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straight; it must bend down stream, and, therefore, raise the lower float. This is also in proportion to the length and size of the cord. This raising of the lower float brings it into a faster current, and, therefore, gives too large velocities as we approach the bottom.
In putting out the floats from the boat they cannot both be thrown out at once without danger of tangling the cord, but the upper one must be held until the lower has gone far enough to keep the cord extended.
Now, the upper float must go enough faster to gain its proper position over the lower before they reach the upper section, otherwise it will run through too fast. Whether it does or not can only be guessed at, and the distance required for the two floats to assume their relative positions will depend upon the length of the connecting cord and their velocity.
Again, when the floats are in their proper relative position they cannot be vertically over one another; but the cord must form the curved hypothenuse of a right-angled triangle, of which the perpendicular is the true depth of the lower float, and the base varies according to the depth, velocity, and relative size of the floats and cord. This also would give the velocity too fast.
Of these errors the first three are uncertain and the last three are always plus; but the sixth appears to be the most important and the most difficult to calculate and eliminate.
These errors, so numerous and so complicated, made me despair of ever being able to obtain the true velocity by means of floats, and forced me to turn to the other methods used by eminent hydraulic engineers in their determinations of the laws for the flow of water. These are principally floating tubes used in canals and feeders so successfully by Mr. J. B. Francis, in the Lowell hydraulic experiments, but which would be too cumbersome for deep rivers:
Pétots's tube, modified by M. Darcy, the most correct instrument ever devised for shallow measurements, but which needs a firm resting place to be used accurately. Brünning's pressure plate, with which he obtained excellent results on the Rhine, but which, in these deep and wide rivers, would be more difficult to use. Woltmann's meter, which is excellent as far as it goes, but it is inconvenient to use, as it has to be raised and lowered at each observation. Borda's wheel, which is a float wheel with a long screw passing through the axle, the number of revolutions being found from the length of the screw passed over; perhaps the most ingenious of all forms of meters, and running with a minimum of friction, but only for a limited time; it was intended only for surface velocities, but was modified by M. Laignel so as to be used at any depth. Lapointe's meter, where the wheel is inclosed in a tube and the train elevated above the meter, thereby increasing the friction, and rendering it only useful in measuring the discharge of reservoirs and the flow of shallow streams. Saxton's meter, which has less friction than Woltmann's, as it has but one gear wheel to record the revolutions, but the time it can be run without raising it is proportionately lessened.
None of these fulfilled the conditions required; but if a meter could be made to record separate from the wheel, then the friction would be reduced to a minimum and it could run for an indefinite time. This I accomplished by attaching the wires of a battery to the meter, so that every revolution of the wheel the electric current would be broken.
Now when a Morse register was placed in the circuit, every revolution of the wheel would make a dot on the moving paper, and from the number of these recorded in a given time the velocity of the current
as easily computed. This was sometimes used, but commonly the number of revolutions was obtained by means of a tell-tale, attached to an ordinary sounder or relay.
The forms of the meters are given in Figs. 1 and 2, and the register is shown in Figs. 3 and 4.
Fig. 1 is a float meter, the cups of a Robinsen's anemometer being hung in a frame between pivots. An arm is fastened to the axle, and at every revolution of the cups it comes in contact with a fine silver wire, which is bent spirally to give it more elasticity. This wire is insulated from the frame, and is connected with one of the battery wires, the other being attached to the frame. The frame is hung in a yoke, and back of it are vanes to keep the cups in the direction of the current as shown in Fig. 5.
Fig. 2 shows one form of propeller used—a modification of a Saxton's meter. An eccentric is placed on the hub of the wheel, on which a roller at the end of an ivory lever is kept by means of an adjustable spring. This lever has a platinum wire in it, which projects at the bottom, where it is kept in contact with a platinum plate on the axle, when the eccentric is at its minimum. This wire is hinged into one of the battery wires, insulated from the meter, and the other battery wire is connected with the axle. This meter has also a supporting yoke and vanes at right angles, not shown in the drawing.
