WATER. 



v?ater, &c. is t\.V,t of ^^^ weight of the water multiplied 

 by -r'o of its velocity. 



Thus it appears that an underfhot water-wheel, conftrufted 

 after the foregoing manner, would only raife one-third part 

 of the water expended to the fame height, as the orignial 

 head or level. This is the utmoft that can be expefted, 

 though often lefs is done ; becaufe here we fuppofe every 

 part exaftly performed, and the water applied to the wheel 

 in the bed manner ; therefore, as we cannot come up to the 

 maximum, we muft come as near it as we can by lofmg the 

 leaft poffible of the power's impulfe. 



It is no advantage to have a very great number of float- 

 boards round the wheel, becaufe when they are (truck by 

 the water, as applied in the beft manner poffible, the fum of 

 the impulfes exerted on the different floats, will but be equal 

 to the impulfe made againft one float-board ftruck by all the 

 water iffuing from the fluice at right angles to its furface. 

 But as this float -board muft move forward, there muft be a 

 fuccefTion of float-boards to receive the impulfe of the 

 water, and fince they cannot receive it at right angles, there 

 will be fome lofs of impulfe in that fucceflion. Befides 

 when the firft float -board is fo far paft the perpendicular, as 

 to have the aftion of the water intercepted by the fucceed- 

 ing one, it is checked by the back water through which it 

 muft pafs in rifing out of the water, and thereby be fo far 

 retai-ded as to take from the full effeA of the impulfe on 

 the following float. Indeed if all the water <:ould run off 

 immediately after having performed its office, this would 

 rot happen ; but it can feldom be effefted in underfhot- 

 mills, efpecially thofe built upon rivers. All the remedy 

 in fuch cafe is, (when the diameter of the wheel is 

 fettled) to fix juft fuch a number of floats upon it, that 

 each one, after it has received the full impulfe of the 

 water, may come out of the water as foon as polfible, 

 that another fucceeding float may be brought to receive the 

 impulfe, otherwife the wheel would remain a moment with- 

 out any impulfe. 



In the article Mill we have given a table for the dimen- 

 fions and proportions for underfhot v/heels, which was cal- 

 culated by Mr. Fergufon. Dr. Brewfter, in his new edition 

 of Mr. Fergufon's works, has given an improved table, 

 which is calculated upon the following principles. 



It is evident that the water-wheel muft always move with 

 lefs velocity than the water, even when there is no work to 

 be performed ; for a part of the impelling power is necef- 

 farily fpent in overcoming the inerlia of the wheel itfelf ; 

 and if the wheel has little or no velocity, it is equally mani- 

 feft that it will produce a very fmall effeft. 



There is confequently a certain proportion between the 

 velocity of the water and tiie wheel, when the effeft is a 

 maximum. Mr. Smeaton has fhewn the greateft efFeft is 

 produced when the velocity of the wheel is between one- 

 third and one-half, but the maximum is much nearer to 

 one-half than one-third. He obferves alfo that one-half 

 would be the true maximum, if nothing were loft by the 

 refinance of the air, the fcattering of the water carried up 

 by the wheel, and thrown off by the centrifugal force, 

 and the leakages of the water between the floats and 

 the water-courfe, all which tend to produce a greater 

 diminution of the effeft at that velocity, which would 

 be the maximum if thefe lofl'es did not take place, than 

 they do when the motion is a little flower. The great 

 hydrauhc machine at Marly, the wheels of which are un- 

 derfhot, was found to produce a maximum effect when 

 the velocity of the wheel was two-fifths that of the cur- 

 rent. Hence Dr. Brewfter concludes that in theory the velo- 

 city of the wheel is one-half that of the current, and that 

 12 



in praftice it is never more than three-eighths of the flream'g 

 velocity, when the effeft is a maximum. 



Dr. Brexuftcr's Table of uruLrfhot Water-Wheeh, in which 

 the velocity of the wheel is three-feventbs of the velocity of 

 the water, and the effeds of fridlion on the velocity of the 

 ftream are 'reduced to computation. The wheel is fup- 

 pofed to be fifteen feet diameter. 



Another Manner of applying Water to an underfhot Wheel 

 —This was propofed by M. Fabre as the refult of much 

 mathematical inveftigation, and has been fo frequently re- 

 commended by authors of eminence, that we fliall give a 

 fhort defcription without entering into all his rules for the 

 proportions. The principal diff'erence in this wheel from 

 that in common ufe is, that the water is made to run down 

 a rapid flope or inclined plane, in order to ftrike the floats 

 of the wheel, inftead of iffuing from an aperture or fluice 

 fituated beneath the furface of the water in the refervoir. 

 A mill is ufually fituated at a diftance from the river, with 

 a canal or water-courfe to conduft the water to the mill; as 

 it is of the higheft importance to have the height of the fall 

 as great as poffible, the bottom of the canal or water, 

 courfe, which condufts the water from the river to the mill, 

 fhould have a very fmall declivity ; for the height of the 

 water-fall at the mill will diminifh in proportion as the 

 declivity of the canal is increafed: it will be fufficient to 

 make it flope about one inch in 200 yards, taking care to 

 make the declivity about half an inch in the firft 48 yards, 

 in order that the water may have a velocity fufficient to 

 prevent it from flowing back into the river. 



When the water is thus brought to the channel in which 

 the wheel is placed, the water is recommended to be con- 

 dufted down a flope or inchned plane, making an angle of 

 64^ degrees with the horizon ; that is, in ? perpendicular of 

 ten feet, the flope ftiould deviate from it 4^ feet .- at the 

 bottom of this flope the water is to be again condufted 

 horizontally, and then to ftrike the float-boards of the 



wheel. 



I 



