TABLES, COEFFICIENTS, AND FORMULÆ,

FOR

FINDING THE DISCHARGE OF WATER

FROM

ORIFICES, NOTCHES, WEIRS, PIPES, AND RIVERS.

BY JOHN NEVILLE,

CIVIL ENGINEER, M. R.I.A.,

COUNTY SURVEYOR OF LOUTH AND OF THE COUNTY OF THE TOWN OF DROGHEDA;
FELLOW OF THE ROYAL GEOLOGICAL SOCIETY OF IRELAND.

Third Edition:

WITH ADDITIONS, CONSISTING OF NEW FORMULE FOR THE DISCHARGE
FROM TIDAL AND FLOOD SLUICES, AND SYPHONS; GENERAL INFOR-
MATION ON RAINFALL, CATCHMENT-BASINS, DRAINAGE, SEWERAGE,
WATER SUPPLY FOR TOWNS, AND MILL POWER.

"In physics the memory disbuchens itself of its cumbrous catalogue of particulars
and caries centuries of observation in a single formula.-EMERSON ON NATURE.

"It ought to be more generally known, that theory is nothing more than the conclusions
of reason from numerous and accurately observed phenomena, and the deductions of the
laws which connect causes with effects; that practice is the application of those general
truths and principles to the common affairs and purposes of life; and that science is the
recorded experience and discoveries of mankind, or, as it has been well defined, the
knowledge of many, orderly and methodically digested, and arranged, so as to become
attainable by one.'"-AMERICAN QUARTERLY REVIEW.

Capio Lumen

LONDON:

LOCKWOOD & CO., 7, STATIONERS' HALL COURT.

1875.

BRADBURY, AGNEW, & Co., PRINTERS, WHITEFRIARS.

INTRODUCTION

TO THE THIRD EDITION.

In order to render this edition more valuable to the hydraulic engineer the work has been again considerably extended by the insertion of several new formulæ, experimental coefficients, and general estimates of cost. It is hoped that the extent and practical nature of these additions, will render the book still more useful than before, to meet the ever-varying requirements of the profession in connexion with rivers and waterworks. The experiments of Mr. Mallet on syphons made in 1843, and printed in Weale's Quarterly Papers on Engineering, have been reduced. New formulæ are given for finding the discharge from syphons, floodsluices, and tidal-sluices. The practical formulæ for gauging by weirs have been added to. The arrangement of the matter is in some places altered, and some portions of the former introductions transferred, at their proper places, to the text, and others are retained here.

At page 85 the erroneous practice of different engineers in giving only two-thirds of the coefficient of discharge for weirs is noticed. This practice assumes that the theoretical discharge from a notch is the same as if all the particles of water had the same mean theoretical velocity as those undermost, which, being too large by one-third, the experimental coefficient has to be reduced in the same proportion to give a correct result. There is no reason for sanctioning a different coefficient for notches, or orifices at the surface, and for sunk orifices. The coefficients when in thin plates, with large cisterns, have nearly the same general value,

615 to 628, for both, and it tends to confusion to adopt in one place a coefficient for a correct formula, and in another a coefficient for an incorrect one; although the final result, by an equality of contrary errors, may be the same. I may here observe how very general the coefficient of two-thirds, and thereabouts, is for all orifices and notches; likewise for the useful effect derived from the application of water power; as well also for the relation of the velocity due to the fall and the velocity of water wheels to give a maximum result. The modifications of coefficients, dependent on the position, thickness, form, and approaches of an orifice, are as yet little understood by the profession. The defects in the ordinary formula when the velocity of approach has to be considered are pointed out in pages 88 to 124, and it is to be regretted

that the authority of some writers on the subject has misled many as to the correct form. Before the effective power of a water-wheel, or water-engine, can be determined, we must know how to gauge the water supplied to it correctly. This can be done only by the application of formule and coefficients varied to suit the circumstances of the case under consideration. From causes, which it is not necessary to enter into here, this has seldom been done, and very little dependence can be placed on results obtained by the formula in common use when applied generally. It is pleasing to follow Mr. Francis and Professor J. Thomson through the steps by which they get the effective power of their wheels, and I have accordingly made considerable use of their labours in Section XIV.

In practice, the irregular, sometimes sloping, broken and jagged crests of most weirs, on larger rivers, render any close estimate of the quantity passing over quite uncertain, especially for lesser depths, unless where the observer has a large scientific experience; and the quantities are generally too large to apply the ordinary notch-gauge. In such cases it is better to measure the flow of the river, stream, or mill-race, from the cross section and the observed mean velocity. Frequently, however, this method presents another difficulty, in an irregular channel, where the depths and velocities vary considerably in the same cross section, and where the cross sections themselves vary in short distances apart.