canals in
Earth.		Channels
encumbered
with
Detritus.
 0.25.83.79.69.51.42
 0.5.84.81.74.58.50
 0.75.84.82.76.63.55
 1.0.85...77.65.58
 2.0...83.79.71.64
 3.0.....80.73.67
 4.0.....81.75.70
 5.0.......76.71
 6.0...84...77.72
 7.0.......78.73
 8.0..........
 9.0.....82...74
10.0..........
15.0.......79.75
20.0.......80.76
30.0.....82...77
40.0..........
50.0..........
∞.........79
Fig. 107.

§ 107. River Bends.—In rivers flowing in alluvial plains, the windings which already exist tend to increase in curvature by the scouring away of material from the outer bank and the deposition of detritus along the inner bank. The sinuosities sometimes increase till a loop is formed with only a narrow strip of land between the two encroaching branches of the river. Finally a “cut off” may occur, a waterway being opened through the strip of land and the loop left separated from the stream, forming a horseshoe shaped lagoon or marsh. Professor James Thomson pointed out (Proc. Roy. Soc., 1877, p. 356; Proc. Inst. of Mech. Eng., 1879, p. 456) that the usual supposition is that the water tending to go forwards in a straight line rushes against the outer bank and scours it, at the same time creating deposits at the inner bank. That view is very far from a complete account of the matter, and Professor Thomson gave a much more ingenious account of the action at the bend, which he completely confirmed by experiment.