Figs. 3 and 4 show a front and back view of the register used. This consists of a simple telegraphic sounder with an escapement lever attached to the armature arm, the pallets being so arranged that they just pass the center of the first gear-wheel, so that each time the armature rises and falls, the gear-wheel advances one tooth. The front wheel contains one hundred teeth and has a ten-leaved pinion on its axle, with which the second wheel of one hundred teeth engages, thus registering one thousand double movements of the armature, which are shown by the hands on the dials. When the register is put into an electric circuit with the meter, as each revolution of the meter wheel breaks and closes the circuit, the armature will rise and fall at the same time, and thus each revolution is recorded, and can be read by means of the hands on the dials.
The method of using the apparatus is shown in Fig. 5. A boat is provided with an ordinary anchor, and a weight for anchoring the wire. One line about two hundred feet long is fastened at the fluke end of the anchor stock, and another into the ring. Rowing out into the stream about two hundred feet above where the current is to be measured, the anchor is thrown overboard, and the boat dropped back, till we come nearly to the end of the line fastened to the ring of the anchor. This end is now made fast to the front ring of the weight, and another line and a strong copper wire are fastened to the upper ring. The weight is now lowered, and the boat dropped back at the same time, till the weight is vertically under the stern of the boat.
The anchor line is made fast in the bow, and the line fastened to the weight is left slack, so that it will be out of the way, and fastened to the stern.
The spring-pole, which runs fore and aft the boat, is now bent down and the copper wire fastened to the after end. This serves to keep the line always taut, and also to take up small motions of the boat.
The yoke in which the meter frame hangs has a swivel ring at top and bottom. To the upper one is attached a measured cord, having spring clasps every five feet, and to the under one is fastened a weight.
There are two eyes in the side of the yoke, which are passed over the copper or standing wire, and on which they slide up or down. The meter being put on the wire, it is lowered to say five feet depth, and the ends of the standing wire and of the insulated wire connected with the battery and register in the boat; each revolution is recorded by the register.
By means of a switch the register can be thrown in or out of circuit in a moment, and the number of revolutions in any given time found.
The meter can be now lowered to any other depth, by means of the measured cord, which is fastened to the wire by the clasps to keep it as nearly perpendicular as possible, and the revolutions found; and so on until the requisite number of observations have been taken at that position.
The position of the boat can be exactly determined by a theodolite on shore.
After having furnished the required observations at one place, we first let the upper end of the standing wire loose, and then pull up the weight by the lines fastened to it, and by means of the connecting line the forward anchor is very easily raised even from clay bottom, as it is fastened to the upper end of the stock, and this lifts the anchor directly.
Assistant A. R. Flint devised the break used on the float meter, the only friction being that of the axle on the steel points, and the striking of the arm against the fine silver wire. In the faster moving propeller wheels this method was not practical, as the time the wires remained connected was too short to allow the register to work, so that with them we had to use a longer break which gave a little more friction, and therefore they required a little faster current to turn them.
By the use of the meter we eliminate all the errors heretofore mentioned, which are inherent to the method of float measurement; for, the base being reduced to a point, only one cross section is needed, and as the meter is free to move in all directions it will give the velocity of any current, no matter at what angle it passes the plane, and the discharge at that point must be equal to the mean of all the velocities past the plane into the area of the cross section. The irregularities of the current can also be eliminated by letting the meter run a suficient time; and its superiority over the floats is seen in the fact, that while the float is but a moment passing any plane, and therefore will only give the velocity of the current at that moment, the meter can be run for any required time, and will give the mean velocity for the whole period. One hundred and fifty floats in a day is about as many as a single party can put out and locate; the mean of the day's work will give the velocity for, say, one hundred and fifty seconds, while from the meter we can obtain it for the whole time or any part thereof. The other errors of the floats do not of course affect the meter. The determination of the coefficient seems to be the only possible error to which we are liable in the use of the meters.
For this, therefore, careful experiments were made by drawing them through still water, and these results were also tested by comparisons with floats.
COEFFICIENT OF METERS.
This was found by fastening the meters about three feet below the center of a small boat, and then drawing them across a pond about five hundred feet wide.
The boat was drawn at different velocities, the number of revolutions of the meter and the time of passage being recorded.
