244 



REPORT 1876. 



coefficient of contraction.'' and by others the " coefficient of cKscharf/e," in order 

 to find the actual discharge per unit of time. 



Th\i.s for the case of a rectangular orifice in a vertical plane face, as in 

 fig. 1 — where AY L is the level of the still-water surface, and A B C D is the 



Fijr. 1. 



Fig. 2. 



vr 



orifice, with two edges A B and C D level, and E F is an infinitely narrow 

 horizontal band extending across the orifice at a depth h below the stiU- 

 water surface-level, and having dh as its breadth vertically measured, while 

 it has Z, the horizontal length of the orifice, as its length, and where, as 

 shown in the figure, the depths of the top and bottom of the orifice below 

 W L are denoted by 7tj and 7i, respectivelj'— if q is put to denote the so-called 

 " theoretical " volume per unit of time, and Q the actual volume per unit of 

 time, it is commonly stated that 



whence 



or 





and then when c is put to denote the so-caUed '^coefficient of contraction" it 

 is stated that the actual quantity flowing per unit of time is 



Q=|cZy/29(A.,^ 



h'\ 



0) 



It is then customary to deduce from this a formula for the case of water 

 flowing in a rectangular notch open above, as in fig. 2, by taking \ = 0, and 

 so deriving, for the open notch, the formula 



^for.ofck^h^'^'^ff 



■^. iJ 



(2) 



These examples may suffice for indicating the nature of the method 

 commonly advanced ; and it may be understood that the same method with 

 the necessary adaptations is usually given for finding the flow through circular 

 orifices, triangular orifices, or orifices of any varied forms whatever. 



Now this method is pervaded by false conceptions, and is thoroughly un- 

 scientific. 



First. Throughout the horizontal extent of each infinitely narrow band 

 of the area the motion of the water has not the same velocity, and has not 



