HYDRODYNAMICS. 



M.nion of 

 Water in 



The numbers in column 5 of the following Table 

 have been computed from the formula 



u = o- 816458 v > 



which gives a precision of between T V and 

 a simplification of the preceding formula. 



, and is Motion , 



Water i 



Pipes an 



CanaU. 



TABLE V. 



Containing Ike observed mean Velocities of Water, compared with those deduced from the superficial 

 Velocities by the Formuhe of Du JBuat and Prony. 



The agreement of the numbers in column 7, with 

 those in column 3, is very striking ; and it is remark, 

 able that the numbers in column 5, calculated from 

 Prony's simple formula, viz. U ^ 0,816458 V, are more 

 accordant with experiment than those in column 4, com- 

 puted from Du Buat's formula. This formula may 

 be reduced to 



U = 0.82 V, or even U = 0.8 V, 



from -which it follows that the mean velocity is four- 



fifths of the superficial velocity. 



Formula Jn order to introduce into the equation which ex- 



for finding p re sses the velocity, the value of the volume of water 

 tie of water wnich flows throu g n anv section in a given time, 

 discharged. Prony calls Q the volume of water, and 3.1416= . 



4 Q 

 and hence U= vjp an ^ these being introduced into 



the equation %gjl) = *U + 'ft U * where * 0.00017, 

 and /s = 0.003*16, gives 



gives 



j D 5 * ' Q D* ft' Q 2 = 0, or since 



a' = 0.000088268 and ft' 0.002258305, we have 

 j D 5 0.000088268 Q D l 0.00225830 Q = 0, 



which expresses the relation between the diameter of a 

 pipe, the quantity of water which it discharges in a se- 

 cond, when its length, its declivity, and the heads of 

 water above its upper and lower orifices are known. 



In this equation^' = - . 



In order to facilitate the application of this formula, 

 Prony has computed the following Table, which gives 

 the relations between D, Q andj, as deduced from the 

 above equation. 



the quanl 

 ties of wa 

 discharge 



