165 



RIVER ENGINEERING. 



RIVER ENGINEERING. 



108 



property ; such rivers are called " fluvii regales," " haut streames le 

 royal rivers " ; not as indicating the property'of the king in the 

 rive'r. but because of their being dedicated to the public use, 

 and all things of public safety and convenience being under his 

 care and protection. Thus a common highway on land is called 

 the king's highway, and navigable rivers are in like manner the 

 king's highway by water. Many of the incidents belonging to a high- 

 way on land attach to such rivers. Accordingly any nuisances or 

 obstructions upon them may be indicted even though the nuisances 

 be in the private soil of any person ; or the nuisances and obstructions 

 may be abated by individuals without process of law. It must not 

 however be inferred that all the incidents of a land highway attach to 

 rivers. Thus, if the highway of the river is obstructed, a 

 iesiii|ji will not be justified, as he would be in the case of a land 

 \; in passing over the adjacent land. And though a river is a 

 public navigable river, there is not therefore any right at common law 

 for parties to use the banks of it as a towing-path. 



If a river which is private in use as well as in property be mode 

 navigable by the owner, it does not therefore become a public river 

 unless from some act it may be presumed that he has dedicated it to 

 the public. The taking of toll is such an act Callis says that the 

 soil of the sea and of royal rivers belongs to the king. But the 

 expression, if intended to apply to all parts of the rivers where the 

 public have a right of passage, appears too comprehensive. 



But there i* no doubt that in some such rivers the property may be 

 in the crown ; 'as it was in the river Thames, the property in which, 

 both as to the water and the soil, was conveyed by charter to the lord 

 mayor and citizens of Ixmdon. And in all rivers as far as the tide 

 flown, the property of the soil is in the king, if no other claims it by 

 prescription. In navigable rivers where the tide flows, the liberty of 

 fishery, is common and public to all persons. (Hale, ' De Jure Maria et 

 Brachiorum ejusdem' ; Callis, ' On Sewers.') 



The property in the mere running water is in no one; but the 

 proprietor of adjoining land a entitled to the reasonable use of it as it 

 runs by his land. "And consequently no proprietor can have the right 

 to use the water to the prejudice of any other proprietor. Without 

 the consent of the other proprietors who may be affected by his 

 operations, no proprietor can either diminish the quantity of water, 

 which would otherwise descend to the proprietors below, or throw the 

 water back upon the proprietors above. Every proprietor who claims 

 a right either to throw the water back above, or to diminish the 

 quantity of water which U to descend below, must, in order to main- 

 t.uii hit claim, either prove an actual grant or license from the 

 proprietors aflected by his operation*, or must prove an uninterrupted 

 enjoyment of twenty years. 



HIVKK ENGINEERING. The laws of hydraulics which apply to 

 the flow of water in rivers may be briefly exproMd as follow- : If .-. 

 uniform velocity be once established, in a channel of whatsoever section, 

 the same quantity of water must paes through that section in the MOM 

 periods of time ; and it follows from this that the velocity of the current 

 must be increased proportionately to the diminution of the area, if the 

 me discharge Uke place. As the rate of flow in open channels depends 

 y upon gravitation, it must increase with the inclination ; and. 

 in . .:.lcr to maintain an equable discharge, the other conditions of cross 

 section must be made to agree with this inclination. In channels 

 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 soon 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 

 never 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 axis of the deep water thi 

 minimum velocity on the 1*<1. lu Buat by direct experiment founi 

 that the mean velocity of a stream, in an open channel, might ! 

 exproaed by the formula r < v ; in which * represents the mean 

 Telocity ; e, a coefficient varying between 070 and <)! I ; and v tht 

 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 

 :.'< r ; but in large rivers it appears that, as in the Seine 

 and in the Neva it is, r = 0'75 v ; the horizontal position o 

 the line of the mean velocity sin ins to range between 0*88 and 0-92 o 

 the depth considered as unity. I in Buat also found that the bottom 

 velocity called r = 2 rv, in which * and v retained their previous sig 

 nification ; and from thence we have, when 



'3 r. It is the bottom velocity which acts by its transportin) 

 powers on the materials of the bed of a river, and bos the greates 

 fleet upon the stability of its banks. 



In a channel of uniform velocity and section, if we call the discharge 

 q, and the sectional area s, t retaining its signification of the mean 



q 

 velocity, we have <)= s r, and from this r - - . The inclination of the 



bed, I, will be found by De Prony's formula I = (a r -t- 6 r 1 ), in which 



r = the wet contour, or the developed length of the wetted surface ; 

 the sectional area; and a and '., coefficients, which he (adopting 



hroughout the dimensions in metres and their subdivision's) made 

 espectively 0'0000444 and 0-000309. Eytelwein made these co- 

 fficieuts a = 0-000024 and 6 = 0-000365, but it appears that De Prony's 

 alne.s are the most correct for small channels, whilst those of 

 Jytelwein are the most correct for large rivers. If again we 

 all the quotient of the transverse sectiou s by the wet contour 



the mean rarfiiw, and represent it by n, we have R = - , and the 

 ormula of De Prouy gives us Bi = 0-0000444 + 0-Q00309i> i '; from 

 hence we obtain r= VO-005163 + 3238-4-2SRI-0-071S5 or r = 56'86 

 0'072. Playfair gives this formula, in English feet and inches, 



= VO'023751 + 32806-6 R 1-0-1541131 ; and from it the value of r 

 an be easily ascertained if I and R be known, or we are enabled to fix 

 ,he rate of inclination I requisite to secure a velocity such as shall 



Q 



ensure that r = - when the other terms are known. 



