DISCUSSION--NOTES ON BUILDING CONSTRUCTION. 27 public officers when the matter came up finally 'or public discus- sion. At present there seemed to be no likelihood that there•
would he any objection. He confessed to disappointment that the paper had not been more actively criticised. He had ventured to proclaim opinions which many gentlemen might differ from very materially. As it happened, those members who had ad- dressed themselves to the subject had been kind enough to say that they agreed with him. That left him nothing further to say.
The PRESIDENT said Colonel Monash and those who had dis- cussed the paper had left very little to say in summing up. In regard to building regulations, he thought that all that they de- sired as engineers was being done.
As to the height of buildings in the wide streets': The fire brigade authorities desired goft., the Institute of Engineers con- sidered 'loft. sufficient, and the Architects, he believed, had fixed upon I2oft. There had been a great deal of discussion, and probably some height between I loft. and I2oft would be decided upon. Melbourne's natural advantages in regard to light and air no doubt might be considered as capital to be fully utilised, but Melbourne could spread indefinitely, whilst New York, for in- stance, could not, and the balance of opinion appeared to be in favour of building generally to medium height rather than having fewer buildings of a great height.
Discussion closed.
PAPER.
COEFFICIENTS OF DISCHARGE FOR CIRCULAR ORIFICES.
BY MR. H. J. I. HILTON.
The discharge of circular orifices has been, perhaps, one of the- most closely investigated subjects in hydraulics, numerous tests having been made by experimenters all the world over. Never- theless the information at present available, although sufficiently approximate for ordinary practical requirements, is contradictory and uncertain in its details.
It is known that the coefficient of velocity at the contracted vein is unity within a small fraction of one per cent, i.e., the- velocity is as nearly as possible equal to the theoretical velocity ./2gH. The coefficient of contraction is usually given as about .62, i.e., the area of the contracted vein is approximately 8 of the area of the orifice, varying as the coefficient of dis- charge. The coefficient of discharge is usually given by the text
books as .62 (the mean of a large number of experiments), But
28 VICTORIAN INSTITUTE OF ENGINEERS:
in reality it varies considerably, according to the head of water and diameter of orifice. In addition to decreasing as the diameter increases, under low heads it decreases rapidly as the head in- creases. For heads of about 5 feet and over it has hitherto been assumed (principally on the basis of experiments made and col- lected by Hamilton Smith, junr.) that it also decreases as the head 'increases, but in less degree, up to a head of 100 feet, under which head it is given as .592* for all diameters from din. to Izin.
Probably amongst the latest experiments are those made by Messrs. Judd and King-- at the Ohio State University, U.S.A., described in the "Engineering News" of Sept. 27th, 1906.
These experiments were carried out on orifices of the following diameters:—yin., 1in., Izin., zin. and 22in., under heads varying from 4 feet to 93 feet. "The results did not show any great change in the coefficient of discharge for an increase of head."
The following results of tests on the zin. orifice will suffice as an example.
TABLE I.
Head in
Coeff. Head in Head in
feet. feet. Coeff.
feet. Coeff.
5'00 •6084 23'24 •6083 57'70 •6081
9'08 '6083 36 .12 '6082 69'99 •6080 17.79 •6080 47'02 •6088 92 .01 •6080
Considering that the average coefficient for the above orifice is .6083, in other words, that the actual discharge averaged 60.83 per cent. of the theoretical, with such small variations, the question naturally arises as to whether the theories hitherto ac-
cepted are correct.
As bearing on the subject it may be mentioned that a large number of experiments were recently made by the writer on small re-entrant pipe mouthpieces, 21 diameters in length, in which he found that the coefficient of discharge clearly decreased as the diameter increased up to a certain diameter, but he could find no difference due to variations in head down to as low a head as 6 inches or to changes in temperature within a range of from 65 to too degrees F. The coefficient of discharge usually given for this type of pipe outlet or mouthpiece is .71. The average results obtained by the writer for various sized outlets are shown on Diagram A.
*Conclusions of Hamilton Smith, Jun., tabulated in " Merriman's Hydraulics," p 79.
tAssistant Professor of Experimental Engineering.
COEFFICIENTS OF DISCHARGE FOR CIRCULAR ORIFICES. 29
DIAGRAM `'A."
Diam. Coeff. Diam. Coeff. Diam. Coeff.
/in. '91 /in. '83 1/in. '77
/in.
