32 



SUMMARY OF HYDRAULICS. 



a pra&ical in 

 fiance 



muft find a mean proportional between the hydraulic mean 

 depth and the fall in two miles, and inquire what relation this 

 bears to the velocity in a particular caie, and thence we may- 

 or n-ioths of expect to determine it in any other. According to Mr. 

 fccond. OCty *** Eytelwein^s formula, this mean proportional is |£ °* tne ve ^°" 



city in a fecond. 

 Confirmation by 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, as Profeflbr Robifon informs 

 us in the article River of the Encyclopaedia Britannica, that in a 

 canal 18 feet wide above, and 7 below, and 4 feet deep, having 

 a fall of 4 inches in a mile, the velocity was 17 inches in a fe- 

 cond at the furface, 14 in the middle, and 10 at the bottom : fo 

 that the mean velocity may be called 14 inches, or fomewhat 

 lefs, in a fecond. Now to find the hydraulic mean depth, we 

 mud divide the area of the feclion, 2. (18-}-7)=50 by the 

 breadth of the bottom and length of the Hoping fides added toge- 

 50 



ther, whence we have 



20.6 



or 29.13 inches: and the fall in 



Another in- 

 fiance. 



True only In a 

 ftrait river, &c. 



Slope of the 

 banks. 



two miles being 8 inches, we have A /(8x29.13) = 15.26 for 

 the mean proportional, of which 4r * s 13.9; agreeing exaclly 

 with Mr. Watt's obfervation. Profeffor Robifon has deduced 

 from Buat's elaborate theorems 12.568 inches for the velocity, 

 which is confiderably lefs accurate. 



For another example we may take the Po, which falls 1 foot 

 in two miles, where its mean depth is 29 feet; and its velocity 

 is obferved to be about 55 inches in a fecond. Our rule gives 

 58, which is perhaps as near as the degree of accuracy of 

 the data will allow. 



On the whole, we have ample reafon to be fatisfied with 

 the unexpected coincidence of fo limple a theorem with obfer- 

 vation: and in order to find the velocity of a river from its 

 fall, or the fall from its velocity, we have only to recollect that 

 the velocity in a fecond is 44 or * a mean proportional between 

 the hydraulic mean depth and the fall in two Englifh miles. 

 This is however only true of a ftraight river flowing through 

 an equable channel. 



For the Hope of the banks of a river or canal, Mr. Eytelwein 

 recommends that the breadth at the bottom fliould be -| of the 

 depth, and at the furface y : the banks will then be in gene- 

 ral capable of retaining their form. The area of fuch a fecrion 



