페이지 이미지
PDF
ePub

ON THE DISCHARGE OF WATER THROUGH SLUICES

AND SIMILAR ORIFICES.

By K. R. BORNEMANN.

Va

;

a

al

VA+ (1+) VO

Foreign Abstracts of Institution of Civil Engineers. The first part of the paper treats of The effective head (h, -h,+k) varied the flow of water through submerged from 21 millimeters to 231 millimeters sluices, and the author gives the results (0.83 to 9.09 inches). of an extensive series of observations The author endeavors to find an made by himself with a view of determ- empirical formula from which u can be ining the coefficients of discharge for calculated so as to agree with the exsuch cases. The experimental sluices periments. He tried successively eleven were made by placing a flat board across different formulæ, and determines the a parallel trough, the board resting coefficients in each case from the experiagainst a strip on each side, the bottom ments by the method of least squares. of the opening being formed by and The two formulæ which give the most flush with the bottom of the trough. satisfactory results for submerged disThe height of the opening was varied charge are by raising or lowering the sluice board, and three different widths of troughs j=a+B and sluices were used. In experiments

h, + 1 to 16 the trough was 1.135 meter wide

2 (44.7 inches), and the clear opening 1.006

1 meter (39.6 inches) wide; in experi-u=a+ß ty ments 17 to 44 the trough was 0.544 meter (21.42 inches), and the opening

2 0.520 meter (20.47 inches) wide; and in With the experimental sluices he finds as the final series 45 to 63 the trough the most probable values of the coeffimeasured 0.802 meter (31.75 inches) cients for the whole sixty-three observawide, and the opening 0.774 meter (30.47 tions : inches) wide.

In the above experiments weir boards For the first formula were inserted in the trough about 11 a=0.54138; p=0.14965 feet 4 inches below the sluice, so as to For the second formula pond up the tail water sufficiently to a=0.43479; B=0.25666; y=0.031212. submerge the issuing stream.

The author also gives some experiLet Q=quantity of water discharged ments on submerged discharge commu

in cubic meters per second. nicated to him long ago by Weisbach. In a=height of opening.

these the trough was 0.363 meter (14.29 b = breadth of opening.

inches) wide, and the opening the same, h,=height of surface of head

there being no side strips. The bottom water above top edge of edge of the sluice was also beveled off opening

on the tail water side. The conditions h=height of surface of tail

of experiments vary too much, and their water above top edge of number is too few to deduce reliable opening

formulæ from them. k=head due to velocity of This part of the paper also contains a

approach of head water. critical examination of some formulæ u=coefficient of discharge. proposed by Linnenbrigge, and pubQ

Iished in 1879 in the Civilingenieur.

These formulæ the author considers unab v2g (h, -h, +k)

satisfactory. g being the acceleration due to gravity.

The second section of the paper deals You XXIV.-No. 5–26.

meters.

Then u =

[ocr errors]

in similar manner with the best extant

The rectangular orifices 0.200 meter observations on free discharge from (7.87 inches) wide, and with contraction sluices; the data used being the experi- all round; for heads up to 1.800 meter ments by Weisbach, by Boileau, and by (5 feet 11 inches) Lesbros. formulæ for the coeffi.

+ 0008844 cient of discharge are as follows: the head to the center of the opening being And for similar orifices 0.020 meter h, and the clear height and width a and (0.787 inch) wide b as before, all in meters.

For sluices built across a trough 0.9 u=0.6262 +0.003291 meter (35.4 inches) wide, the opening

h reaching the whole width, and the bottom being flush, along the top of opening only, for heads to 0.580 meter (22.8 For openings 0.200 meter (8 inches) inches)

wide, but without contraction along the

bottom edge u=0.5805 – 0.018981 +0.00144

h

u=0.5074+0.021267 +0.3958 b For sluices 0.364 meter (14.33 inches)

h

2(a+b). wide, and of a similar construction, but For orifices 0.200 meter wide, with conwith the lower edge of the sluice rounded, traction along the top and bottom, but and with low heads

not at the sides

+0.0002063 (1).

a

[ocr errors]

44(2).

[ocr errors]

a

[ocr errors]

a

a +6

-0.07884 u=0.8624-0.21947 + 0.00219

h

latbl h

For orifices fitted with a trough-shaped For sluices 0.6 meter (23.62 inches) wide, mouthpiece in front, and contraction at in which the bottom and sides of the the top and sides, but not at the botopening are distant from the sides of the tom trough, so that contraction takes place all round, for heads to 1.800 meter u=0.6945 -0.13641

V

h (5 feet 11 inches)

6

+0.005651 1

2(a+b) u=0.5732 +0.013551 V +0.021097

h

For similar orifices, with contraction at

the top and the bottom, but not at the For sluices similar to the last, but with sides

, (2 )

-0.06244 heads to 1.800 meter

h

6 An appendix to the paper examines u

h +0.51222(a+63 the formulæ given by Weisbach and

Grashoff for correcting coefficients of The author remarks upon the great discharge for partial or incomplete convariation which the above coefficients traction; the author finds that these all show, and considers that till a much fail when used beyond the limits of the greater number of systematic experi- observations from which they were dements have been made, the use of sluices termined.—Der Civilingenier. for gauging water is only permissible in those cases in which the conditions and dimensions are within the limits of those An English engineer recently returned of the present experiments.

home from a visit to American steel The third section of the paper dis- works, where enormous output is secured cusses the experiments by Poncelet and per converter, says: “They do it, I do Lesbros on the discharge through or- not know how, but the men seem smartifices in thin plates. Retaining the nota- er, everything is ready, and the men foltion as in the second section, the author low each other up in their duties with finds:

rapidity and intelligence.”