87 /in. '81 2in. '76/gin. '85 1in. •79 2/in. 75
The curve on the above diagram would appear to indicate that for an infinitely small diameter of mouthpiece the coefficient of discharge would be unity, subject to the effects of capillarity, vis- cosity, cohesion, etc.
Experiments on circular orifices do not appear to have been systematically carried out on diameters of less than fin., and it occurred to the writer that if experiments were made on a , series. of orifices of small diameter commencing at very low heads, some
further light might be thrown on the subject.
The text books are usually careful to state that the coeffi•. cients given are for standard vertical orifices, i.e., orifices in a thin vertical plate, sometimes called frictionless orifices. The coefficient of discharge for orifices on a horizontal plane and at intermediate angles between the vertical and horizontal do not appear to have been investigated, so that some experiments in these directions were warranted.
ORIFICES.
The orifices used in the writer's experiments were of the fol- lowing diameters:--.o25 (41, in.), .05 ( in.), .r, .15, .2, .25,
In tabulated form the following are the coefficients as read from the diagram :—
TABLE II.
Co-efficients of discharge for sharp edged, square cut re-entrant pipe mouth pieces,
2i
diameters in length.NMI MIN
MI M I MIN
~~IIIIIIIIIIIII~~i~~~1"'!!f'f-,
.212
-TS 80 85
—COEFFICIENT OF
F0a DISCHARGE —
3O VICTORIAN INSTITUTE OF ENGINEERS :
-3, .4, -.5, .6, and .75 inches. The orifice plates were of brass,
~1r in to hin. thick. The diameter of each plate was at least seven times the diameter of the orifice, and for the six smallest was
2 inches. A brass gauge was made for each orifice except the tin., bin., and tin., for which standard steel gauges were used.
The brass gauges were made to exactly the diameter required, several being made for each of the smallest orifices and the most accurate selected. For measuring their diameters a i ö ú ö o in.
Starrett spring touch micrometer was used. The orifices were first made slightly smaller than the gauges, then countersunk to as nearly as possible a feather edge, and finally rimered out until the gauge could only be forced through the orifice by being held exactly at right angles and twisted through with considerable exertion. It is thought that the diameter of the larger orifices would not vary more than inch, and of the small ones more than y-6 0;1 inch from the true diameter. It is computed that an error of 4 o na in. in the diameter of the .75 in. orifice would have a negligible effect on the coefficients of discharge; that a similar error in the tin. orifice would affect the coefficients about one unit in the third decimal place; that an error of ó ó o ú inch in the hin.
.orifice would affect the coefficients to the extent of two units, and in the ys in..orifice to the extent of six units in the third decimal place.
The three smallest orifices were originally made similar to the others, in brass plates countersunk. The results obtained were so erratic as to almost lead to the abandonment of the .experi-
ments. Careful observation, however; showed that capillary at- traction caused a globule of water to form in the countersunk portion immediately under the jet, suppressing contraction and increasing the discharge by to to 15 per cent. These plates were consequently abandoned and new orifices made in specially rolled sheet brass .005 in. thick, about z in. diam. These were spun flush into the back of 4'a- in. plates, 2 in. in diameter, having holes in the centre about three times the diameter of the orifice proper. To the writer's surprise, the results obtained from these minute orifices, especially the Ili; in., were as consistent and satis- factory as those of any of the larger ones, and have been of de- cided assistance in determining the curves on Diagram C.
MEASURING VESSELS.
The vessels in which the discharges were measured were of the following cubic contents :—.o26o8, .1565, .7758, 1.454, 2.005 and 7.4 cubic feet, ranging in round figures from 6th gallon to 46 gallons. The two smallest were narrow necked glass flasks.
The largest was a square open tank, and the intermediates were circular galvanised iron vessels with conical tops and vertical mouthpieces. The cubic contents were obtained by weighing the water contents at or about 55 deg. F., with standard weights on a balance, the larger vessels being weighed on reliable scales. In -the absence of a recognised international standard for the weight
COEFFICIENTS OF DISCHARGE FOR. CIRCULAR ORIFICES. 31 per cub. foot of distilled water, and of specific information., as to the weight of Melbourne water,. the writer preferred to take the mean results obtained by Depretz, Kopp, Pierre, Hagen, and Matthiesen* in preference to. those of the older authorities. These mean results when plotted to a curve fell into line with the weight of 62.27861bs. per cub. foot at .62° F. given by Mr.. H. J. Chaneyt, of the Standards Department of the British Board of Trade for water twice distilled and boiled to free it from air. The writer found that the Melbourne water, which is almost as soft as dis- tilled water, and well aerated, weighed only l'4 th of one per cent.
more than water once distilled, unboiled and slightly aerated, and finally adopted 62.32 lbs. per cubic foot as its approximate weight at 55 deg. F., this being the average temperature of the water with which the majority of the tests were made. Should the weight of 62.3951ós. per cub. ft, at 55deg. as given by the earlier authorities, ,be more correct, the effect would be to reduce all the coefficients obtained in these experiments by approximately one unit in the
third decimal place.
