At a late meeting of the Institution of Civil Engineers, the paper read
was on "Recent Hydraulic Experiments," by Major Allan Cunningham, R.E.
This paper was mainly a general account of some extensive experiments on
the flow of water in the Ganges Canal, lasting over four years--1874-79.
Their principal object was to find a good mode of discharge measurements
for large canals, and to test existing formulae. There are about 50,000
velocity, and 600 surface-slope measurements, besides many special
experiments. The Ganges Canal, from its great size, from the variety of
its branches abounding in long straight reaches, and from the power of
control over the water in it, was eminently suited for such experiments.
An important feature was the great range of conditions, and, therefore,
also of results obtained. Thus the chief work was done at thirteen sites
in brickwork and in earth, some being rectangular and others
trapezoidal, and varying from 193 ft. to 13 ft. in breadth, and from 11
ft. to 7 in. in depth, with surface-slopes from 480 to 24 per million,
velocities from 7.7 ft. to 0.6 ft. per second, and discharges from 7,364
to 114 cubic feet per second. For all systematic velocity measurements,
floats were exclusively used, viz., surface floats, double floats, and
loaded rods. Their advantages and disadvantages had been fully discussed
in the detailed treatise "Roorkee Hydraulic Experiments"--1881. They
measured only "forward velocity," the practically useful part of the
actual velocity. The motion of water, even when tranquil to the eye, was
found to be technically "unsteady;" it was inferred that there is no
definite velocity at any point, and that the velocity varies everywhere
largely, both in direction and in magnitude. The average of, say, fifty
forward velocity measurements at any one point was pretty constant, so
that there must be probably average steady motion. Hence average forward
velocity measurements would be the only ones of much practical use. To
obtain these would be tedious and costly, and special arrangements would
be required to obviate the effects of a change in the state of water,
which often occurred in a long experiment, as when velocities at many
points were wanted.
As to surface-slope its measurement--from nearly 600 trials--was found
to be such a delicate operation that the result would be of doubtful
utility. This would affect the application of all formulas into which it
entered. The water surface was ascertained, on the average of its
oscillations, to be sensibly level across, not convex, as supposed by
some writers. There were 565 sets of vertical velocity measurements
combined into forty-six series. The forty-six average curves were all
very flat and convex down stream--except near an irregular bank--and
were approximately parabolas with horizontal axes; the data determined
the parameters only very roughly; the maximum velocity line was usually
below the service, and sank in a rectangular channel, from the center
outward down to about mid-depth near the banks. Its depression seemed
not to depend on the depth, slope, velocity, or wind; probably the air
itself, being a continuous source of surface retardation, would
permanently depress the maximum velocity, while wind failed to effect
this, owing to its short duration. On any vertical the mid-depth
velocity was greater than the mean, and the bed velocity was the least.
The details showed that the mid-depth velocity was nearly as variable
from instant to instant as any other, instead of being nearly constant,
as suggested by the Mississippi experimenters.
The measurement of the mean velocity past a vertical was thought to be
of fundamental importance. Loaded rods seemed by far the best for both
accuracy and convenience in depths under 15 ft. They should be immersed
only 0.94 of the full depth. The chief objection to their use,
that--from not dipping into the slack water near the bed--they moved too
quickly, was thus for the first time removed. A double float with two
similar sub-floats at depths of 0.211 and 0.789 of the full depth would
also give this mean with more accuracy and convenience than any
instrument of its class; this instrument is new. Measurement of the
velocity at five eighths depth would also afford a fair approximation.
One hundred and fourteen average transverse velocity curves were
prepared from 714 separate curves. These average curves were all very
flat, and were convex down stream--over a level or concave bed--and
nearly symmetric in a symmetric section. The velocity was greatest near
the center, or deepest channel, decreased very slowly at first toward
both banks, more rapidly with approach to the banks or with shallowing
of the depth, very rapidly close to the banks, and was very small at the
edges, possibly zero. The figure of the curve was found to be determined
by the figure of the bed, a convexity in the bed producing a concavity
in the curve and _vice versa_, and more markedly in shallow than in deep
water. Curves on the same transversal, at the same site, and with
similar conditions, but differing in general velocity, were nearly
parallel projections. At the edges there was a strong transverse surface
flow from the edge toward mid-channel, decreasing rapidly with distance
from the edge. The discussion showed that it was almost hopeless to seek
the geometric figure of the curves from mere experiment.
Five hundred and eighty-one cubic discharges were measured under very
varied conditions. The process adopted contained three steps: (1)
Sounding along about fifteen float courses, scattered across the site in
eight cross sections; time, say four hours. (2) Measurement of the mean
velocities through the full depths in those float courses, each thrice
repeated; time, say four hours. (3) Computation, say two hours. This
process was direct and wholly experimental; each step was done in a time
which gave some chance of a constant state of water. From an extended
comparison of all results under similar conditions, it appeared that the
above process yielded, under favorable circumstances, results not likely
to differ more than 5 per cent. The sequel showed that in a channel with
variable regimen, a discharge table for a given site must be of at least
double entry, as dependent on the local gauge-reading, and on the
velocity or surface-slope.
Special attention was paid to rapid approximations to mean sectional
velocity. The mean velocity past the central vertical, the central
surface velocity, and Chezy's quasi-velocity--i.e.,