RIVER ENO IN EEIt ING. The Lews of hydraulics which apply to the flow of water In rivers may be briefly expressed as follows :—If a uniform velocity be once established, in a channel of whatsoever section, the same quantity of water must pass through that section In the same period,' of time ; and it follows from this that the velocity of the current must le increased proportionately to the diminution of the arca, If the Jame discharge take place. As the rate of flow In open channels depends entirely upon gravitation, it most increase with the inclination ; and, in order to maintain an equable discharge, the other conditions of cross section Inuit be made to agree with this Inclination. In channel/3, however, of uniform Inclination and section, the rate of flow rapidly attains uniformity; for the friction of the water upon the sides and the bottom of the beds 'loon counteracts the accelerating force of gravity. It also follows, from the effects, of the friction upon the wet contour, that the velocities of the different films of the transverse section are nevsr uniform ; because those which are in contact with the sides are retarded in their rate of flow, and they, in their turn, act to retard the flow of the films immediately around themselves ; the maximum velocity being on the surface and on the exit of the deep water—the minimum velocity on the Ind. Du Bust by direct experiment found that the mean velocity of a stream, in an open channel, might 14 expressed by the formula r=e v ; in which v represents the meat, velocity ; c, a coefficient varying between 016 and 0•89i ; and v the surface velocity. In practice it is usual to consider that, for surface velocities of from 8 inches to 5 feet per second, r= v, or that v = I 25 r ; but in large rivers It appears that, as In the Seine a= 0'62v ; and in the SOYA it r v ; the horizontal position of the line of the mean velocity seems to range between 0.89 and 0.02 of the depth considered as unity. Du Bunt also found that the bottom velocity called r=2 rv, in which r and v retained their previous trig niflcation ; and from thence we have, when v r, =015 r ; 01 r= I'33 C. It is the bottom velocity which acts by its trammortinE powers on the material,' of the bed of a river, and has the greateS effect upon the stability of its bank,.
In a channel of uniform velocity and section, If we call the discharge and the sectional area s, r retaining its signification of the meal velocity, we have q = s is, and from this r = The inclination of the bed, I, will be found by De Prony'n formula t= (o r t 6 r'), in whicl r+.• the wet tontine, or the developed length of tho wetted surface
= the sectional arm; and a and 6, coefficients, which he (adopting throughout the dimensions in metres and their subdivisiode) made respectively and Eytelwein made these co efficients a=0.000024 and but it appears that Dc Prong's values are the most correct for small channels, whilst those of Eytelwein are the most correct for large rivers. if again we call the quotient of the transverse section s by the wet contour r the mean radius, and represent it by n, we have it = , and the formula of De Prouy gives Ile n =0.0000444v + from thence we obtain r= n or r=56.86 ? u r Playfair gives this formula, in English feet and inches, 0= V0•02375I R — 0-1541131 ; and from it the value of v can be easily ascertained if 1 and it be known, or we are enabled to fix the rate of inclination 1 requisite to secure a velocity such as shall ensure that r = — when the other terms are known.
De Prong e formal se, modified, if needs be, by Eytelwein's observa tions, will serve not only to calculate the discharge, and the other con ditions of the flow of water in a regular uniform channel, hut also to calculate the conditions of the flow of water in rivers, provided a length of about 500 yards can be found upon it, where the channel is of a tolerably uniform section, and the velocity is regular. A cross section of the stream will give a and r, from whence it will be derived; and I will be ascertained by actual levelling. When the cross section is not constant the average area of a number of cross sections will suffice for ordinary calculations, and the inclination may at any time be ascertained from r by actual observation, when it is not possible to level the line of the inid-streani. If the river should happen to le divided into two branches, with marked inequalities of bed and flow, it would be preferable to consider each of them seperately. For rough approximate calculations the volume of a river may be likewise ascer tained by the formula Q=s v) in which s signifies as before the sectional area, and v the surface velocity ; but it is essential that every possible precaution should be taken to secure a correct value for v.