HEAD MEASUREMENTS.
Various methods were adopted for measuring the head of water under which the tests were made, which ranged from 2 in.
to loo in. For heads below 12 in. the vertical orifice plates were placed at the required distance below the top of the water vessel, being held in position by two small brass clips with a white lead or soft leather joint. The head was measured as the distance of the centre of the orifice below the surface of the water, which was maintained as nearly as possible just on the point of overflow.
For the horizontal orifices a vertical gauge was used, the head being measured above the plane of the orifice. The vessels for
*D. A. Dow, " Pocket Book for Mechanical F,ngineers," p. 344.
tChaney, " Our Weights and Measures," p. 88, and " Trans. Royal 'Society, 1892," pp. 331-334.
EFFECTS OF TEMPERATURE.
The errors in the capacities of the measuring vessels due to the differing temperatures at which the experiments were made (ranging from 5o to 7o deg.), were found, by weighing, to be so small as to have a negligible effect on the coefficients of discharge.
As regards the orifices, Hamilton Smith found that the discharge was diminished one per cent. by a rise of 55 degrees in tempera- ture, with an orifice .24 in diam. under heads from .56 to 3.2 feet.
Prof. Unwin found that it diminished one per cent by a rise 'of 144 degrees with an orifice .396in diam. under heads from I to 1.5 ft. Within the range of temperature under which the writer's experiments were made these figures would only have the effect of reducing the coefficients of discharge in the fourth decimal place, which would not he observable on the diagrams.
VICTORIAN INSTITUTE OF ENGINEERS:
maintaining the required head and in which the orifice plates were- fixed, were of various shapes and sizes. The smallest was of five gallons capacity, the next consisted of a drum to in. diam., 20 in high, the next a carcular tank 2 ft. diam., 3o in. high (used.
for both vertical and horizontal orifices), and, for the greater heads, a 4 in. diam. tube, 5 feet high, with a bend at the bottom (used for small horizontal and sloping jets), and a 9 in. diam. tube, 8 ft. 6 in. high (used for the vertical or downward jets). In the tanks and tubes ,yin. holes were made at the required intervals of height and the level regulated so that the water would just trickle out. The water was supplied to the tank and tubes by a hose, the end of which was turned upwards in tests on the small orifices, and was fixed so as to discharge into an internal submerged vessel for the larger ones. The object of this was . to prevent, as much as possible, currents and eddies, to maintain a head of still water, and to avoid velocity of approach, due to the energy of the hose jet.
The accurate measurement of the heads below 2 feet was a.
matter of difficulty, not so much on account of the measuring as on account of the difficulty in regulating the supply so as to main- tain exactly the head required. It is thought that an error of or or even i',, in. in the head may have occurred in any of the experi-
ments. While this error would be negligible under the greater heads, it would have a material effect on the coefficients for the small heads, and to this the writer principally attributes the erratic results under the low heads observable on the diagrams.
VELOCITY OF APPROACH.
Care was taken that the diameters of the tanks and tubes wiere sufficiently large in proportion to those of the orifices so as not to cause the coefficients to be materially affected by velocity of approach. The extreme case was that of the 4 in. orifice in the 9 in. tube under a head of loo inches, in which the velocity of ap- proach computes to about 1 in. per second, as against a velocity of 23 ft. per second at the vena contracta of the jet. In the hori- zontal orifices much difficulty was experienced in preventing the whirling of the water and the spiral motion and swaying of the jet under low heads. With the .3 in. orifice it was found that even in a tank eft. 6in. diam. containing still water, a vortex com-
menced to form and a whirling motion of the water to set in when the water level dropped to 15 in. head. The effect was a slow spiral motion of the jet, which (probably on account of contrac- tion being suppressed along, the line of the spiral) increased the discharge. As the head dropped the whirling increased and the normal discharge decreased, till finally the jet came as spray in the form of an inverted cup, and the normal discharge was greatly diminished. This difficulty was finally overcome by placing four vertical baffle plates or wings 2 feet long, in the bottom of the g in. tube, reaching to within 6 inches of the orifice plate.
