HYDRAULICS.] HYDROMECHANICS 503 It has been attempted to express the decrease of the rate of flood discharge with the increase of extent of the catchment basin by empirical fonnulte. Thus Colonel O Connell proposes the formula j/= M/>> where M is a constant called the modulus of the river, the value of which depends on the amount of rainfall, the physical char acters of the basin, and the extent to which the floods are moderated by storage of the water. If M is small for any given river, it shows thiit the rainfall is small, or that the permeability or slope of the sides of the valley is such that the water does not drain rapidly to the river, or that lakes and river bed moderate the rise of the floods. If values of M are known for a number of rivers, they may be used in inferring the probable discharge of other similar rivers. For British rivers M varies from 43 fora small stream draining meadow land to 37 for the Tyue. Generally it is about 15 or 20. For large European rivers M varies from 16 for the Seine to 67 5 for the Danube. For the Nile 51 = 11, a low value which results from the immense length of the Nile throughout which it receives no affluent, and probably also from the influence of lakes. For different tributaries of the Mississippi M varies from 13 to 56. For various Indian rivers it varies from 40 to 303, this variation being due to the great variations of rainfall, slope, and character of Indian rivers. In some of the tank projects in India, the flood discharge has been calculated from the formula D = C /n?, where D is the dis charge in cubic yards per hour from n square miles of basin. The constant C was taken = 61, 523 in the designs for the Ekrooka tank, = 75,000 on Ganges and Godavery works, and= 10,000 on 51adras works. 114. Action of a Stream on its Bed. If the velocity of a stream exceeds a certain limit, depending on its size, and on the size, heavi ness, form, and coherence of the material of which its bed is composed, it scours its bed and carries forward the materials. The quantity of material which a given _ -.___,.._. - __ -_- stream can carry in suspension depends on the size and density ,---"f ~~--^ of the particles in suspension, ,- "* " and is greater as the velocity of the stream is greater. If in one part of its course the velo- -p. -, city of a stream is great enough to scour the bed and the water becomes loaded with silt, and in a subsequent part of the river s course the velocity is diminished, then part of the transported material must be deposited. Probably deposit and scour .___ --..__ - - =^ go on simultane ously over the whole river bed, but in some parts the rate ]) of scour is in excess of the rate of de posit, and in other parts the rate of de posit is in excess of ** iai - the rate of scour. Deep streams appear to have the greatest scour ing [tower at any given velocity. It is possible that the difference is strictly a difference of transporting, not of scouring action. Let fig. 130 represent a section of a stream. The material lifted at a will be diffused through the mass of the stream and deposited at different distances down stream. The average path of a particle lifted at a will be some such curve as abc, and the average distance of transport each time a particle is lifted will be represented by ac. In a deeper stream such as that in fig. 131, the average height to which [(articles are lifted, and, since the rate of vertical fall through the water may be assumed . the same as before, the average distance a c of ^^ transport, will be greater. Consequently, al- ^ though the scouring action may be identical in the two streams, the velocity of transport of material down stream is greater as the depth of the stream is greater. The effect is that the deep stream excavates its bed more rapidly than the shallow stream. 115. Bottom Velocity at which Scour commences.- The following bottom velocities were determined by Dubuat to be the maximum velocities consistent with stability of the stream bed for different materials. Dairy and Bnzin give, for the relation of the mean velocity r m and bottom velocity r&, and from obtained :- this the following values of the mean velocity are Bottom Velocity = n . Mean Velocity 1. Soft earth 25 33 2. Loam 5 ) 65 3. Sand I OO 1 30 4. Gravel 2 -QO 2 69 5. Pebbles 3 40 4 46 6. Broken stone, flint 4 00 5 25 7. Chalk, soft shale 5 00 6 56 8. Rock in beds 6 00 7 "87 9. Hard rock 10 00 13 12 The following table of velocities which should not be exceeded in channels is given in the Inyenieurs Taschenbuch of the Vereiu "Hiitte": Surface Velocity. Mean Velocity. Bottom Velocity. Slimy earth or brown clay 49 36 26 Clay . . 98 75 52 Firm sand 1-97 1 51 1 02 Pebbly bed 4-00 3 15 2-30 Boulder bed . 5-00 4 03 3 08 Conglomerate of slaty fragments Stratified rocks 7 28 8 00 6-10 7 45 4 90 6 - 00 Hard rocks 14-00 12-15 10 36 116. Regime of a River Channel. A river channel is said to be in a state of regime, or stability, when it changes little in draught or form in a series of years. In some rivers the deepest part of the channel changes its position perpetually, and is seldom found in the same place in two successive years. The sinuousness of the river also changes by the erosion of the banks, so that in time the position of the river is completely altered. In other rivers the change from year to year is very small, but probably the regime is never perfectly stable except where the rivers flow over a rocky bed. If a river had a constant discharge it would gradually modify its bed till a permanent regime was established. But as the volume discharged is constantly changing, and therefore the velocity, silt is deposited when the velocity decreases, and scour goes on when the velocity increases in the same place. When the scouring and silt ing are considerable, a perfect balance between the two is rarely established, and hence continual variations occur in the form of the river and the direction of its currents. In other cases, where the action is less violent, a tolerable balance may be established, and the deepening of the bed by scour at one time is compensated by the silting at another. In that case the general regime is permanent, though alteration is constantly going on. This is more likely to happen if by artificial means the erosion of the banks is prevented. If a river flows in soil incapable of resisting its tendency to scour it is necessarily sinuous ( 103), for the slightest deflexion of the current to either side begins an erosion which increases progres sively till a considerable bend is formed. If such a river is straightened it becomes sinuous again unless its banks are pro tected from scour. 117. Longitudinal Section of River Bed. The declivity of rivers decreases from source to mouth. In their higher parts rapid and R. Tyne 3-S/f + 10-87 V But Taking a mean value for , we get torrential, flowing over beds of gravel or boulders, they enlarge in volume by receiving affluent streams, their slope diminishes, their bed consists of smaller materials, and finally they reach the sea. Fig. 132 shows the length in miles, and the surface fall in feet per
mile, of the Tyne and its tributaries.
