§ 123. _Catchment Basin._--A stream or river is the channel for the
discharge of the available rainfall of a district, termed its
catchment basin. The catchment basin is surrounded by a ridge or
watershed line, continuous except at the point where the river finds
an outlet. The area of the catchment basin may be determined from a
suitable contoured map on a scale of at least 1 in 100,000. Of the
whole rainfall on the catchment basin, a part only finds its way to
the stream. Part is directly re-evaporated, part is absorbed by
vegetation, part may escape by percolation into neighbouring
districts. The following table gives the relation of the average
stream discharge to the average rainfall on the catchment basin
(Tiefenbacher).
+-----------------------------+-----------------+--------------------+
| |Ratio of average |Loss by Evaporation,|
| | Discharge to | &c., in per cent of|
| |average Rainfall.| total Rainfall. |
+-----------------------------+-----------------+--------------------+
| Cultivated land and spring- | | |
| forming declivities. | .3 to .33 | 67 to 70 |
| Wooded hilly slopes. | .35 to .45 | 55 to 65 |
| Naked unfissured mountains | .55 to .60 | 40 to 45 |
+-----------------------------+-----------------+--------------------+
§ 124. _Flood Discharge._--The flood discharge can generally only be
determined by examining the greatest height to which floods have been
known to rise. To produce a flood the rainfall must be heavy and
widely distributed, and to produce a flood of exceptional height the
duration of the rainfall must be so great that the flood waters of the
most distant affluents reach the point considered, simultaneously with
those from nearer points. The larger the catchment basin the less
probable is it that all the conditions tending to produce a maximum
discharge should simultaneously occur. Further, lakes and the river
bed itself act as storage reservoirs during the rise of water level
and diminish the rate of discharge, or serve as flood moderators. The
influence of these is often important, because very heavy rain storms
are in most countries of comparatively short duration. Tiefenbacher
gives the following estimate of the flood discharge of streams in
Europe:--
Flood discharge of Streams
per Second per Square Mile
of Catchment Basin.
In flat country 8.7 to 12.5 cub. ft.
In hilly districts 17.5 to 22.5 "
In moderately mountainous districts 36.2 to 45.0 "
In very mountainous districts 50.0 to 75.0 "
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 formulae. Thus Colonel P. P. L. O'Connell proposed the
formula y = M [root]x, where M is a constant called the modulus of the
river, the value of which depends on the amount of rainfall, the
physical characters 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 that 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 0.43 for a small stream
draining meadow land to 37 for the Tyne. 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 M = 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[3root]n², where D is the discharge
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 Madras works.
[Illustration: FIG. 129.]
[Illustration: FIG. 130.]
§ 125. _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,
heaviness, 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 of the particles in suspension, and is
greater as the velocity of the stream is greater. If in one part of
its course the velocity 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 simultaneously over the whole river bed, but in some parts the rate
of scour is in excess of the rate of deposit, and in other parts the
rate of deposit is in excess of the rate of scour. Deep streams appear
to have the greatest scouring power at any given velocity. It is
possible that the difference is strictly a difference of transporting,
not of scouring action. Let fig. 129 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. 130, the
average height to which particles 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,
although 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.
§ 126. _Bottom Velocity at which Scour commences._--The following
bottom velocities were determined by P. L. G. Dubuat to be the maximum
velocities consistent with stability of the stream bed for different
materials.
Darcy and Bazin give, for the relation of the mean velocity v_m and
bottom velocity v_b.
v_m = v_b + 10.87 [root](mi).