COEFFICIENTS OF DISCHARGE FOR CIRCULAR ORIFICES. 33 UPWARD JETS.
In addition to the experiments on vertical and horizontal orifices, a few were tried at an intermediate angle of 45 deg.
(upward jets) with the four smallest orifices. The results are shown by crosses on the diagrams. They indicate that however much the effective energy of the jet may vary, the discharge of any orifice under a given head is just the same, whether the jet is vertical, horizontal, or at any intermediate angle, provided it is steady.
DURATION OF TESTS.
The length of run or duration of test varied from three minutes to 40 minutes, the approximate average time being five to eight minutes. It is thought that the error in timing would not have exceeded one second. Such error would make no appreciable difference in the coefficients, except in the shortest runs, in which they might be affected to the extent of three or four units in the third decimal place. To reduce these errors as much as possible, all short runs, particularly with the .75 in. orifice, were made twice and occasionally three times, and the mean time computed to the nearest half second. An example of the working out as adopted in all the experiments is given in table VI. The writer has pre- ferred to give the heads and diameters in inches instead of in feet,.
as is usual, the meaning of the figures being more easily grasped.
CRITICAL HEADS AND NORMAL COEFFICIENTS.
The results of the tests are plotted diagramatically in detail on sheets A and B. It will be observed that each orifice has a critical head, above which its coefficients of discharge appear to remain constant or
"
n•ormal." On the diagram for the z in. orifice, sheet A, is a line c.d., which represents a drop of four units in the third decimal place between heads of 4 ft. and 8 ft. A similar line, e.f., on sheet B, represents a decrease of nine units for the in. orifice. These lines indicate the relative decreases deduced from Hamilton Smith's results, as given in Merriman's Hydraulics.There appears to be no evidence of such decrease in the coefficients above the critical heads in any of the diagrams submitted.
All the curves in Sheets A and B are reproduced in Diagram C, on which are also shown in detail the results of the experi- ments on the three smallest orifices. It is somewhat remarkable that the curves, when extended as shown by the dotted lines, all converge on a point Q below the base line of the diagram.
Advantage of this has been taken in plotting the curves for the larger orifices. On diagram D the curves for the various critical heads have been plotted from readings of the intersections on Diagram C, and it will be observed that the normal coefficients from the .15 to the .75 orifices fall into a straight line, decreasing by three units in the third decimal place for every - in. increase
D
~~
34 VICTORIAN INSTITUTE OF ENGINEERS :
in the diameter of the orifice. All the curves converge on the ,coefficient :748 for the 4 in. orifice, and, the inference is that an infinitely small orifice under all heads would, as is also inferred for re-entrant pipe mouthpieces, have unity as its coefficient of discharge, assuming the effects of capillarity, , viscosity, cohe- sion, etc., , to be eliminated. These normal . coefficients have been arrived at by consideration not only of each group of experiments, but also of their relative positions as regards each other, and in each case represent a true mean of means. The following is a table showing the normal coefficients of discharge and approxi- mate critical heads for. various diameters, as obtained by the writer.
TABLE III.
Diam. of orifice
in inches •15 •2 '25 '3 '4 •5 '6 '75 1 an
over Normal Coeff
of discharge '631 '630 '6285 •627 '624 '621 •618 '613 — Critical head
in inches 65 55 45 32 25 22?-2 20 18 17
A study of the experimental results of tests on larger orifices leads the writer to no more definite conclusion than that the nor-
mal coefficient of discharge for the larger orifices lies between .59 and .6o. The exact figure to the third decimal place is probably indeterminate. Most of the experiments on the larger orifices are under comparatively low heads. The mean coefficient of Hamilton Smith's results for orifices from 2.4 to 12 inches in diameter under heads of 2 ft. 6 in. and 3 ft. is .598 (Merriman's abridged Table), while his mean coefficient for the same orifices for all heads is .596. For a 2 in. orifice under all heads his mean is .598. This figure agrees with that obtained by M. Hazin* for a 7.87 inch orifice under 3.28 feet head, and is probably a fair approximation for all orifices of 2i in. and over in diameter for all heads above the critical head of 17 inches. The following table shows a comparison of. the coefficients suggested by the writer with those obtained by Messrs. Judd and King and by several other investigators.
