WATER. 



ftiall be difcliarged, we mult know the mean velocity of the 

 water. 



Ratit between the mean Velocity of running Water am! the 

 Velocity of the Top and Bottom of a Channel. — M. Du Buat 

 ftates, that the i'upeificial velocity of a flrtam of water 

 always bears a certain relation to the mean velocity, fo that 

 we can derive one from the other by an arithmetical rule. 



From a great number of experiments, he difcovered the 

 following laws : ill, That the velocity at the furface in the 

 middle of the Itream, (in flow motions, ) is to the velocity at 

 the bottom of the ftream, in a ratio of confiderable inequa- 

 lity. 2d, This ratio diminiflies as the velocity increafes, and 

 in very great velocities approaches to the ratio of equality. 

 3d, What was moft remarkable, was, that neither the mag- 

 nitude of the channel, nor its flope, had any influence in 

 changing this proportion, whilft the mean velocity remained 

 the fame. Whether the ftream ran in a channel with the 

 bottom covered with pebbles, or coarfe fand, the propor- 

 tions between the two velocities was, as nearly as poflible, 

 the fame as when it ran in a fmooth channel. 4th, If the 

 velocity at the furface in the middle of the ftream be con- 

 ftant, the velocity at the bottom will be alfo conltant, and 

 will not be affcfted by the depth of water or magnitude of 

 the ftream. In fome experiments, the depth was thrice the 

 width, and in others the width was thrice the depth. This 

 changed the proportion of the magnitude of the feftion, 

 to the magnitude of the rubbing part, but made no change 

 in the ratio between the velocities at the top and bottom. 



The place of the mean velocity in the feftion of the 

 ftream could not be difcovered with any precifion. In 

 moderate velocities, it was not more than one-fourth or one- 

 fifth of the depth diftant from the bottom. In very great 

 velocities, it was fenfibly higher, but never in the middle of 

 the depth. 



In all cafes he computed the mean velocity by meafur- 

 ing the quantities of water difcharged in a given time. His 

 method of meafuring the bottom velocity was fimple, and 

 probably juft ; he threw in a goofeberry, as nearly as poflible 

 of the fame fpecific gravity with the water ; it was carried 

 along the bottom without touching it. We have already ob- 

 ferved, that the ratio between the velocity at the furface in 

 the middle, and the velocity at the bottom, diminiftied as the 

 mean velocity was increafed. This variation lie was enabled 

 to exprefs in a very fimple manner, fo as to be eafily re- 

 membered, and to enable us to find any one of them from 

 having obferved another. 



Dr. Robifon ftates, that if we take unity from the fquare 

 root of the fuperficial velocity, in the middle of the ftream, 

 exprefled in inches/icr fecond, the fquare of the remainder is 

 the velocity at the bottom ; and the mean velocity is the 

 half fum of thefe two. Thus, if the velocity of the furface 

 in the middle of the ftream be twenty-five inches per fecond, 

 its fquare root is five ; from which if we take unity, there 

 remains four. The fquare of this, or 16, is the velocity 



at the bottom, and ~ — - — -, or 20^, is the mean velocity. 



This is a very curious and moft ufeful piece of inform- 

 ation. The velocity of the furface in the middle of the 

 ftream, is the eafieft meafured of all, by any light fmall body 

 floating down it, or by a ftream-meafurer ; and the mean 

 velocity is the one which regulates the difcharge, and all 

 the moft important confequcnces. 



Dr. Robifon gives the following table of thefe three 

 velocities, which will fave the trouble of calculation in fome 

 of the moft frequent queftions of hydraulics. 



The knowledge of the velocity at the bottom is of life to 

 an engineer, to enable him to judge of the aftion of a ftream 

 on its bed. Every kind of foil will bear a certain velocity 

 without changing the form of the channel. A greater velo- 

 city would enable the water to tear it up, and a fmallcr ve- 

 locity would permit the depofition of more moveable mate- 

 O 2 rials 