The distance traveled being divided by the number of seconds, the velocity in feet per second was determined.
Then the number of revolutions per second were grouped for each half foot of velocity per second, as shown in the following table:
TABLE I.-Showing the number of revolutions per second for each half foot of velocity for
the several meters.
These quantities appear to follow some general law of increase approx imating to a straight line, but to obtain the coefficient of the meter it is necessary to divide severally the velocities per second by the revolutions
This is done in the following table under the head of observed coefficient:
TABLE II.-Showing the comparison of the obserred and computed revolutions and coefficient
for the several meters.
0.3 0.000 0.000
14. 573 0.5 0.431 0.0391 0.0394 12. 778 12. 704 +0.074
2. 390 0.65 0. 694
1. 880 1.0 0.961 0.0900 0. 0894 11. 123 11. 190 -0.067 0.558 0.573 1.757 1.744 +0.013 0.440 0.446 2. 271 2. 282 -0.011 1.5 1.2140. 1461 0.1454 10.263 10.300 -0.032 0.8720.896 1.680 1. 673 +0.007 0.696 0.698 2. 153 2. 149 +0.004 2.0 1, 3950. 2057 0.2070 9. 7:22 9.662 +0.060 1.213 1.228 1. 629 1. 627 +0.002 0.959 0. 964 2. 087 2. 085 +0.002 2.5 1.524 0.27150.2715 9. 208 9. 208 -0.000 1.514 1. 567 1.584 1. 595 -0.011 1.223 1.226 2. 044 2. 040 +0.004 3.0 1.6170. 3375 0.3378 8.888 8.881 +0.007 1.897 1. 308 1.562 1.572 -0.010 1. 494 1. 494 2.007 2. 007 -0.000 3.5 1.678 0.40500. 4030 8.638 8.686 -0.048 2. 229 2. 252 1.550 1. 556 -0.006 1.761 1. 764 1. 987 1.984 +0.003 4.0 1.712 0.4657 0.4681 8. 589 8. 546 +0.043 2. 635 2.589 1. 544 1. 545 -0.001 2. 034 2. 032 1. 965 1. 969 -0.004 4.5 1.720 0.5292 0.5283 8.504 8.518 -0.014 2. 947 2. 922 1. 542 1. 540 +0,002 2. 296 2. 295 1. 959 1.960 001
Su ms. Mean..
It was found, that an ellipse having a minor axis of 3.44, and major axis of 8.2, would best satisfy the condition of variation in these quantities.
In the first column of the table the ordinates of this curve for each half foot of velocity are given.
Plotting this curve and placing the vertex at the zero of the meter,
that is, at the velocity at which it begins to turn, we can by changing
=% we have for the different velocities
a-60.5 Yo.5 =
41.0 = These quantities being compared with the ordinates of the curve, a series will be found which will approximate very nearly to them.
Taking this series and dividing severally by x and subtracting the quotient from a, we have the computed coefficients given in the table, which can be compared with the coefficient as observed.
Thus we have for the float meter the assumed coefficient of the zero ...
= 14.573 the common divisor x
= 3.528 and the velocity of the water at the zero of the meter.... 0.3 foot.
The differences between the observed and computed coefficients given in the table are very small, and are probably mostly due to errors of observations.
M. Morin (Hydraulique, page 100 et seq.) gives certain observations for the determination of the coefficient of the Lapointe's meter, by noting the number of revolutions and corresponding time during which a reservoir of known size was being filled by water passing through the meter at different velocities.
He gives a formula for the meter of the form Q = a + bn, in which Q the discharge, n= the number of revolutions, and a + b are constants to be found by experiment.
This it will be seen is the formula of a straight line, and it agrees very well with his observations. But it is only applicable to an enclosed meter, where the area of the volume of water passing the meter is known.
I have taken his data and have found the coefficient of the meter reduced to English feet, for each half foot of velocity.
In the table below are given these observed coefficients and the coefficient as computed by the formula previously given.
TABLE III.-Showing the comparison of the observed and computed coefficient of Lapointe's
Velocity in feet per
0.000 +0.005 +0.003 +0.001 -0.003 -0.004 +0.007 +0.0009