* Bazin, Contraction of the Liquid Vein," 1896, p. 9.
COEFFICIENTS OF DISCHARG$ FOR CIRCliLAR ORIFICES. 85
Diam. of Orifice in inches.
Suggested Normal Coefficients
(Author).
Judd ana King's Averages for Heads,
4ft. to 93ft..
Various.
7'87
7'2 •598
'598 '598
Bazin Hm. Smith.
2h to 3ft head.
Hm. Smith's ay. for all heads
'598 '6000 '5956 •5955
'6083 '6082 '6085 '6051 '6097 '6115
•6111 •6134 Bovey
Bovey
•6053 '598
'599 ' 603 '608 '613 '621 '6285 2/
2 1/
0~
0/
0/
On diagram E is shown the curve from which the writer's suggested coefficients in the above table have been read. The open circles on this diagram represent Messrs. Judd and King's results by calibration, the crosses represent their results by Pitot tube, and the black spots represent the writer's results.
The following table of coefficients is submitted as embodying the results of the investigations described in this paper :—
TABLE V.
Co-efficients of discharge for Standard Circular Orifices.
Diameter of Orifice in inches.
Head in inches.
45 '598 '599 '603 '608 •613 '621 .6285
and over
22 „ „ >, „ „ '621 '638
18 ,, ,, „ ,, '613 '623 '643
17 "598 '599 : '603 '608 '614 '624 •645 12 '600 '601 •606 '612 •618 '630 •653 9 •604 '606 •612 •619 •623 '637 '660 6 •610 '612 '618 '626 •632 '643 '669
3 — — — '640 ,'646 '657 '680
2 — — — — — '663 '683
NOTE.—The critical heads and corresponding normal co-efficients are in bold figures.
36 VICTORIAN INSTITUTE OF ENGINEERS:
TABLE VI.
e o
O O
aD
E
17
Ú
O
O 0 •
J O O O
O O
O V
-o--O
O
a
xm
o- O O
-
O O O O . ® O 6s s s
-.-Ç3H7N' NI 131I31.1.=- E 2
COEFFICIENTS OF DISCHARGE FOR CIRCULAR ORIFICES. 37
VIÇTORIAN INSTITUTE OF ENGINEERS :
-- HEAD IN INCHES—
Z
~
$ ~
e — — O
O —w—
ci
•
m
o
• o O
A -0 a (7
• O O
Q~~
COEFFICIENTS OF DISCHARGE FOR CIRCULAR. ORIFICES. 39
x zgnl1.iId . n0 . ,. 00 o `
u.o.ATIA3 a9..4As,àp i40.3
1®11M ■
In®/ I ■
®IM®ME' ■
.~®~/~Y,■
®-NI41/1M / MAN .NSIDI
~~/~'■■~%ialsrd/ //./1 ■■
--/~%~~~/~%~~ ■■
~~=%%%%~-~ i%/~ ■■
~/~%%~i~°°~ ■■
~„'%/~ ~■■
~° ° –~—~~ ~~ -~ ~i~i~® ■■
~~~~~~~ ■■
—33I4INQ AU 11313WYIQ—,_
~
W P. $ ., n N
—$7113N1 NI QY3H- 4
4 D
40 VICTORIAN INSTITUTE OF ENGINEERS :
The writer's conclusions may be shortly expressed in words as follows :--
I.• The assumption that a coefficient of discharge common to all orifices from 1 in. to 12 in. diameter is reached at a head of too feet is erroneous.
2. That in order to obtain complete and perfect contraction, a certain minimum diameter and head are required. These appear to be approximately 21 inches and 17 inches re- spectively.
3. That orifices of 22 in. diameter and over, under heads of 17 inches and over, have a common coefficient of discharge, lying between .59 and .6o, but which is probably about .598 (subject to the head being not less than 2 or 3 diameters).
4. That in the case of orifioes smaller than 22 in. diameter, contraction is never perfect and complete under any head, but is suppressed more and more as the diameter decreases, each size of orifice having its own constant or
"
normal" coefficient of discharge and its own criticalhead.
5. That as the diameter decreases,. the normal coefficient in- creases, as also the critical head.
6. That in an infinitely small orifice contraction is entirely suppressed and unity becomes the coefficient of discharge for all heads (subject to the effects of capillarity, cohe- sion, viscosity, temperature, etc.).
