ON HYDRAULICS AS A BRANCH OF ENGINEERING. 173 



In the allowance for flexure, the product of its square, multi- 

 plied by the sum of the sines of the several angles of inflection, 

 and then by '0038, will give the degree of pressure employed 

 in overcoming the resistance occasioned by the angles ; and de- 

 ducting this height from the height corresponding to the velo- 

 city, will give the corrected velocity*. 



M. Eytelwein investigates, both theoretically and experi- 

 mentally, the discharge of water by compovind pipes, — the mo- 

 tions of jets, and their impulses against plane and oblique sur- 

 faces, as in water-wheels, in which it is shown that the hydraulic 

 pressure must be twice the weight of the generating column, as 

 deduced from the experiments of Bossut and Langsdorft ; and 

 in the case of oblique surfaces, the effect is stated to vary as the 

 square of the sine of the angle of incidence ; but for motions 

 in open water about f ths of the difference of the sine from the 

 radius must be added to this square. 



The author is evidently wrong in calculating upon impulse 

 as forming part of the motion of overshot wheels; but his 

 theory, that the perimeter of a water-wheel should move with 

 half the velocity of a given stream to produce a maximum effect, 

 agrees perfectly with the experiments of Smeaton and others-}-. 



The author concludes his highly interesting work by exa- 

 mining the effects of air as far as they relate to hydraulic ma- 

 chines, including its impulse against plane surfaces on siphons 



* Hence, if / denote the height due to the friction, 

 d = the diameter of the pipe, 

 a = a constant quantity, 



we shall have, / = V^ ^ and V^ = -^J^. 



' a a I 



But the height employed in overcoming the friction corresponds to the differ- 

 ence between the actual velocity and the actual height, that is, f= h — -r^, 

 where b is the coefficient for finding the velocity from the height. 



Hence we have, V^ = ^^-^ and V = V — -. 



ab^ I ab^l -\- d 



Now Duhuat found b to be 6-6, and a b^ was foimd to be 0-02 11, particularly 

 when the velocity is between six and twenty-four inches per second. Hence 



or more accurately, V =: 50 V ( ^ ^ |. 



^ \l+50d/ 



+ The author of this paper has made a great many experiments on the max- 

 imum effect of water-wheels ; but the recent experiments of the Franklin Insti- 

 tution, made on a more magnificent scale, and now in the course of trial, eclipse 

 everything that has yet been effected on this subject. See also Poncelet, Me- 

 moire sur les Roues Hydraidiques, and Aubes Courbes par dessovs, ^c. 1827. 