De Prony's formulae, modified, if needs be, by Eytelwein's observa- 

 aons, will serve not only to calculate the discharge, and the other con- 

 ditions of the flow of water in a regular uniform channel, but also to 

 calculate the conditions of the flow of water in rivers, provided a 

 ength of about 500 yards can be fouml upon it, where the channel is 

 of a tolerably uniform section, and the velocity is regular. A cross 

 section of the stream will give s and r, from whence u will be derived; 

 and I will be ascertained by actual levelling. When the cross section 

 s not constant the average area of a number of cross sections will 

 suffice for ordinary calculations, and the inclination may at any time 

 ;>e ascertained from v by actual observation, when it is not possible to 

 evel the line of the mid stream. If the river should happen to be 

 Hviiied into two branches, with marked inequalities of bed and flow, 

 it wuuld be preferable to consider each of them separately. For rough 

 approximate calculations the volume of a river may be likewise ascer- 

 tained by the formula <j = 8 (O'OSv) in which s signifies as before the 

 sectional area, and T the surface velocity ; but it is essential that 

 every possible precaution should be token to secure a correct value 

 for v. 



It must not be supposed that the transverse section of any flowing 

 body of water is perfectly horizontal on its upper surface, because it 

 will be found that immediately over the portion of the section where 

 the greatest velocity prevails, the surface will be slightly raised above 

 the level of the shallower portions of the stream. In small rivers it is 

 not possible to distinguish this species of surelevation ; but in larger 

 ones it is at times strongly marked. A phenomenon of more import- 

 ance to the stability of banks consists in the existence of a zone of still 

 water, comparatively in close proximity to the shore in consequence of 

 the greater resistance to the flow through the friction of the banks ; 

 and in Uiu part of the stream may also be observed a series of small 

 cddic-i produced by the impulsion of the current. The principal direc- 

 tion of these eddies appears to be directly opposed to that of the main 

 stream; and moreover it will be found that when any obstacle is. 

 offered to the onward flow of the water, the latter will in the first 

 place heap up against this object, and finally give rise to a dis- 

 tinctly marked counter current, technically known as a buei'-iradr. If 

 the obstacle should extend across the whole stream, the upper surface 

 of the water will assume a sensibly parabolic longitudinal section, the 

 apex of which will be situated at a considerable distance up stream, 

 ;u ! I the axis upon the deep water-line. If the obstacle, however, 

 ohonlil only be upon one bank, the back-water will not extend for any 

 great distance : but it may frequently happen that the effect of the 

 counter current would be so great as seriously to endanger the stability 

 of the bank itself. The spurs, which arc in many cases introduced for 

 the purpose of defending the shores of rivers, when they extend far 

 into the stream, produce this particular etiivt ; and they may often be 

 observed to give rise to a series of eddies, currents, and luck water, 

 which wear away the shore at the points when- they are joined to the 

 land, on the upside especially. Another effect produced by a projec- 

 tion into the line of flow of a stream is that the portion of the current 

 which does not go to form the back-water, is deflected from its course, 

 and may perhaps be made to impinge in a dangerous manner on the 

 opposite bank. At any rate the current at the foot of a spur into a. 

 main stream is sure to deepen the bed of the river at its foot, and to 

 carry the channel towards the convex aide of the bank ; indeed this, 

 law holds universally, and in rivers it is always found that the deep 

 water channel follows the convex side of the meandering*, and that 

 the channel thus naturally tends to straighten itself by the more rapid 

 abrasion which takes place against the projection;*. Krom these re- 

 marks it would follow that whenever it is desired to regularise thft 

 courses of rivers it is preferable to do so by means of longitudinal 

 parallel walls, rather than by spurs ; and that the direction of the new 

 channel should be made as far as possible rectilineal, or at least with 

 curves of very large radii. M. Defontaine observed on the Rhine that 

 elbows of 8300 feet radius produced but small effects upon the In-, I. ..> 

 banks, of that river, notwithstanding that they were composed of easily 

 transported materials ; and it may be inferred from this that a liend 

 whose radius should be not less than twelve times the width of the 

 maximum water line may be admitted in permanent works of this 

 description. The above reasoning of course applies in the most exclu- 

 sive manner to rivers whose flow is in only one direction ; when the 



