34^ SUMMARY OF HYDRAULICS. 



rate of motion of the Ganges islefs than three miles an hour in 

 the dry months ;" that is, its fuperficial velocity. Now allow- 

 ing a little for the banks or (helving fides, we may take exactly 

 30 feet as the hydraulic mean depth ; then if the fall in two 

 miles were precifely .J, we mould have |x 30=20; and -y/20 

 =4.47 for the velocity in a fecond, or 3.05 miles in the hour : 

 which is a little greater than the obferved velocity, becaufe the 

 fall was aflumed fomewhat too great. 



Again (p. 110), " the river when full, has thrice the volume 

 of water in it, and its motion is alfo accelerated in the propor- 

 tion of .5 to 3. We may aflame, that the hydraulic mean depth 

 is doubled at the time of the inundation, whence the velocity 

 will be increafed in the ratio of 7 to 5: but the inclination of 

 the furface is probably fomewhat increafed at the fame time, 

 which may eafily be fuppofed to increafe the velocity ftill fur- 

 ther, from 1.4 to 1.7. 

 Theeffcfts of Chapter 8. Of the difcharge and the fwell in the cafe of 



We T S, <v I 1 - an weres, falls, and contractions, in rivers and canals, 

 contractions m ' * ' 



river*. The methods employed in the third chapter require here 



fome modification, fince the water arrives at the place of de- 

 fcent with a confiderable velocity ; and it is evident from me- 

 chanical, as well as from hydraulic considerations, that the 

 ultimate velocity will exceed that which is due to the depth of 

 the dream at the place of its defcent, and that it will corre- 

 f'pond to a height equal to the fum of the heights capable of 

 producing thefe velocities. Hence we may calculate the effect 

 of a bar in elevating the furface of a river ; how broad a were 

 muft be, in order to produce a certain elevation, and how much 

 water will run over a given were according to collateral cir- 

 cumftances. When a bar is below the level of the lower water, 

 we muft confider the difference of the two levels as conftitut- 

 ing the fall ; the whole of the ftream below the level of the 

 lower water deriving its additional velocity from this difference 

 only. 



The extent of the fwell produced by a given elevation of 

 the furface of a river in confequence of the effect of a were or 

 bar, may be determined by calculating from the rules for find- 

 ing the velocity of rivers, the inclination neceflary for pro- 

 ducing a given difcharge ; the depth being greater, the inclina- 

 tion immediately above the bar will be lefs, but the effect of 

 the fwell does not terminate at the point where the new furface, 

 4 if 



