CURVED WEIRS 



147 



heads from '3 to 1*7 feet the variation from the formula of either 

 Francis or Bazin in no case exceeded 1'7 per cent., while the variation 

 from the Hamilton Smith formula increased steadily from '7 per cent, 

 with '3 foot head to 7 '9 per cent, with 1*7 feet head. 



Discharge over a Curved Weir. Where a curved weir has a large radius 

 of curvature, and discharges radially inwards, the discharge per foot run 

 may be expected to be but slightly less than the discharge over a straight 

 weir under the same head. 



An extreme case of the curved weir with inward or outward flow is found 

 in the case of flow over the upper edge of an open vertical stand pipe. 



Experiments carried out at Cornell University 1 on a series of snch 

 pipes of diameters 2, 4, 6, 9, and 12 inches with outward flow, show that, 

 if D is the diameter in feet, for heads less than '028 D 1 * 04 the flow is 

 similar to that over a sharp-crested weir, while for heads greater than 

 '107 i) 1<03 the flow becomes similar to that of a jet. 



The discharge for weir flow is given by the formula 

 Q = 8'8 Z) r29 H 1 cub. ft. per sec. 



(} 1-29 

 I H I 



Here I is the length of the crest, I and H both being in feet. 

 For jet flow the discharge is given by 



Q = 5-7 D 2 H ' 58 c.f.s. 



= CA VT^H' 53 c.f.s. 

 where A is the area and G = '905. 



In similar experiments on pipes of 6*9, 10*1, 13*7, 19'4, and 25'9 inches 

 outside diameter, with flow radially inwards, 2 the discharge was given by 



Q = K I H 1 42 cub. ft. per sec. 

 where K has the following values : 



These constants hold for heads up to one-fifth of the diameter of 

 ihe weir. 



1 Proc. Am. Soc. O.K.," 1906, p. 479. 



H. J. F. Gourley, Proc. Inst. C.E.," vol. 184, 191011, pt. 2, p. 297. 



L 2 



