WATER. 



rials from above. It is not enough, then, for the perma- 

 nency of a river, that the accelerating forces are fo adjufted 

 to the fize and figure of its channel, that the current may ac- 

 quire an uniform velocity, and ceafe to accelerate. It muft 

 alfo be in equilibrio with the tenacity of the channel. 



It appears from obfervation, that a velocity of three 

 inches per fecond at the bottom, will jiift begin to work upon 

 fine clay fit for pottery, and however firm and compaft it may 

 be, it will tear it up. Yet no beds are more liable than 

 clay, when the velocities do not exceed this, for the water 

 foon takes away the impalpable particles of the fuperficial 

 clay, leaving the particles of fand fticking by their lower 

 half in the reft of the clay, which they now proteft, making 

 a very permanent bottom, if the ftream does not bring down 

 gravel or coarfe fand, which will rub off this very thin 

 cruft, and allow another layer to be worn off. A velocity 

 of fix inches per fecond, will lift fine fand ; eight inches will 

 lift fand as coarfe as linfeed ; twelve inches will fweep along 

 fine gravel; twenty-four inches will roll along rounded 

 pebbles an inch in diameter ; and it requires three feet per 

 fecond at the bottom to fweep along Ihivered angular ftones 

 of the fize of an egg. 



Dr. Young gives an excellent fimple rule for the fame ob- 

 jeft, which is only a trifle different from Dr. Robifon's ; he 

 Hates, that from a mean of all the beft. experiments, he found 

 that, if the fquare root of the mean velocity of any ftream 

 (running in an uniform open channel) be added to fuch mean 

 velocity, it will give the fuperficial or top velocity in the 

 middle ; or if dedufted therefrom, it will leave the bottom 

 velocity : whence we have deduced the foUowsing practical 

 rule, w'z. 



1. Having found the top velocity, expreffed in any con- 

 venient meafure, which will correfpond with the refult 

 required. 



To find the bottom velocity, add the conftant number .25 

 (or ^) to the top velocity ; extraft the fquare root of the 

 fum, and double it ; again add i to the top velocity, and 

 from the fum deduft the double root before found : the re- 

 mainder is the bottom velocity of the ftream. 



2. To find the mean velocity from the top velocity, add 

 the conftant number .5, (or i'l to the top velocity, and from 

 their fum deduft the fquare root found in the firft rule ; 

 the remainder is the mean velocity. 



Or, 3. To find the mean velocity from the bottom velo- 

 city, add the conftant number .25, (or \) to the bottom ve- 

 locity, and extraft the fquare root of the fum ; then to this 

 fquare root add the bottom velocity, and the conftant num- 

 ber, .5, and their fum is the mean velocity. 



Thefe are true in all cafes, provided the top and bottom 

 velocities are related to each other, as Dr. Young ftates. 

 For example, Mr. Watt obfcrved the furface of the water 

 in an open canal to move with a velocity of 17 inches ^fr fe- 

 cond : What was the bottom velocity ? 



By our firft rule 1 7 -|- .25 = 1 7.25, of which extraft the 

 fquare root; it is 4.15 ; twice this is 8.3. Again, to 

 the top velocity 17 add i = 18, and deduft 8.3, it leaves 

 9.7 for the bottom velocity. Mr. Watt obferved the bot- 

 tom velocity to be 10 inches per fecond. 



2. To find the mean velocity, add .5 to the top velocity 

 17, it gives 17.5 ; deduft 4.18, and we get 13.32 inches 



per fecond for the mean velocity. 



3. If we take Mr. Watt's obfervation of the bottom ve- 

 locity of 10 inches ^fr fecond, inftead of the top ; then to 

 fiodthe mean velocity 10-)- .25= 10.25, of which the fquare 

 root is 3.201 ; and 10 -|- .5 = 10.5 ; add thefe together, 

 thus (3.201 -f- 10.5) = 13.701 inches />£•>• fecond for the 



mean velocity ; which only exceeds that deduced from the 

 top velocity by little more than ^d of an inch in a 

 fecond. 



By the aid of this rule, and the wheel ftream-meafurer 

 before defcribed, great accuracy may be obtained. Care 

 mull be taken to apply the wheel in the centre of the ftream, 

 on the furface, or rather at that place where the velocity of 

 the furface is found to be the greateft. 



Second Method of tneafuring the Flotving of Water in an 



open Canal When a river flows with an uniform motion, 



and is neither accelerated nor retarded by the aftion of 

 gravitation, it is obvious that the whole weiglit of the water 

 muft be employed in overcoming the friftion of the water 

 again ft the bottom and fides. 



The principal part of this friftion is as the fquare of 

 the velocity, and the friftion is nearly the fame at all depths : 

 for profelfor Rnbifon found, that the flow of the fluid 

 through a bent tube was not increafed by increafing the 

 preffure againft the fides, being nearly the fame when the 

 bended part of the tube was fituated horizontally, as when 

 vertically, the fame difference of level being preferved. 



The quantity of friftion will, however, vary, according 

 to the furface of the fluid which is in contaft with the folid, 

 in proportion to thi whole quantity of fluid ; that is, the 

 friftion for any given quantity of water will be, as the fur- 

 face of the bottom and fides of a river direftly, and as the 

 w'hole quantity of water in the river inverfely; thus, fup- 

 pofing the whole quantity of water to be fpread on a hori- 

 zontal furface equal to the bottom and fides of the river, 

 the friftion is inverfely as the depth at which the river 

 would then ftand. This is called the hydraulic mean 

 depth. 



If the inclination or flope of the furface of water in a 

 river varies, the defcending weight, or the force that urges 

 the particles down the inclined plane, will vary as the 

 height of the fall in a given diftance ; confequently, the 

 friftion, which is equal to the defcending weight, muft 

 vary as the fall ; and the velocity being as the fquare root 

 of the friftion, muft alfo be as the fquare root of the fall. 

 Suppofing the hydraulic mean depth to be increafed or 

 diminiflied, the iiichnation remaining the fame, the friftion 

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

 therefore, in order to preferve its equality with the defcend- 

 ing weight, the friftion muft be increafed or diminiflied, by 

 increafing the velocity in the ratio of its fquare to the 

 ■ hydraulic mean depth ; that is, increafing the velocity in the 

 ratio of the fqu.ire root of the hydrauhc mean depth. 



Mr. Eytelwein's Rule is, that the velocity of a ftream will 

 be in the joint proportion of the fquare root of the hydraulic 

 mean depth, and the fquare root of the fall in a given diftance ; 

 or as a mean proportional between thefe two quantities. 



Taking two Englifti miles for a given length upon a 

 ftream, we muft find a mean proportional between its hy- 

 draulic mean depth and its fall in two miles in inches, and 

 inquire what relation this bears to the velocity in a par- 

 ticular cafe. We may thence expeft to determine it in any 

 other. According to Mr. Eytelwein's formula, this mean 

 proportional is -{.^ths of the velocity in a fecond in inches. 



In order to examine the accuracy of this rule, we may 

 take an example, which could not have been known to Mr. 

 Eytelwein. Mr. Watt obferved, that in a canal 18 feet wide 

 .ibove, and 7 below, and 4 feet deep, having a fall of 4 inches 

 in a mile, the velocity was 17 inches per lecond at the fur- 

 face, 14 in the middle, and 10 at the bottom. The mean 

 velocity may be called I3f inches, in a fecond. Now to 

 find the hycjrauhc mean depth, we muft divide the area of 



the 



