The effect of bends on the velocity of a stream is not well understood. In case of a bend of 90° the increased resistance to flow when the bend is absolutely sudden (a sudden bend is known as an “elbow”) amounts perhaps to V2/(2g). Whether it is greater or less in the case of a gentle bend of 90° is not known. In the case of a pipe there is a certain radius which gives a minimum resistance (Hydraulics, Chap. V.). The increased resistance at a bend is due partly to the fact that the maximum velocity is no longer in the centre of the stream, and partly to the fact that the velocities at the different parts of the cross-section have to be rearranged at the commencement of the bend and again at its termination. Thus the effect of a bend of 45° is a good deal more than half of that of a bend of 90°. Two bends of 45°, both in the same direction, with a straight reach between them, will cause more resistance than a single bend of 90° with the straight reach above or below the bend. If the two bends of 45° are in different directions the resistance will be still greater. A succession of sharp bends may produce a serious effect, amounting to an increase in roughness of the channel. A succession of gentle bends, of any considerable angle, cannot of course occur within a moderate length of channel.
When there is head to spare there is clearly no objection to bends, except that the bank may need protection. At a place where the bank has in any case to be protected, e.g. at a weir, there is no objection to an elbow.
9. General Tendencies of Streams.—Since the velocity is greater as the area of the cross-section is less, a stream always tends to scour where narrow or shallow, and to silt where wide or deep. The cross-section thus tends to become uniform in size. Suppose two cross-sections to be equal in size but different in shape. The velocities of the two sections will be equal. The tendency of the bed to silt will (Art. 6) be greater at the deeper section and, when silting has occurred on the bed, the section will be reduced and there will be a tendency to scour at the sides. Thus the cross-sections tend to become also uniform in shape. If a bank of silt has formed in a stream, the tendency is for scour to occur. There is also a tendency for silt to deposit just below the point where the bank ends. Hence a silt bank often moves downstream.
Owing to the tendency to scour alongside of, or downstream of, obstructions (Art. 1), it is clear that a stream constantly tends to destroy obstructions.
There is an obvious tendency for silt to deposit where the bed slope of a stream flattens, and for scour to take place where it steepens (Hydraulics, figs. 16 and 17, pp. 24 and 25), and thus the tendency is for the slope to become uniform.
In a natural stream flowing from hilly country to a lake or sea, the slope is steepest at the commencement and gradually flattens. There is thus a tendency for the bed to rise except at the mouth of the stream. This rising tends to increase the slope and velocity in the lower reaches, and this again enhances the tendency, described in the preceding article, of the stream to increase in tortuosity.
When a silt-bearing stream overflows its banks the depth of water on the flooded bank is probably small and its velocity very low, and a deposit of silt takes place on the bank. When the deposit has reached a certain height it acts like a weir on the water of the next flood, which flows quickly over it and, instead of raising it higher, deposits its silt further away from the stream. In this way a strip of country along the stream gradually becomes raised, the raising being greatest close to the stream. The country slopes downwards in going away from the stream. In other words, the stream runs on a ridge. If the bank becomes raised so high that flooding no longer occurs, the raising action ceases, but if, as is likely in alluvial country, the bed of the stream also rises, the action may continue and the ridge become very pronounced.
Some rivers have very wide and soft channels which are only filled from bank to bank in floods, if then. The deep stream winds about in the channel, and the rest of it is occupied by sandbanks and minor arms. The winding is the result of the velocity being too great for the channel. The streams, especially the main stream, constantly shift their courses by scouring one bank or the other. Now and then the main stream takes a short cut, either down a minor arm or across an easily eroded sandbank. This is a very different matter from a short cut across high ground. The sandbanks receive deposits of silt in floods, but are constantly being cut away at the sides. Such rivers frequently erode their banks to an extraordinary extent. The Indus sometimes cuts into its bank 100 feet or more in a day, and it may cut for half a mile or more without cessation. The tortuosity of such a stream increases as it gets nearer the sea. The actual length of the Indus in the 400 miles nearest the sea is 39 per cent. greater than its course measured along the bank. In the reach from the 600th to the 700th mile from the sea, the difference is only 3 per cent. For a detailed description of some such rivers, see Punjab Rivers and Works.
Sometimes general statements are made regarding silting or scour in connection, for instance, with a stream which is confined between embankments or training walls, or has overflowed its banks or is held up by a weir. It is impossible to say that any such condition, or any condition, will cause silting or scour, unless the velocity depth and silt charge are known.