Taking it as in Fig. 1 at any point of time t, with its corresponding head on emptying valves h, surface area of the lock A and area of emptying valves a, we have the following relations:

The outflow is at the rate of m a √2 gh, where m corresponds to a coefficient of efflux through whatever forms or combination of forms the emptying may be effected. While any volume withdrawn from the lock is represented by A. Ah. In a differential interval of time, therefore,

= outflow

but C

m. a. V2 g h. dt.

A

A dh.
2A

or dt: =

h-dh; or t=

m. a. V 2 g

O as t and h become zero together, and the equation of emptying becomes

and the same equation holds for filling the lock, by taking in that case time and head measured from the level of the lock full.

In this equation I the first factor

has for the only variable in it the head

h, and it expresses a purely mathematical relation between force and velocity. It may be computed once for all through a range that will cover the lift of all locks, and its value in all at a given point of h is the same.

The second factor

expresses all that variation between the volume to be drained at any level in any lock and the area of the valves that are designed to drain it. It is an expression wholly of the geometry of the design. And as this enters the equation of time in the ratio of these areas, its value is not affected by the absolute magnitude of these quantities. So far as this factor is concerned, a lock may be large or small as long as there is a square foot of valve area to a given number of square feet of lock surface to be drained, the time of draining given heads will be the same.

m

The third factor involves all that is known or unknown of resistance to flow in the different forms and different types of form, that have been designed, summed as it all is in m, generally termed the coefficient of efflux or discharge; and as this is the one unknown element, the study is aimed to bring the values of m in the different data into comparison.

This is most readily done by bringing the observed times to a time standard, This is arbitrarily

which corresponds to a fixed value of the second factor {4}

assumed for the standard as 200, approximately a mean of general practice; and it is plain that in any actual lock where there was less than 200 square feet of surface to each square foot of valve area, the observed time of draining between any levels would be correspondingly shorter than the standard; while if its actual value

A

of {4}

a

was greater than 200, its observed intervals of time would be correspondingly longer than the standard. We have, therefore, calling t the standard time, and tobs the observed time.

By this equation all the observed intervals of time were reduced to this standard and in what follows only this standard time will be generally referred to.

It may be worth mentioning that not only is this reduction to standard time necessary to compare observations on different locks, but often in the same lock and notably between filling and emptying; where there is a batter in the walls or the upper miter sill becomes exposed, the value of A changes, and while in filling, these smaller areas at the bottom are filled with the fastest inflow and the greater ones at the top with the slowest; the reverse is the case in emptying and with identical valves, the observed time of emptying from this cause may be distinctly shorter than that of filling, while the curves of observed time have this arbitrary variation in them.

The observed intervals reduced to standard times and summed from the levels of the lock full or empty, respectively, give from point to point the corresponding ENG 97-247

time has now become t=2

values may be calculated for various assumed

values of time and head by observations, while from equation I, which in standard
h 200
2g m
values of m, and have been so calculated and are given in tabulation, and shown
platted as curves on Pl. I, while the curves given by the observations are shown
an Pls. II to VIII.

In some cases it is stated that the observations were not carried through to the exact point at which the lock was full or empty, while in other cases it was evident that the same course had been followed; this then would only give the curve from some point above its origin up to the range of the lift in the lock at that time, and to complete it for comparison and study it must be sketched into its approximate origin. This is done with sufficient accuracy by adjusting the incomplete curve, platted on transparent cross-section paper, over the group of calculated curves of Pl. I, drawn from a common origin and covering the general variations in the value of m; where the run of the incomplete curve as a whole may be approximately traced down to its zero.

By the same process of study in other cases the interval of time in the last stage of filling or emptying has been corrected. Here, as from ten to thirty seconds will be required for the last half-tenth of rise or fall, it is easy to make considerable errors in time, which in the form of the study effect the value of time at all points of the curve. It is true, however, with both of these forms of correction, that the original observation may be right in fact, and the appearance of error given it by the change of head in the upper or lower pool, which would depend entirely upon the local conditions of the waterway. But even where this may be the case, the necessity of comparison requires us to bring the curve to its zero at the zero of the average head under the action of which it has been formed.

