WATER POWER UNDERSHOT- WHEEW.] APPLIED MECHANICS. 



82? 



power, are reckoned in feet per minute. Taking a 

 horse-power as 33,0001bs. lifted one foot high in one 

 minute, and assuming the circumferential speed of an 

 undershot-wheel as one-third of that of the current, we 

 may estimate its power as a mover of machinery by the 

 following rule : 



Multiply the surface of the float (in square feet) three 

 times by the velocity of the stream (in feet per second), 

 and divide the product by 3,800 ; the quotient expresses 

 the horse-power. 



Example. An undershot -wheel, having floats 2 feet 

 deep and 10 feet wide, is moved by a stream running at 

 7J miles per hour : required its power. 



Here the surface of a float is 10 X 2 20 square feet. 



The velocity is 7i miles per hour : or (as a mile is 

 6,280 feet, and an hour 3,600 seconds) the velocity is 



- ^=11 feet per second. 



The power therefore is 20 X 11 X 11 X 11 



power. 



The speed of the floats being Jrd of that of the cur- 



~ feet per second, or i^-* 

 3 3 



rent, is ~ feet per second, or \ - = 220 feet per 



minute. We may take this as the speed of the middle 

 part <;f the fl< >at ; and if the wheel be 23 feet in extreme 

 diameter, its diameter at the middle of the floats would 

 be 21 f.;et, and circumference there 66 feet ; if this move 

 at the rate of 220 feet per minute, the wheel must make 



^r = 3J revolutions per minute. 



The speed of a stream may be generally estimated by 

 throwing on it a body that floats, but is immersed some 

 depth as a bar of wood loaded at one end to float ver- 

 tically and watching the time occupied by its passage 

 over a certain known distance. Care should be taken 

 that the body fairly attain the speed of the current be- 

 fore its motion is reckoned in the time. 



It is advantageous to make the inner edges of the floats 

 to stand somewhat above the general level of the water, 

 which becomes heaped up behind them, and would other- 

 wise pour over the edges (Fig. 114). Indeed, the dif- 



Fig. 111. 



ference of level caused by this heaping up of the water 

 behind, and its hollowing in front of a float, almost 

 measures the head of water pressing on it. When prac- 

 ticable, the stream should be narrowed to the width of 

 the wheel (Fig. 115), as by this means not only is its 



Fig. 119. 



of water passing more quickly through a diminished 

 channel ; but also the water, acting on the floats, is pre- 

 vented from escaping sideways without giving its full 

 effect. 



As the velocity of streams to which undershot-wheels 

 are applicable is never very great, and as the velocity of 

 the floats should not much exceed one-third of that of 

 the stream, such wheels are necessarily slow in their 

 revolution, and can therefore be applied with most ad- 

 vantage, in driving machinery where quick speeds are 

 not required. When it is necessary to convert the slow 

 revolution of the wheel to rapid motions in the ma- 

 chinery, there are considerable losses from the friction of 

 the gearing. For such purposes as that of working 

 pumps or fulling-mills, and generally for slow, heavy 

 work, these wheels are very serviceable. The principal 

 objection to their use arises from the circumstance, that 

 with a stream of average rapidity, very little power is 

 obtained without a very large and cumbrous wheel, in- 

 volving considerable outlay, and extending over a great 

 breadth of the stream. By making the diameter of the 

 wheel large, no greater power is obtained, except what 

 may be attributable to the more direct action of the 

 water on the floats, which enter and leave the water 

 more vertically when the wheel is large. The circum- 

 ference of a large wheel should move with the same 

 speed as that of a small one ; and, therefore, the greater 

 the wheel, the smaller number of revolutions does it 

 make in a given time. The only way of increasing the 

 power is to extend the surface of the floats. This may 

 be done by making them deeper or wider. Additional 

 depth of the float, even where the depth of the stream 

 permits it, is by no means so effective as additional width ; 

 for a wide shallow float enters and leaves the water with 

 ease, while a deeper one presses the surface of the water 

 down in entering, and lifts it up in leaving, and thereby 

 encounters considerable resistance to its motion. 



Occasionally undershot-wheels have been made liko 

 the feathering paddles of steam- vessels, where the floats 

 are capable of being turned on pivots (Fig. 116) so as to 

 maintain a vertical position while immersed in the water, 

 and thus receive its most direct impulse, while they enter 

 and leave it with the least possible resistance. 



Fig. 111. 



velocity augmented by the necessity of a certain body I 



When it is considered that twice in every day a great 

 tidal stream flows and ebbs along our coast and in our 

 estuaries, it is surprising that advantage has not more 

 frequently been taken of this enormous power by the 

 erection of undershot-wheels along the course of the tidal 

 currents. In this country tide-mills are rare ; and 

 neither their number nor magnitude render them im- 

 portant as sources of power. Occasionally, however, 

 they have been employed with advantage. Where there 

 is a great tidal stream, and consequently a 

 considerable difference between the levels of 

 high and low-water, fixed wheels would be 

 almost useless ; for at high-water they would 

 be too much immersed, and at low-water too 

 little. It is in such cases necessary to mount 

 them on a floating stage or barge, so that the 

 whole mill may rise and fall with the tide, 

 the amount of immersion remaining con- 

 stant. Again, as the tide flows alternately 

 in opposite directions, when it is required 

 that the machinery move only in one direc- 

 tion, it is necessary that tide-mills, in such cases, should 



