HYDROSTATICS. 



are turned by the water, and regintar, by moans of clock- 

 work, the number of revolutions they make, is sometime* used. 

 ThiH is fiied to a pole, and held in some part of the stream for 

 a given time ; the velocity at this point is thus noted, au-1 in .1 

 .-inn! a- way it may be found at other points and a mean taken. 

 A Ampler way, however, is to observe the velocity at the surface. 

 A substance of nearly the same specific gravity as the water is 

 thrown in, and the time occupied in passing between two point* 

 noted ; from this we easily find its speed per second. Now the 

 mean velocity i found to vary from about } to { of that at the 

 surface, and tables have been constructed showing the mean 

 velocity corresponding to each surface velocity. If we multiply 

 this moan velocity by the area, we ascertain the amount of water 

 passing per second. 



ng thus seen the power there is in a stream, we must 

 notice the different machines employed to utilise it. 



The simplest and most common of these is the water-wheel. 

 This consists essentially of a wheel turning on a horizontal axis, 

 and carrying on its circumference a number of floats or boards. 

 The water strikes against these, and thus causes the wheel to 

 turn with considerable force, and the motion is by means of cog- 

 wheels transmitted from it to the machinery which has to be 



Water-wheels are divided into three classes, according to the 

 way in which the water acts on them, or rather the point of 

 their circumference at which it is applied. 



Sometimes the wheel is placed so that its lower floats just dip 

 into the stream, and it is then called an under slwt wheel (Fig. 24). 

 When the water is confined by an em- 

 bankment, and allowed to flow against the 

 wheel a little below its middle, it is called 

 a breast wheel ; and when the water is re- 

 ceived on the upper port, it is an overshot 

 wheel. The first of these three is the 

 simplest in construction, no embankment 

 or artificial channel for the water being 

 absolutely necessary, though a much 

 greater power is gained when the wheel is 

 made to fit into a properly-shaped water- 

 course, so that no water can pass without 

 turning it. Less power is, however, de- 



Fig. 24. 



rived from this than from the other kind of wheel, as the water 

 strikes violently against the floats, and thus expends much of 

 its force uselessly in straining the wheel. It is always found 

 that there is the greatest advantage gained when the water 

 strikes the wheel with as little velocity as possible, but acts 

 merely by its weight and pressure. 



At first the floats were arranged to stand out perpendicularly 

 from the wheel, but experience shows that it is better to let 

 them have an inclination towards the stream of twenty or thirty 

 degrees, as thus they break the violence of the current, and 

 allow it to act more advantageously. 



Another matter to be considered is the proportion which should 

 exist between the speed of the wheel and that of the stream. It 

 is evident that there are two extreme cases which may occur. If 

 the circumference of the wheel move at exactly the same velocity 

 as the stream, no power can be derived from its motion ; and if 

 the motion be reduced to a minimum, nearly all the power would 

 be lost. The greatest amount of work is accomplished when 

 the motion is about midway between these two extremes 

 that is, when the wheel moves at about half the rate of the 

 stream. 



There is one other advantage of the undershot water-wheel 

 which should be just noticed, and that is that when made in its 

 simplest form, with the floats radiating directly from it, it can 

 be used in a tidal stream. 



In any other kind of wheel, the water must flow in one uniform 

 direction. The level should also be nearly even, as the height at 

 which the water strikes the wheel makes a great difference in its 

 working. With thie kind, however, we have merely to fix tho 

 wheel between moortd barges, so that it may rise and fall with 

 the tide, and we shall have it almost constantly at work, part 

 of the time turning in one direction, and part in the other. Only 

 a small portion of the force of the stream will, it is true, be 

 utilised ; but, as there is usually in tidal rivers very much more 

 power than is needed, this is of little moment provided enough 

 power is gained to perform the required work. 



We now pass on to the second class, called breast wheels 



(Fig. 25). These have usually an advantage orer the claM wo 

 have just spoken of, though they an inferior in power to over- 



\ 



The stream here, instead of being allowed to ran in He natural 

 bed, is stopped by a dam or embankment built acroa* it The 

 water accumulate* behind thu till it rises to the lev*! of the top. 

 and then flows over at the tame rate M before. A oanred ehane*! 

 i* made for it, in which the wheel is placed, with it* floats nearly 

 touching the tide*, *o that little water oaa escape. Mocbthere- 

 fore depend* upon the accuracy of the workmanship ; if the 

 water leaks by between the float* and the brickwork, there i* a 

 corresponding lose 

 of power ; while, on 

 the other hand, if 

 the floats scrape 

 against the side*, 

 there i* a loss by 

 friction. In this -_ 

 wheel the float* are 

 frequently curved or J 

 bent in the middle, 

 o a* to hold the 

 water better. It is 



important to take Tig. . 



care that the water, 



after it has left the wheel, flow* away without obstructing it* 

 motion, as a great loss of power sometime* results from this not 

 being done. A step is frequently put in the coarse, a* shown 

 in the illustration, so th it, as soon a* the water ha* reached the- 

 lowest point of the wheel, it falls out of contact with it Where 

 this cannot well be done, part of the water i* allowed to run by 

 a channel at the side of the wheel, and by it momentum 

 produces a current which aid* in carrying away the tafl- 

 water. 



In the overshot wheel, which is represented in Fig. 26, the 

 water is usually diverted from the stream and conducted by a 

 series of troughs to the top of the wheel, where it pours into th* 

 buckets. The end of the trough is sometimes open, so that the 

 water flows on with tho impulse it has acquired; the better 

 plan, however, is for it to bo closed, and an opening made 

 underneath, as shown in the figure, through which the water 

 may flow. 



In this way it falls on the wheel without any momentum, and 

 all strain is avoided. With this wheel nearly all the power of 

 the water may be employed, as it may be made of such a width 

 that none of the stream runs to waste. It is found beet to let 

 the wheel turn very slowly, as thus there is very little momentum 

 left in the water when it ?< aves the wheel, and all low from the 

 water being thrown off by centrifugal force is avoided. Cog* 

 are, therefore, usually placed round one edge of the wheel ; 

 these work in a pinion, and the motion is imparted to the 

 machinery from this pinion instead of from the axis of the wheel. 

 The shape of the buckets is, perhaps, of more importance in 

 this than in the other descriptions of wheel, for, since the weight 

 of the water is the moving power, it is important to retain a* 

 much of it as possible in the buckets until they arrive at the- 

 lowest point. Sometimes 

 they are made of the shape 

 shown in the figure, and ma- 

 sonry erected to confine the 

 water, as in the case of the 

 breast wheel, but more fre- 

 quently the buckets are made 

 to curve upwards, and thus 

 retain the water. 



Another matter has, how- 

 ever, to be considered in de- 

 ciding on the best shape of 

 bucket, and that is to allow 

 the air to escape. As tho 

 stream pours in it has to dis- 

 place the air, and with some 



shapes of bucket this opposes and scatter* the water in a much 

 greater degree than would at first be expected. Openings are 

 sometimes mnde in th* cylinder for this purpoee. In the beat 

 constructed wheel* of this class, about 80 per cent, of the 

 power may be utilised. 



Having thus noticed the wheels with horizontal axes, we mast 