These corrections are simply a to the time or head of the last interval of filling or emptying, and are given with the platted data in such cases, so that if it is thought desirable to repeat observations it may be readily determined whether the original was a real error or simply due to a local variation in head. They only effect the interval between the origin and the first point of the curve as plated-from which all other points follow, deduced from the intervals of time and head as observed.

Pl. II shows the emptying of ten locks of the Fox River canals. They are arbitrarily numbered, and all points in the emptying curve of each lock are indicated by the corresponding number, with a fair curve sketched through them. The wholly arbitrary part at the top during the time that the valves were being opened are shown branching off from these curves, and for a further comparison the fair curves are in all cases carried up to at least a 10-foot head.

These locks are all emptied through balanced valves in the lower gates, with no great difference in the size of the valves, as seen from their number and total area. We might therefore expect to find in all about the same curve of emptying, and we do find this to be the case in Nos. 1, 3, 4, 6, 7, 10, but Nos. 9 and 5 show much larger values of time (smaller coefficient of efflux), while 8 is distinctly smaller time than the average, and 2 is so small that it would seem that here some mistake must have been made in the valve area.

With attention called to these variations, the engineer in charge can probably readily find their explanation in his special knowledge of the lock. They may be features of construction, the valves may not have been fully opened, or there may be local characteristics of the waterway to account for them, while the explanation in connection with this determination of the magnitude of its effect would be most interesting to the engineer engaged in such work.

Pl. III shows the filling of the same set of locks. Here but five of them are filled through valves in the gates, and this group as a whole shows a larger value of time than the average of emptying. It covers, as may be noted in a comparison, approximately the range between the average and the extreme of the emptying curves. If no other explanation may be formed, it will probably indicate a relative check to inflow due to the confined area of the lock. The second group, where the locks are filled through chambers or culverts, show the marked increase in time due to this difference in design.

Pl. IV shows the emptying and filling curves of the Muskingum River locks as numbered. There seems to have been some difficulty here in carrying the observations to their true levels, and in most cases the final interval required a correction. The emptying is certainly rapid for the combination of valves and culverts, and, in contrast with the slow filling, is very striking. The valves are large in both cases, but the culverts are curved in emptying and have sharp corners in filling, but it hardly seems that this would account for the difference. The screens at the filling

portals must have been a serious resistance, and indeed between the first and second filling of Lock No. 6 (numbered on curves 6, and 62) the wide divergence can only be accounted for by the difference between a clean and a foul screen.

Pl. V shows the curves of another series of locks. Perhaps here some closer adjustment to the correct origin might have been made; in fact, the divergence shown in filling can hardly be explained except in this way. But as the Erie locks were only measured between even feet, leaving an undetermined interval of both time and head to the origin, no very close adjustment was attempted, and the other data was evidently close enough to fairly correspond with this in precision. True, No. 5 emptying is wide of the rest, but there through all the period covered by the four upper points the valves were being opened, so that there is not much of a true curve left to judge from.

On Pl. VI the locks of the Kentucky River, Nos. 1 and 2, show the difference between valves in gates and culverts, in which the greater efficiency of the valves in gates is most marked, while No. 3 of the Louisville locks, also operated with valves in gates, but confirms the above conclusion. The filling and emptying curves of each lock are also shown here in contrast. However, in the case of filling No. 1, as the valves are only fully submerged through the last three feet, the filling is of course more rapid, and its curve is not comparable with the others. It approaches, as we see, what would be its theoretic form if the valves were discharged into air-a straight line of a given inclination determined by their coefficient of efflux and the constant head of the upper pool upon them. It serves, however, even in this case, to show that the coefficient is distinctly smaller in filling than in emptying, as is also markedly shown by the divergence of the curves in the other cases.

As the data furnished for the above locks gives no difference in the design for filling and emptying we would be led to conclude that there was a large element of resistance to flow which was a characteristic of filling alone, did not the data presented on Pl. VII lead us to an opposite conclusion. Here in the Des Moines locks we might have anticipated a slower filling through the long culverts in the side walls, but find it for both locks the same and between the two emptying curves, which with shorter culverts and the same design show quite a divergence. While again in the Galena lock, though the filling valves are only submerged through about half the range, there is enough to show a close correspondence between filling and emptying.

