156 HYDRAULICS AND ITS APPLICATIONS 



sides, and the discharge Q due to a head H is obtained by adding the values 

 of Q, as calculated for two such notches. 



5Cifl + -C,totffl (1) 



Assuming Ci = C% = C this becomes 



Q = C V^JH* || b + ^ H tan 0}. (2) 



Francis's formula for a rectangular notch shows that the two end 

 contractions reduce the effective breadth by '2 H, and the discharge by 

 an amount 



2 H X ! C V^g .H% = ^C VZg.BP. 



If then the ends of the weir, instead of being vertical, are inclined out- 

 wards so that the added area counterbalances the increased contraction 



of section of the stream, the coefficient K in the formula Q = K b H^ 

 should be independent of the head. 

 For this to be so we have 



== C V 2 g . H* = ^ C V 2 g tan H 2 , 

 15 15 



so that tan 9 = \, or the sides are to be inclined outwards with a slope of 

 1 in 4. This is termed a Cippoletti l Weir. 



From his own experiments and those of Francis, on heads from 3 to 24 



* 3 



inches, Cippoletti made Q = 3*367 b H 2 cub. ft. per sec., the Francis 



velocity correction being used. 



Experiments by Messrs. Flinn and Dyer* on weirs having sill lengths 

 of from 3 feet to 9 feet, and heads from -3 foot to T25 feet, gave, as the 

 mean of thirty-two experiments, K = 3'283. In this formula, however, 

 the velocity correction of Hamilton Smith (effective head H -f- 1*4 h) 

 was used. Had the Francis correction been applied this coefficient would 

 have been in close accord with that of Cippoletti. 



If Ci = *623 (Francis mean value) and <7 2 = '593 (Thomson's value for 

 a right-angled notch), the inclination of the sides becomes 1 to 4*2. 

 Experiments by J. C. Stevens 3 on weirs having lengths of 6 inches and 

 of 1, 2, and 3 feet, with side inclinations of 1 to 4, and with heads ranging 

 from '08 foot to *8 foot, indicate that for small lengths, the discharge is 



1 First described by C. Cippoletti. See " Giornale del Genies Civiles," 1886. 



2 "Trans. Am. Soc. C.E.," vol. 32, 1894, pp. 933. 



8 Engineering News, New York, August 18, 1910, p. 171. 



