uons. 



SUMMARY OF HYDRAULICS. 31 



contaft with the fides and bottom muft be defteaed, in confe- 

 quence of the minute irregularities of the furfaces on which 

 they Aide, nearly into the fame curvilinear path, whatever their 

 velocity may be. 



At any rate we may fafely fet out with the hypothefis, that Elementary pofi- 

 the principal part of the fridion is as the fquare of the velocity. *° n > an 

 And the friction is nearly the fame at all depths : for Profeffor 

 Robifon found that the time of the ofcillation of the fluid in a 

 bent tube was not increafed by increafing the preffure againft 

 the (ides, being nearly the fame when the principal part of the 

 tube was fituated horizontally as when vertically. The fric- 

 tion will however vary according to the furface of the fluid 

 which is in contact with the folid, in proportion to the whole 

 quantity of fluid : that is, the friction for any given quantity of 

 water will be as the furface of the bottom and fides of a river 

 directly, and as the whole quantity of water in the river in- 

 verfely : or fuppofing the whole quantity of water to be fpread 

 on a horizontal furface, equal to the bottom and fides, the 

 friction is inverfely as the height at which the river would then 

 fland, which is called the hydraulic mean depth. 



Now when a river flows with an uniform motion, and is 

 neither accelerated nor retarded by the action of gravitation, it 

 is obvious that the whole weight of the water muft be employ- 

 ed in overcoming this friction ; and if the inclination vary, the 

 relative weight or the force that urges the particles along the 

 inclined plane, will vary as the height of the plane when the 

 length is given, or as the fall in a given diftance (Young's Syl- 

 labus, 54) ; confequently the friction, which is equal to the 

 relative weight, muft vary as the fall, and the velocity which is 

 as the fquare root of the friction, muft be as the fquare root of 

 the fall; and fuppofing the hydraulic mean depth to be in- 

 creafed or dimini flied, the inclination remaining the fame, the 

 friction would be diminifhed or increafed in the fame ratio; and 

 therefore in order to preferve its equality with the relative 

 weight, it muft be proportionally increafed or diminifhed by 

 increafing the fquare of the velocity in the ratio of the hydrau- 

 lic mean depth, or the velocity in the ratio of its fquare root. 

 We may therefore expect that the velocities will be conjointly The velocities 



as the fquare root of the hydraulic mean depth and of the fall Wl11 be ? s a m , ean 

 . J • , , ,/- proportional be- 



in a given diftance, or as a mean proportional between tnele tween the hy- 



rwo lines. Taking two Englifh miles for a given length, we drau hc meaa 

 00 n de P th and the 



muftfal]; 