7. That the discharge of 'a circular orifice under any given head is the same, whether the jet be horizontal, vertical, or at any intermediate angle.
42 VICTORIAN INSTITUTE OF ENGINEERS :
The Hon. Geo. Swinburne had suggested that a visit to the- Waranga Basin and Goulburn weir might be of interest to members. Arrangements would be made.
Messrs. C. HATTON and G. LORIMER acted as scrutineers, and.
declared, as a result of a ballot,: that Messrs. MAURICE E. KERNOT and FRANCIS N. LOCK had been elected Members.
The PRESIDENT trusted that -members: would bring forward candidates in the two grades in which the Institute was some- what weak—associates and juniór members. It was particularly desirable that the younger men should join the Institute and grow up with it.
The discussion upon Mr. H. J. I. BILTON's paper on "Co- efficients of Discharge for Circular Orifices" was continued, and, after the author had replied, closed.
Mr. J. T. NOBLE ANDERSON then read his paper on "The Economising of Water in Irrigation Work."
The PRESIDENT said that Mr. Anderson had contributed an exceedingly interesting and thought-worthy paper upon a matter of vital interest to Australia. The author had touched upon eo many phases that the material would doubtless provide food for discussion at several meetings.
Mr. T. W. FOWLER said he had listened with very great interest to Mr. Anderson's paper. He had pleasure in moving a hearty vote of thanks to the author for his contribution.
Mr. WM. FYVIE trusted that the paper would be discussed very fully. He had pleasure in seconding.
The motion was carried by acclamation.
The meeting closed at 10.20 p.m.
DISCUSSION.
THE COEFFICIENTS OF DISCHARGE FOR CIRCULAR ORIFICES.
The PRESIDENT said he had read Mr. Bilton's paper on "The Coefficients of Discharge for Circular Orifices" closely and with much pleasure, and appreciated the careful, honest work of investigation disclosed and the useful material placed on re- cord. He was, however, at issue with the Author in regard to some of the conclusions Mr. Bilton deduced from his materials.
He did not question the conclusions as defining the Author's re- sults within the limit of experimental error, or with sufficient accuracy for practical work, but he did not think they could be accepted without reservation as absolute laws.
The text, the diagrams, and the conclusions supported a certain point of view i.e., that the coefficient when plotted in relation to head gave a curve that became tangent, and either
DISCUSSION-THE COEFFICIENTS OF DISCHARGE. 43
parallel to or coincident, with an ordinate. Sheets A and B.
showed this clearly. This `broken curve' indicated discon- tinuity ; and as a consequence each experiment was isolated: and could not form part of a strictly homogeneous whole. The Author's
"critical point," or junction point, would indicate that some function that had been operative at lower heads was at that point eliminated.
He did not agree with this. The factors to be considered' were head, aperture and friction, internal and external, of the fluid. These were operative at the lower limit and continued operative throughout. The head might be indefinitely increased, or the aperture indefinitely decreased, but there would always be- an expressible ratio between them determining the stream lines.
Therefore, unless the head became great to infinity, or the aper- ture small to extinction, these two factors would always operate.
So also with viscosity, and the frictional losses.. These meant,. if stream flows were considered [illustrating by blackboard sketches], that some portion of the energy due . to head, that would be wholly converted into energy of motion in a perfect fluid, would be partially converted into heat and only partially into energy of motion in an imperfect fluid, such as water, the ratio varying with every variation of head and aperture.
Therefore, it would appear that no factor was eliminated;.
hence ` strictly, that the plottings should lie on an asymp- totic curve, ever approaching an asymptote or ordinate, never coinciding with it.
The differences in question might not be great, numerically,. but in regard to portion of conclusions 2, 3, 4, and 5, it might affect abstract principles based upon them.
As to conclusion 7, "that the discharge of a circular 'orifice is the same whether the jet be vertical or at any intermediate angle :' r this might be approximately correct within the limits of the ex- periment, or were the apertures small in relation to the head, but not otherwise. [The speaker illustrated by sketches that for- instance, the tendency to flow in the extreme . case of a two feet horizontal orifice under one foot head, would be different to that in the same orifice when it had assumed a vertical position by rota- tion about a fixed horizontal diameter.]
He noted that the diagrams on sheets A and B were drawn, as regarded the lower portions of the curves, through points re- lating to vertical orifices, and as regarded the upper or tangent portion, through points relating to horizontal orifices. This would introduce a discrepancy, though probably in this case prac- tically negligible in amount.
