152 HYDKAULICS AND ITS APPLICATIONS 



To get this into a form available for practical use we must write 



C' [^H*-H% I 2 - 2 W\~\- C H* 

 ' Ll5^ 13 5 Hi] "IS 6 f ' 



So that C = C' 1 1 - (|pY (2-6 - 1-5 ~\ \ . 



Equation (2) then becomes 



Q = CBV^H% (3) 



the formula obtained by integrating the expression (1) between the limits 

 H and 0. 



T> f\ 



Putting fr = H tan - , where is the angle included between the sides 



~i 2i 



of the notch, this becomes 



e = ^OV r 7tan|H* (4) 



= 4-28 C tan | JF7^ (5) 



a 



The coefficient (7 here includes both variables C' and H'. Since the 



T> 



ratio -~ is constant for any one notch, it is to be expected that the 



JjL 



value of C with different heads will be more nearly constant than in 

 the case of a rectangular notch. Experiments by Professor James 

 Thomson 1 indicate that this is so, the value increasing very slightly as the 

 head diminishes. With a right-angled notch the variation was less than 



1 per cent, under a range of heads from 2 inches to 7 inches, while with 



/i 

 a notch having sides inclined at 2 horizontal to 1 vertical (tan - = 2) 



a 



the value of C increased by about 2 per cent, as the head was 

 reduced. 



As the result of these experiments Professor Thomson estimated the 

 mean value of C for a right-angled notch as "593, thus giving a 

 discharge 



Q = 2'536 HZ cubic feet per second. 



n 



With a notch having side inclinations of 2 to 1 (tan - = 2), the mean 

 value of C was found to be '618, making 



Q = 5-29 H* cubic feet per second, 



while as the angle is still further increased, C appears to approach a 

 limiting value '620. 



1 " British Association Report," 18fil. p. 3'>1. 



