WATER. 



ments, the wheel is placed in a conduit or race, to which the 



float-boards are cxaftly adapted, and the water cannot 



otherwife efcape than by moving along with the wheel. It 



is obfervable in a wheel working in this manner, that as 



loon as the water meets the float, it receives a fudden check, 



and rifes up againft the float, like a wave againft a fixed ob- 



jeft, infomuch that when the flieet of water is not a quarter 



of an inch thick before it meets the float, this (heet will 



[ aft upon the whole furface of a float, whofe height is three 



I inches ; and confequently, where the float is no higher than 



; the thicknefs of the (heet of water, as theory alfo fuppofes, 



a great part of the force would have been loft by the water 



daftiing over the float. 



The wheel which Mr. Smeaton ufed had originally twenty- 

 . four floats, and was afterwards reduced to twelve, which 

 I caufed a diminution in the effeft, on account of a greater 

 ! quantity of water efcaping between the floats and the floor 

 of the channel in which it moved; but a circular fweep 

 being adapted thereto, of fuch a length, that one float en- 

 tered the curve before the precedmg one quitted it, the 

 'effeft came fo near to the former as not to give hopes of 

 I advancing it, by increafing the number of floats beyond 

 twenty-four in this particular wheel. 



' Mr. Smeaton obferves that, in many of the experiments, 

 ;the refults were by different ratios than thofe which his 

 maxims fuppofed ; but as the deviations were never very 

 confiderable, the greateft being about one-eighth of the 

 quantities in queftion, and as it is not praflicable to make 

 experiments of fo compound a nature with abfolute preci- 

 fion, he fuppofes, that the lefler powers are attended with 

 fome friftion or work under fome difadvantages, which have 

 ;iot been duly accounted for ; and, therefore, he concludes 

 that thefe maxims will liold very nearly, when applied to 

 works in large. 



Application of thefe Principles to PraSice The firft thing 



to be done in a fituation where an underfliot wheel is in- 

 tended to be fixed, is to confider whether the water can run 

 off clear from the wheel, fo as to have no back water to im- 

 pede its motion ; and whether the fall wliich can be obtained 

 by conftrufting a proper dam to pen up the water and 

 fluice for it to pafs through, will caufe it to ftrike the float- 

 boards of the wheel with a fufficient velocity to impel them 

 rorcibly forwards ; and alfo, whether the quantity of the 

 iupply will be fufBcient to keep a wheel at work for a cer- 

 tain number of hours each day. 



When we have afcertained the height of the fall of water, 

 that is, the height of the furface above the centre of the 

 opening of the fluice, we muft find what will be the con- 

 tinual velocity of the water ilTuing out from fuch opening. 



In fome cafes, we have the velocity of the water given 

 when it iiTnes from the opening of the fluice, and we then 

 i require to know what height of column will produce that 

 velocity. Thefe two things we may find by a fingle rule, 

 and an eafy arithmetical operation, which is as follows : 



ift. The perpendicular height of the fall of water being 

 given in feet and decimals of feet, the velocity that the 

 water will acquire per fecond, exprelTed in feet and decimals, 

 may be found by the following rule : 



Multiply the conllant number 64.2882 by the given 

 height, and the fquare root of the produft is the velocity 

 required. 



Example I. — If the height is two feet, the velocity will 

 be found 11. 34 feet per fecond. 



Example 2. — If the height is 16,0913 feet, the velocity 

 will be 32,1826 im per fecond. 



Example 3. — If the height is fifty feet, the velocity will 

 be 56,68 [eetfer fecond. 



Note. The velocities thus obtained will be only the theoretic 

 velocity, that is, the velocity any body would acquire by 

 falling through fuch height in -vacuo, the velocity in reality 

 will be lefs, generally fix or feven-tenths. 



The uniform velocity of a fluid being given, exprefled in 

 feet and decimals of feet per fecond, the height of the co- 

 lumn or fall to produce fuch a velocity may be found by 

 the following rule : 



Multiply the given velocity into itfelf, and divide the pro- 

 duft by 64,2882 ; the quotient will be the height required, 

 exprefled in feet and decimals. 



Example i If the velocity given is three feet per fe- 

 cond, the height will be 0.139 of a foot. 



Example 2 — If the velocity given is 32,1826 feet per 

 fecond, the height viiW be found 16,0913 feet. 



Example 3. — Let the velocity be 100 feet per fecond, 

 the height will be 155,649 feet. 



The knowledge of the foregoing particulars is abfolutely 

 neceflary for confl:rufting an underfliot water-wheel ; but 

 the moft advantageous method of fetting it to work, and to 

 find out the utmoft it could perform, would be very dif- 

 ficult, if we were not furniflied with the maximum which 

 Mr. Smeaton fettled, by fliewing, that an underfliot water- 

 wheel will aft to the greateft advantage, when the velocity 

 of its float-boards is equal to two-fifths or four-tenth parts 

 of that of the water which gives it motion. 



To illuftrate this, let us confider awheel equally balanced 

 on all fides, and turning freely round upon its pivots, its 

 circumference would foon move as faft as the current it 

 was placed in. Suppofe the water to move at the rate of 

 three feet in a fecond, the circumference of the wheel 

 would pafs through three feet in a fecond. In this cafe, 

 the wheel performs no work, and the effeft produced is 

 nothing. 



Now in attempting to apply the power of this wheel to turn 

 any kind of machinery, fuppofe the work to be fo proportion- 

 ed, that the refiftance would caufe the wheel to ftand Itill and 

 flop the water, or make it run over the floats, in confequence 

 of its not having fufficient force to carry the float-boards 

 along with it. In this cafe alfo, there being no motion, 

 there could be no mechanical effeft produced ; but if the 

 refiftance be diminiftied by degrees, the wheel would be- 

 gin to partake of the motion of the current of water, and 

 being loaded, would produce a mechanical eff'eft propor- 

 tioned to the load and velocity. The wheel would increafe 

 in its velocity in proportion as the refiftance was dimi- 

 niftied, and the mechanical effeft would increafe alfo until a 

 certain point when the wheel moved fo faft, that the water 

 would not ftrike the float-boards quick enough to produce 

 the greateft effeft : tins is found to be as before mentioned, 

 when the floats move four-tenths as faft as the water, be- 

 caufe then fix-tenths of the water is employed in driving 

 the wheel with a force proportional to the fquare of its 

 velocity. 



If we multiply the furface or area of the opening by the 

 height of the column, we (hall afcertain the body or column 

 of water which (hould prefs againft that float -board, which 

 is immediately under the wheel, fuppofing it has no motion ; 

 but it will be found, that a fmall proportion of the weight 

 of the original column hung on the oppofite fide of the 

 wheel, would arrcft its motion entirely ; but when we would 

 have it to move with a proper velocity, that is, two-fifths of 

 that velocity with which the water moves, tWd of the 

 weight of the original column, is the wtight which the 

 wheel would raife with four-tenths of the velocity that the 

 water moves with, and the power which the wheel would 

 exert on the machinery to grind corn, lift hammers, raife 



water, 



