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80
[ON STREAMS
HYDRAULICS


them visible they may have a vertical painted stem. In experiments on the Seine, cork balls 1% in. diameter were used, loaded to float flush with the water, and provided with a stem. In A. J. C. Cunningham's observations at Roorkee, the floats were thin circular disks of English deal, 3 in. diameter and l in. thick. For observations near the banks, floats I in. diameter and lf in. thick were used. To render them visible a tuft of cotton wool was used loosely hxed in a hole at the centre.

The velocity is obtained by allowing the float to be carried down, and noting the time of passage over a measured length of the stream. If 2' is the velocity of any float, 2 the time of passing over a length I, then v=l/t. To mark out distinctly the length of stream over which the floats pass, two ropes may be stretched across the stream at a distance apart, which varies usually from 50 to 250 ft., according to the size and rapidity of the river. In the Roorkce experiments a length of run of 50 ft. was found best for the central two-fifths of the width, and 25 ft. for the remainder, except very close to the banks, where the run was made 12% ft. only. The longer the run the less is the proportionate error of the time observations, but on the other hand the greater the deviation of the floats from a straight course parallel to the axis of the stream. To mark the precise position at which the floats cross the ropes, Cunningham used short white rope pendants, hanging so as nearly to touch the surface of the water. In this case the streams were 80 to 180 ft. in width. In wider streams the use of ropes to mark the length of run is impossible, and recourse must be had to box sextants or theodolites to mark the path of the floats. Let AB (fig. 136) be a measured base line strictly parallel to the thread of the stream, and AAI, BB1 lines at right angles to AB marked out by ranging rods at A1 and Bl. Suppose observers stationed at A A rl C, Il; A, and B with sextants or theodolites, and <f?°'°ff";"'T°"f'°' "'°°°'9 let CD be the path of any float down

§ , ' stream. As the float approaches AA1,

1 / 1 the observeratB keepsit on the cross wire

I/, of his instrument. The observer at A
~y, if observes the instant of the float reaching

| fl, J' the line AAi, and signals to B who then llil' ' reads oil the angle ABC. Similarly, as | I/l' l the float approaches BB1, the observer

, ll ' at A keeps it in sight, and when signalled

illl K to by B reads the angle BAD. The data 1 If l so obtained are sufficient for plotting 1 I/ the path of the float and determining 2 / 1 ' the distances AC, BD.

<|§ se i >, , {, The time taken by the float in passing B ll 1 .D; fill BJ over the measured distance may be ob-I, l served by a chronograph, started as the " float passes the upper rope or line, and FIG. 136. stopped when it passes the lower. In Cunningham's observations two chronometers were sometimes used, the time of passing one end of the run being noted on one, and that of passing the other end of the run being noted on the other. The chronometers were compared immediately before the observations. In other cases a single chronometer was used placed midway of the run. The moment of the floats passing the ends of the run was signalled to a timekeeper at the chronometer by shouting. It was found quite possible to count the chronometer beats to the nearest half second, and in some cases to the nearest quarter second. § 137. Sub-surface Floats.~The velocity at different depths below the surface of a stream may be obtained by sub-surface floats, used precisely in the same way as surface floats. The most usual arrangement is to have a large float. of slightly greater density than water, very light surface float. The motion connected with a small and

/ of the combined arrangement is not Egg S RT sensibly different from that of the large §§ : "i § ?';".5T'-F float, and the small surface float enables " T" “' ' ' an observer to note the path and velo-I city of the sub-surface float. The in; strument is, however, not free from | objection. If the large submerged | float is made of very nearly the same | density as water, then it is liable to be thrown upwards by very slight edclies in the water, and it does not maintain its position at the depth at which it is M ...W intended to float. On the other hand, »»lll' *f., if the large float is made sensibly i ii' llTllri, l§§ heavier than water, the indicating or § "§ ll, fM#;l»| 'l'3 surface float must be made rather large, fl” ' " ill and then it to some extent influences the motion of the submerged float.

FIG. 137. Fig. 137 shows one form of subsurface float. It consists of a couple

of tin plates bent at a right angle and soldered together at the angle. This is connected with a wooden ball at the surface by a very thin wire or cord. As the tin alone makes a heavy submerged float, it is better to attach to the tin float some pieces of wood to diminish its weight in water. Fig. 138 shows the form of submerged float used by Cunningham. It consists of a hollow metal ball connected to a slice of cork, which serves as the surface float. § 138. Twin Floats.-Suppose two equal and similar floats (fig. 139) connected by a wire. Let one float be a little lighter and the other Then the velocity of the combined

a little heavier than water.

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Flo. 138. FIG. 139.floats

will be the mean of the surface velocity and the velocity at the depth at which the heavier float swims, which is determined by the length of the connecting wire. Thus if 11, is the surface velocity and 11,1 the velocity at the depth to which the lower float is sunk, the velocity of the combined floats will be U = %<U¢'l”7-'d)-Consequently,

if v is observed, and 'vs determined by an experiment with a single float

vd=2v-fu..

According to Cunningham, the twin float gives better results than the sub-surface float.

§ 139. Velocity Rods.-Another form of float is shown in fig. 140. This consists of a cylindrical rod loaded at the lower end so as to float nearly vertical in water. A wooden rod, with a metal cap at the

bottom in which shot can be placed, answers better than anything else, and sometimes the wooden rod is made in » lengths, which can be screwed together so as to suit streams of different depths. A tuft of cotton wool at the top serves to make the float more easily visible. Such a rod, so adjusted in length that it sinks nearly to the bed of the stream, gives directly the mean velocity of the whole vertical section in which it floats. '§ 140. Re'/Jy's Current Meter.-No instrument has been so much used in

directly determining the velocity of a stream at a given point as the screw current meter. Of this there are a If dozen varieties at least. As an example of the instrument in its simplest form, Revy's meter may be selected. This is an ordinary screw meter of a larger size than /jf' ”

usual, more carefully made, and with its details carefully studied (figs. I4:I, 142). FIG 140 It was designed after experience in gauging the great South American rivers. The screw, which is actuated by the water, is 6 in. in diameter, and is of the type of the Griffiths screw used in ships. The hollow spherical boss serves to make the weight of the screw sensibly equal to its displacement, so that friction is much reduced. On the axis aa of the screw is a worm which drives the counter. This consists of two worm wheels g and h fixed on a common axis. The worm wheels are carried on a frame attached to the pin l. By means of a string attached to I they can be pulled into gear with the worm, or dropped out of gear and stopped at any instant. A nut m can be screwed up, if necessary, to keep the counter permanently in gear. The worm is two-threaded, and the worm wheel g has 200 teeth. Consequently it makes one rotation for Ioo rotations of the screw, and the number of rotations up to IO0 is marked by the passage of the graduations on its edge in front of a fixed index.. The second worm wheel has 196 teeth, and its edge is divided into 49 divisions. Hence it falls behind the first wheel one division for a complete rotation of the latter. The number of hundreds of rotations of the screw are therefore shown by the number of divisions on h passed over by an index fixed to g. One difficulty in the use of the ordinary screw meter is that particles of grit, getting into the working parts, very sensibly alter the friction, and therefore the speed of the meter. Revy obviates this by enclosing the counter in a brass box with a glass face. This box is filled with pure water, which ensures a constant coefficient of friction for the rubbing parts, and prevents any mud or grit finding its way in. In order that the meter may place itself with the axis parallel to the current, it is pivoted on a vertical axis and directed by a large vane shown in fig. 142. To give the vane f »

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