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 Chézy's quasi-velocity - i.e.,
100 × √( R × S )
where R=the hydraulic mean depth, and S=surface slope - were tried in detail; thus 100, 76, and 83 average values thereof respectively were taken from 581, 313, and 363 detail values. The ratios of these three velocities to the mean velocity were taken out, and compared in detail with Bazin's and Cutter's coefficients. Other formulae were contrasted also in slight detail. Kutter's alone seemed to be of general applicability; when the surface slope measurement is good, and the rugosity coefficient known for the site - both doubtful matters - it would probably give results within 7½ per cent. of error. Improvement in formulae could at present be obtained only by increased complexity, and the tentative research would be excessively laborious. Now the first two ratios varied far less than the third; thus their use would probably involve less error than the third, or approximation would be more likely from direct velocity measurement than from any use of surface slope. The connection between velocities was probably a closer one than between velocity and slope; the former being perhaps only a geometric, and the latter a physical one.
The mean velocity past the central vertical was recommended for use, as not being affected by wind; the reduction coefficient could at present only be found by special experiment for each site. Three current meters were tried for some time with a special lift, contrived to grip the meter firmly parallel to the current axis, so as to register only forward velocity, and with a nearly rigid gearing wire. No useful general results were obtained. Ninety specimens of silt were collected, but no connection could be traced between silt and velocity; it seemed that the silt at any point varied greatly from instant to instant, and that the quantity depended not on the mean velocity, but probably on the silt in the supply water. Forty measurements of the evaporation from the canal surface were made in a floating pan, during twenty five months. The average daily evaporation was only about 1/10 in. The smallness of this result seemed to be due to the coldness of the water - only 63 deg. in May, with 165 deg. in the sun and 105 deg. in shade.
Lastly, it must suffice to say that great care was taken to insure accuracy in both fieldwork and computation.