It cannot be said that the exact relations between D and V are yet known, but it is of great practical importance to know that V must vary with D. The precise manner in which it must vary does not, for moderate changes, make very much difference. In designing a channel a suitable relation of depth to velocity can be arranged for, and one quantity or the other kept in the ascendant, according as scouring or silting is the evil to be guarded against.
The old idea was that an increase in V, even if accompanied by an increase in D, e.g. simply running a higher supply in a given channel, gave increased silt-transporting power. In a stream of very shallow section this is probably correct, for V increases faster than D·64 (Hydraulics, Chap. VI., Art. 2). In a stream of deep section a decrease in D gives increased silt-transporting power. If the discharge is fixed, a change in the depth or width must be met by a change of the opposite kind in the other quantity. In this case widening or narrowing the channel may be proper according to circumstances. In a deep section widening will decrease the depth of water, and may also increase the velocity, and it will thus give increased scouring power. In a shallow section, narrowing will increase the velocity more than it increases D·64. In a medium section it is a matter of exact calculation to find out whether widening or narrowing will improve matters.
If the water entering a channel has a higher silt-charge than can be carried in the channel, some of it must deposit. Suppose an increased discharge to be run, and that this gives a higher silt-carrying power and a smaller rate of deposit per cubic foot of discharge, it does not follow that the deposit will be less. The quantity of silt entering the channel is now greater than before. Owing to want of knowledge regarding the proportions of silt and rolled material, and to want of exactness in the formulæ, reliable calculations regarding proportions deposited cannot be made.
The channels in which the observations above referred to were made have all assumed nearly rectangular cross-sections, the sides having become vertical by the deposit on them of finer silt; but the formula probably applies approximately to any channel if D is the mean depth from side to side, and V the mean velocity in the whole section.
If the ratio of V to D differs in different parts of a cross-section, there is a tendency towards deposit in the parts where the ratio is least, or to scour where it is greatest. There is a tendency for the silt-charge to adjust itself, that is, to become less where the above ratio is less, but the irregular movements of the stream cause a transference of water among all parts, and this tends to equalise the silt-charge.
Dubuat gives the following as the velocities close to the bed which will enable a stream to scour or roll various materials. The bed velocity is probably less than the mean velocity in the ratio of about ·6 to 1 in rough channels, and about ·7 to 1 in smooth channels:—
| Gravel as large as peas | ·70 feet per second |
| Gravel as large as French beans | 1·0 feet per second |
| Gravel 1 inch in diameter | 2·25 feet per second |
| Pebbles 1½ inch in diameter | 3·33 feet per second |
| Heavy shingle | 4·0 feet per second |
| Soft rock, brick, earthenware | 4·5 feet per second |
| Rock of various kinds | 6·0 feet per second |
| and upward. |
The figures for brick, earthenware, and rock can apply only to materials of exceedingly poor quality. Masonry of good hard stone will stand 20 feet per second, and instances have occurred in which brickwork has withstood a velocity of 90 feet per second without injury so long as the water did not carry sand and merely flowed along the brickwork. If there are abrupt changes in the stream, causing eddies, or if there is impact and shock, or if sand, gravel, shingle, or boulders are liable to be carried along, velocities must be limited.
7. Action on the Sides of a Channel.—It has been seen that the laws of silting and scour on the bed of a channel depend on the ratio of the depth to the velocity. The same laws probably hold good in the case of a gently shelving bank, so that here again V ought to vary as D·64. The velocity near the angle where the slope meets the water surface seems to decrease faster than D·64. At all events, silt tends to deposit in the angle and the slope to become steep.
When the slope is steep the law seems to be different, the tendency for deposit or scour to occur on the bank depending on the actual velocity without much relation to the depth. The velocity very near to a steep bank is always low relatively to that in the rest of the stream. Thus there is often a tendency for silt to deposit on the bank, especially in the upper part, and for the side to become vertical except for a slight rounding at the lower corner. A bank may receive deposits when the bed may be receiving none, and it may have a persistent tendency to grow out towards the stream. The growth of the bank is generally regular, the line of the bank being preserved, but it may be irregular, especially if vegetation, other than small grass, becomes established on the new deposits.