82 



SUMMARY OF HYDRAULICS. 



verfing their ro 

 tation 



Underfliot 

 wheels. 



Floatboards 

 fhould rife [ 

 pendicularly. 



into two parts, one derived from the weight of the water in the? 

 cells or buckets, the other from the impulfe of the water falling 

 on it : the effect of the firft is conftant, that of the fecond varies 

 with the velocity : the maximum is found to be when the ve- 

 locity is half that of the water received ; but the variable part 

 being the fmaller, the rule is of little practical confequence, 

 and the velocity of the wheel is generally greater than this, 

 advantage of re- y ne au thor obierves, that by turning the ftream back upon the 

 nearer half of the wheel, we remove the refiftance of the lower 

 water, fince it runs off in the fame direction with that of the 

 water- wheel. 



Chapter 13. Of under (hot water-wheels* 



The author enters into a minute description of the parts of 

 an underfoot water-wheel : he obierves, that the moft advan- 

 tageous pofition for the floatboards in a ft raight channel is, when 



'endicutari *?' the ? are P er P endicular to the water at the time that the y rife 

 out of it: that only one half of each mould ever be below the 

 furface, and that from three to five Ihould be immerfed at once, 

 according to the magnitude of the wheel. When there is fuf- 

 ficient fall, the floatboards (hould be divided and made into 

 i buckets, fo that the wheel may become a bread wheel ; the 



pofition of the external portion being fuch, that a line drawn 

 through it at the time when the water enters, may divide the 

 vertical radius in the fame proportion that it divides the qua- 

 drant of the circumference ; that is, if the water is received, 

 for inftance, at one third of the quadrant from the bottom, the 

 line mull leave one third of the radius above it. A formula i& 

 laid down for calculating the actual force of a given ftream of 



Underfhot wheel water on a wheel, and it is fliown, that half the velocity of the 



°" ght L t( ? r w ? rk ftream is that which gives the maximum of effect, the theory 

 with half the ™ . 



velocity of the agreeing perfectly with the experiments ot Smeaton and others: 



for, fince the effect is eftimated by the product of the force into 

 the velocity of the parts upon which it acts, and fince the force 

 is in this cafe fimply as the relative velocity, becauie the quan- 

 tity of water is given, and the whole of it is fuppofedin all cafes 

 to act; therefore, the effect will be expreffed by the product of 

 the relative and abfolutc velocity of the wheel, or,c=^a; but 

 r=zv— a, v being Lire velocity of the ftream, and ra=av—aa, 

 which is obvioufly grealeft when v= ( 2a, as is evident either by 

 taking the fluxion, or by confidering that the greateft ordinate 

 of a femicircle is the radius. 



To 



ftraam. 