Mr. Bilton's plotting on diagram E was supported by Messrs.
Judd and King's conclusions, shown on the same sheet, still any one of several slightly differing curves would fairly average, graphically, the station points. Hamilton Smith, junr's., results.
(sheets A and B) differed from diagram "E."
44 VICTORIAN INSTITUTE OF ENGINEERS:
He trusted that Mr. Bilton would see his way to give the Institute the benefit of other of his researches.
Mr. BILTON, in replying to the discussion, said there was no doubt a great deal in the points the President had raised.
The dotted lines e d and e f on the diagrams, showing the co- efficients as hitherto accepted, certainly indicated a very con- siderahe decrease with an increase of head, whereas, according to the latest evidence no definite decrease had been observed under heads up to about 100 feet. He had given in the paper in ;fable I, some of the results obtained by Messrs. Judd and King, from which it would be seen that the coefficients to the third decimal place were exactly the same throughout. These results were contradictory to those hitherto accepted.
With reference to the curve on Diagram E and the constant .598 which he had adopted for all the larger orifices, he had searched for all the evidence available, and would like to quote the results of 'experiments on larger orifices by General Ellis (shown in the following table) :—
Diam.
2 feet
„
Head. Coeff. Mean C.
1 .7 feet 5 8
588 ~
'609 .604
9'6 '615
I foot 1.14 .574
Ió88 'S94 j} '589
17'74 '599
'5 foot 2.15 '600
9'06 17.26
'6oI
'S96 '599
Mean of Means, '597.
The mean result was .597 for orifices from 6 inches to 2 feet -diameter. He had adopted .598 as the approximate normal' co-
efficient for orifices of 21 inches and upwards. There seemed to he fairly good evidence in support of that figure.
With regard to small orifices, he had made another experi- ment with the .15 inch orifice, which was of some interest. It had been made by means of a double headed fire hydrant with a pressure gauge attached, which had been tested and graded cor- rectly as nearly as could be between 60 and 100 lbs. per square inch. He had found great difficulty in getting a steady pressure from the main, but succeeded in obtaining one test under a sustained pressure of exactly 75 Ibs., during which the needle of the gauge remained perfectly steady. That was equivalent to
DISCUSSION—THE, COEFFICIENTS OF DISCHARGE. 45
173 feet head, which was unaffected by velocity or approach.
He had worked it out, and it gave a coefficient of .629. As shown on sheet B the normal coefficient for the .15 orifice was- .631, to which the result obtained closely approximated; so that again the vertical lines on the diagrams, although perhaps not theoretically correct, for all practical purposes appeared to be so.
At the previous meeting reference had been made to the gaugings of the "head." He would like members to realise what a great difference a small error in head would make. Re- ferring, for instance, to the diagram for the YIs inch orifice on sheet B, they would see at the bottom under 2 inches head a semicircle to the extreme right of the diagram, about 8 points in the third decimal place to the right of the curve. Assuming the position of that semicircle to be caused entirely by error in hea.d,. an error of inch would place it in the position shown.
'There was another extreme as regarded timing, the worst case being also on sheet B in connection with the 20 inch orifice under 80 inches head. There they would see a circle 4 points in the third decimal place to the left of the vertical line. That posi- tion might be accounted for by an error of one inch in the head.
He was certain, however, that there had not been-such an ,error.
He had stated in the paper that there might have been an error of s inch or -flu inch in any of the experiments, but in saying so he considered he had exaggerated rather than underrated the facts. This was a particularly short timed experiment, which had only taken about four minutes and which he had neglected to repeat. Assuming the error to have been entirely due to the timing he found that an error of one second would in this case have placed the circle in the position indicated. It was a case in which a very small error in timing led to a very erratic result.
Under the intermediate heads the coefficients might be equally affected by errors in head and timing, but the two examples given would serve to indicate the care with which experiments on such small orifices must be made and how easily erratic re- sults might be obtained.
Discussion closed.
PAPER.
THE ECONOMISING OF WATER IN IRRIGATION WORK.
By JOSHUA T. NOBLE ANDERSON.- (Past President). I
PREFACE.
In a pursuit of such antiquity, coeval with the dawn of civilization, there is ancient precedent for almost every modern development. Thus perennial irrigation, which is generally deemed
to mark modern practice as distinct from the methods of the