We must not conclude from the above that there may not be a greater resistance to filling than to emptying, for indeed we would expect the flow into the lower pool to be freer than into the confined and agitated volume of the lock, while taking the data altogether there is a decided preponderance in favor of this conclusion. The contrast here between Pls. VI and VII has been mainly noted to show that it is not safe to take the suggestions from a few cases as a measure of this.

It is thought that the much more decided effects of the different designs should be determined first, and these can not be said to be yet determined, for while they are the most apparent on the data, we have not enough general information on the subject of the designs to explain the differences that perhaps may be easily explained, while possibly some of the differences can only be explained by imperfectly set valves or unknown obstructions. With the data freed from these uncertainties in the determination of about the correct coefficient for given types operated in a waterway whose levels are not effected by filling and emptying, the general difference between filling and emptying would show itself in its true values. To illustrate the effect of change in level of the pools, the data of the "Soo Lock" was selected, and is presented on Pl. VIII. This data was very carefully taken, the levels in the lock being determined by the rise or fail of a large steam barge, the changes being read with the level from the rod, held about at the center of buoyancy of the barge, while the time element was measured upon an observatory chronograph. At the same time in the case of filling there was quite a large oscillation in the level of the upper pool, which is shown in the plate with the filling curve, on its corresponding time scale, as nearly as it could be reproduced from the diagram

of the data.

The two levels are of course identical at the origin of the filling curve, the point where the lock is full, and the standard times are platted to their actual stages in the lock below this point, but here this does not correspond with the head on the filling valves, for the level of the upper pool at the same time is below or above this point, by the value in its variation of the ordinate Ah, which is platted to the same zero and the same scale as h. The actual head at any point with which the lock is filling is therefore (h-Ah), and this is the head to which the observed intervals of time correspond, while in a representative curve they should have corresponded with h.

dt

As, however, dh or the time rate at any point, varies as

1

the standard intervals

V h

At, may be further corrected to the intervals of this representative curve ▲t by the proportion

which, strictly speaking, is a differential equation to be integrated between the limits, but which in the observed variation of Ah to time may be approximated altogether as closely as the data justifies by taking the mean of its value at each end of the foot intervals as a mean for the whole interval, and correcting the standard intervals of time by this simple proportion. This has been done, and through the points so corrected the filling curve is drawn, which is the deduced curve for a full value of head on filling valves.

Points show the corrected and A the uncorrected values of time in this case, and between them the distortion due to this change of head may be noted. It is seen that a very small excess of head, due to momentum in the approach, through the last stages of filling serves to counterbalance quite a large deficiency in the earlier stages, and materially changes the shape of the curve near the origin. It is in the direction of a divergence from the form of computed curve with a constant coefficient that has been noted all through the data, and which is also thought to include an increase of coefficient with the small velocities in the last stages of filling or emptying. The two combine in the same direction to give a special character to this part of the curve; one element the local phenomena and the other a general law of coefficients, but which can not be satisfactorily separated without fuller data on this part of the curve and the changes of head.

Aside from the above, the data as a whole may be said to show a fairly constant coefficient of efflux through the greater part of the range. The curves define a very regular law in each case, and the extreme divergence of the points in general amount to but a tenth or so in level or a few seconds in time, which might be expected as accidental errors of the individual observations; and while there is almost uniformly the noted divergence near the origin, and in some cases continued through the range, still there is altogether enough parallelism between the actual and the calculated curves, when taken in the light of possible distortions from changing head, to lead us to accept a constant coefficient as the general character of this flow, though of course it is understood that this constant is but an empiric expression for a slight variation, which only generally begins to have an appreciable value as we approach the origin.

As an aid to the study of this general coefficient Pl. IX was prepared, where the calculated curves of Pl. I, in the place of being brought to a common zero at the origin, are brought to the common zero at the stage of 10 feet, up to which value of h all the curves of the data were sketched. By superimposing the data upon such a group we have an accurate means of estimating the actual coefficient in this part of the filling and emptying where it has its least variation, and can be but little affected by variations of head on values, or errors of level or time, that may also materially affect it below.

The coefficient estimated in this way is indicated by mo, and its value is given upon the various observed curves; while mo upon the same curve is the constant coefficient, which is equivalent as a whole in time to the observed curve at this 10-foot stage. It is estimated by superimposing the data upon the group of Pl. I and interpolating the value of m that it reaches at a 10-foot value of h. While with the transparent plates of the study these data could be superimposed at will, in blue prints it is not so easy; and simply to illustrate the process a number of the curves, lettered A to F, are shown dotted upon those groups of Pls. I to IX.

