ON HYDRAULICS AS A BRANCH OF ENGINEERING. 171 



tube was not increased by increasing the pressure against the 

 sides, being nearly the same when the principal part was si- 

 tuated horizontally, as when vertically. The friction will, how- 

 ever, vary, according to the surface of the fluid which is in 

 contact with the solid, in proportion to the whole quantity of 

 fluid ; that is, the friction for any given quantity of water will 

 be as the surface of the bottom and sides of a river directly, 

 and as the whole quantity in the river inversely ; or, supposing 

 the whole quantity of water to be spread on a horizontal sur- 

 face equal to the bottom and sides, the friction is inversely as 

 the height at which the river would then stand, which is called 

 the hydraulic mean depth*." It is, therefore, calculated that 

 the velocities will be a mean proportional between the hydraulic 

 mean depth and the fall, or -j-^tlis of the velocity per second. 



Professor Robison informs us, that by the experiments of 

 Mr. Watt on a canal eighteen feet wide at the top, seven feet 

 at the bottom, and four feet deep, having a fall of four inches 

 per mile, the velocities were seventeen inches per second at the 

 surface, fourteen inches per second in the middle, and ten inches 

 per second at the bottom, making a mean velocity of fourteen 

 inches per second ; then finding the hydraulic mean depth, and 



dividing the area of the section by the perimeter, we have „„ „ , 



or 29*13 inches ; and the fall in two miles being eight inches, 

 we have v'(8 x 29*13) = 15*26 for the mean proportional of 

 ■j-^ths, or 13*9 inches, which agrees very nearly with Mr. Watt's 

 velocity. 



The Professor has, however, deduced from Dubuat's elabo- 

 rate theories 12*568 inches. But this simple theorem applies 

 only to the straight and equable channels of a river. In a 

 curved channel the theorem becomes more complicated ; and, 

 from observations made in the Po, Arno, Rhine, and other 

 rivers, there appears to be no general rule for the decrease of 

 velocity going downwards. M. Eytelwein directs us to deduct 

 from the superficial velocity ^-^^ for every foot of the whole 

 depth. Dr. Young thinks y^g*^^ ^^ *^^ superficial velocity suf- 

 ficient. According to Major Rennell, the windings of the river 

 Ganges in a length of sixty miles are so numerous as to reduce 

 the declivity of the bed to four inches per mile, the medium 

 rate of motion being about three miles per hour, so that a mean 

 hydraulic depth of thirty feet, as stated to be f rds of the 

 velocity per second, will be 4*47 feet, or three miles per hour. 

 Again, the river when full has thrice the volume of water in it, 

 and its motion is also accelerated in the proportion of 5 to 3 ; 



* See Nicholsons Journal for 1802, vol. iii. p. 31. 