!

AN INSTRUMENT FOR THE DETERMINATION OF LATITUDE.

By S. C. CHANDLER, Jr.

From Proceedings of the Society of Arts.

It requires a great deal of temerity to the telescope turns cannot be made perclaim anything novel in the determina- fectly circular, and are not of absolutely tion of time and latitude, and even more the same size; and this deviation from to claim an improvement in this respect. the perfectly circular form, and from abNevertheless, I believe that the principle solute equality in size, causes irreguinvolved in the instrument I have de- larity in the motion of the telescope. vised is novel, for, after a careful investi 2. Error in collimation. This error is gation, I have not been able to discover due to the telescope not being perpenany instance where it has been used in dicular to the axis on which it turns ; the same way.

and causes the telescope to describe a The nearest approach to it, in previous small circle of the heavens to one side of constructions, is to be found, I believe, the meridian. The correction for this in the floating collameter which Captain is determined by observing some slowly Cater invented in 1805, for obtaining the moving star, and then, before it has zero point of a vertical graduated circle; crossed the field, reversing the telescope but no one seems to have had the idea in the Y's and observing again. of floating a telescope on mercury. Thus 3. Error in level. The deviation of the fax the astronomical transit instrument instrument, on account of the axis on has been the universally acknowledged which it turns not being horizontal, is means for the accurate determination of ascertained by means of a level supported time. Astronomical transits vary in size, on the two pivots, the errors of the from those which are as small as the level itself being eliminated by reversordinary surveyor's transit to those of ing it. eight inches aperture and ten feet focal 4. The error in azimuth has to be delength, and two or three thousand pounds termined by astronomical observations. weight. These instruments are placed We thus have in the transit four errors in the plane of the meridian, and it is in- to be allowed for, viz. : error in pivots, tended that, as the telescope turns in in level, in collimation, and in azimuth. the Y's, its axis shall remain always in In the instrument which I have devised the plane of the meridian.

three of these errors are eliminated, and The measurement of time means there only remains one error, which is merely the measurement of the angle analogous to the error in collimation of which a point in the celestial sphere has the transit. described.

This instrument, made by Mr. Clacey, In order to determine the error of a of this city, consists of a base of walnut time-piece, therefore, by means of the with approximate leveling screws at the transit instrument moving in the plane four corners. From the middle of this of the meridian, it is only necessary to base rises a pillar of black walnut, firmly observe by means of this time-piece the bolted to the base, and surrounded by time at which a certain star crosses the collars of hard brass. An outside sleeve meridian, and then, knowing the time at of hard brass, which turns on these colwhich it should cross the meridian, we lars, supports the remainder of the inhave in the difference the error of the strument-this sleeve being rotated in clock.

azimuth by a rack and pinion movement, Certain difficulties are met with, on and provided at its base with a graduated account of the inaccuracy of the con- setting circle. On top of this sleeve is struction, and of these the following four a wooden cross head which supports a are the principal ones, viz. ;

wooden trough in the form of a hollow 1. Error in pivots. The axles on which rectangle, and in this trough is placed

mercury to a depth of one-eighth of an in the case of the transit, but by observinch. The trough is constructed of wood ation of the stars, in a similar way to instead of brass, because the mercury that by which the azimuth error of the would attack brass. Whether it would transit is found. As to the disturbance be better to use cast iron is an open of the instrument by oscillations, the question.

most violent oscillations I have been able In this trough, on the mercury, there to produce have required thirty seconds floats a wooden float, also in the form of to have their effect dissipated, and after a hollow rectangle, and nearly as large as this time had elapsed the instrument is the inside of the trough, this float being as quiescent as though it were mounted held in position at the middle of the two on stone. sides by two cast iron pins which move It is, of course, specially adapted for in vertical slots in the sides of the float, observing equal altitudes, and can also and which are sufficiently loose not to be used to observe the transit of stars interfere with its floating freely, but across any desired small circle having which serve to prevent any violent or the zenith for a pole, and hence the reasudden motion.

son why the cross hairs are horizontal The above-mentioned float has attached instead of vertical. to it two brass arms which support the All observations are influenced by retelescope, the latter projecting through fraction, but refraction operates to elethe hollows of the hollow rectangles of vate all the stars equally at the same the float and trough.

time. Hence, we can disregard the error The trough is not supported in the of refraction in a series of observations, middle, but nearer one end, in order to taken so, near each other that there is no allow of zenith observation ; and on this probability that the coefficient of refracaccount a counterpoise is attached at the tion of the air has changed, and we can other end of the trough.