But turning from the nature of this variation to actual values of it, we can not but be struck, in even a glance at the data, at the wide range that is found between different cases. Brought, as all these observations are, on to a standard-time scale, where the divergence expresses only a difference in the coefficient of efflux, we see differences, say at a stage of 10 feet, where in some cases the value is more than two and a half times as great as in others, and in making his plans, whatever purpose an engineer might have in mind here, it would seem possible that in this range he might miss his purpose by as much as 100 per cent.

It is true that this question is not now an important one with many of the locks, but it may be with some, and may come to be with others. The few minutes' delay to a single boat, even in a difference between four and eight lockages an hour, is of no great moment; but where at any time this limitation of its service may cause a block to traffic, it is a different thing, and here it begins to have a magnitude whose value can only finally be measured by the cost of a second lock.

It would therefore seem desirable to get together in small sketches to go with these data the details of the different designs for filling and emptying, and this, with such

information as can be obtained of special cases like those that have been noted as requiring further explanation, will give the engineer at least a basis from which to make a fair estimate of what his lock will do.

In case any of the observations were to be repeated or a closer study of the form of the curve near the origin was to be made, the following method of observation is suggested: In the place of a gauge use the rise or fall of a barge, as in the case of the Soo Lock. This could probably be most conveniently done by reading the changes with a level from a tape suspended at the center and plumbed to a vertical. It would be best in this case to call even intervals of time-say every ten secondsand at each call of time have the tape read and recorded. This would practically eliminate all error in the time observation and give a simultaneous observation of the stage in the lock, so far as the average of the area covered by the barge would represent it. The calling of time might begin approximately at the beginning of opening the valves (exact coincidence in the beginning is of no importance here), while at the end, as soon as motion had stopped, the man at the level should call this to the timekeeper, and the fraction of an interval there be recorded. In case there was a restricted waterway, a gauge above or below the lock should be read at intervals to give the coincident variation of head, as in the data of the Soo Lock. With data so taken, the intervals of time reduced to the standard, and in case of any variation further corrected to a constant head of pool, as in the Soo data, when summed for total time and platted to the corresponding observed elevations, would give, in comparison with the group of curves on Pl. I, the value and the character of the actual coefficient of efflux in the lock with great accuracy, and could hardly fail to develop, in its comparison with other data, a fairly definite series of values for the coefficients corresponding to different types of design.

Since the plates were made up, several sets of observations have been received that are not included in this study, and in the process a number of locks where there was but a small lift were not considered, since between the opening of the valves and the final level there was but little data from which to determine a regular coefficient. Very respectfully, your obedient servant,

Capt. HIRAM M. CHITTENDEN,

Corps of Engineers, U. S. A.,

JAMES A. SEDDON, Assistant Engineer.

Secretary Missouri River Commission.

APPENDIX M.

CEMENT TESTS BY MR. F. B. MALTBY, ASSISTANT ENGINEER.

ST. LOUIS, May 30, 1897. CAPTAIN: I have the honor to submit the following report of the results of experiments made with cement to determine the adhesion of Portland and natural to each other when mixed at the same time; also the results of some experiments made with concrete bars.

Neat cement of the two different kinds was mixed separately and placed in the opposite ends of the same briquet mold.

The two cements were kept apart by a knife blade placed as near the center of the mold as possible, until the mold was filled. The knife was then withdrawn and the cement firmly pressed and rammed into the mold. Thirty-six briquets of various combinations of cement were made. They were allowed to stand in air twenty-four hours and in water six days, and then broken. Not a single specimen broke through the joint, but in every instance the break was in the natural cement, sometimes as much as one-fourth inch from the joint, showing that the adhesion of the two cements was greater than the strength of the weaker cement.

By the kind permission of Mr. M. L. Holman, water commissioner of St. Louis, the experiments were made at the city testing laboratory, at 2322 Clark avenue, by Mr. A. S. Ferguson, who is in direct charge.

The appliances and methods used are those of the best modern practice, and as all the cements used by the city in the water, sewer, and street departments are tested here, the assistants are thoroughly experienced in the necessary manipulations for making accurate tests. For these reasons I have great confidence in the reliability of the results attained.