simply account it as part of the instruThe attempt has also been made to so mental error; it having the same coeffiproportion the parts as to bring the cen- cient, hence, when the observations are ter of gravity of the floating part as reduced to middle time, this error is near the axis of oscillation of the tele- almost wholly eliminated. Next, as to the scope as possible, in order to reduce results that can be obtained by this instruoscillations due to jars, etc.

ment, I have not yet been able to make The illumination is effected by a series a great many observations, but those that of reflectors, and comes from the side. I have made encourage me to believe The cross hairs are horizontal, and not that when as good mounting is given to vertical as in the transit. The reason it as is given to an astronomical transit, for this will be explained later. In using better results can be obtained with it the instrument the telescope is set at a than with the latter. I have used it very certain inclination to the vertical, and, as roughly, making observations from the the instrument is rotated in azimuth, the roof of my house, which was subjected line of sight sweeps out a horizontal, to a constant jarring from the teaming in small circle of the heavens, i. e., a circle the street below, and where the instruof which the zenith is the pole.

ment was exposed to the wind. For the determination of the zenith, All the observations that I have made the free, upper surface of a liquid is are the following: used, and we have dispensed with the Showing the determination of clock error of pivots, the error of level and correction on various dates, by combinthe error of azimuth, and have left only ing stars in pairs, east and west, after what is, in a certain sense, analogous to latitude correction had been introduced. the error of collimation in a transit in- It should be noted that the instrument strument, the characteristic of both is of one and three-quarters inches apererrors being that the telescope describes ture, and twenty-five inches focal length, a small circle parallel but very close to provided with but five threads, whose the circle in which it is intended to re- intervals have, as yet, been only impervolve. The amount of this deviation in fectly determined, and that it was mounted this instrument is not, however, deter- in the open air, over a box of sand, and mined by reversals of the telescope, as was entirely unprotected from the wind.

[ocr errors]

(6

4th " 5th " 6th "

The observations of the 5th of January The above are all the observations were made from the middle of the roof taken thus far, and form an exceedingly of a four-story dwelling.

good set of results. I have not at pres

ent access to any results obtained with January 25, 1880.

portable transits of the same size, with Chronometer Correction.

which to compare them, but do not be1st pair.

-24.93 seconds of time. lieve that as good results can be obtained 2d - 25.12

with the latter instruments. I have, 3d

- 25.06 4th -- 25.08

however, compared my results with those 5th -25.06

of larger coast-survey transits, and mine 6th -25.14

are the best. 7th

- 25.06 8th

I have not yet determined all the con- 24.99 9th -25.11

stants of the instrument. I find that

the wind does interfere with it somewhat February 8, 1880.

when employed in the open air, and un1st pair...

+38.06 protected, but the deflections from this 2d

+37.92 3d

cause are but momentary, and errors due

+38.03 4th

+38.02 to a draught would be nearly eliminated 5th

+38.14 were a greater number of cross hairs 6th

+38.25 used. From Roof.

Next, as to latitude. The transit inJanuary 5, 1880.

strument, when placed in the meridian, 1st pair. -6.34 seconds of time.

is used only for time; it can be used for 2d -6.13

the determination of latitude if placed in 3d -6.12

the prime vertical. The Coast Survey -6.31

have introduced for this purpose the -6.15 -6.62

zenith telescope, and have obtained with 7th -6.44

it the very best results. To compare my

instrument with this is a very severe Probable Errors. test; but it will be seen that, although I No. of

have had only three evenings on which I Stars 1880. Observed.

Of Chron. Single could make observations for latitude, the
Correction. Observation. results obtained are remarkably good.

The claims, therefore, that I make Jan. 5. 15

+0.040 +0.156 Jan, 25. 21 +0.045 +0.206

for my instrument are the following, Feb. 8. 16 +0.047 +0.183

viz, :

1. The ability to use any part of the The following were the probable errors heavens that are not obscured by clouds. on nights when observations were made In using the transit it is often impossifor both latitude and time, the large ble to obtain observations when clouds probable errors being due to the use of hang in the meridian, even though there stars near the meridian, which move very may be any amount of clear sky on either slowly in altitude:

side. With my instrument we can use

any region of clear sky in the heavens, Probable Error.

as we can use any horizontal circle whatStars

Single ever; although the use of the same circle 1880. Observed. Chron. Observation. all the time renders the computations Correction.

easier. Jan. 31. 14 #.087 +0.323

2. There is only one instrumental error Feb. 5. 15

£.061

+0.355

to determine inatead of four.

3. This instrument is unaffected by The following are the results for lati- errors in mounting. tude :

4. Simplicity in use; requiring no

Probable readings of level nor reversals. In the 1880. Latitude.

Error.

use of the transit about one-half the time January 31.... 42° 20' 24."95

+0."90 February 5 42° 20' 24,"80

+0."85

is taken up by these processes, which are February 8 42° 20' 23."25 +0."84 / unnecessary with my instrument.

« 이전계속 »