882 EXPERIMENT STATION RECORD. 



notches with thin edges and full contractions to determine the accuracy of the 

 Francis and CipoUetti formulas for notches of the sizes ordinarily used in irri- 

 gation practice are reported. 



It was found that " the discharges through rectangular and CipoUetti notches 

 when plotted logarithmically do not give straight lines and therefore can not 

 be represented correctly by a formula of the type Q = CLH". It was found, 

 however, in the case of the rectangular notches experimented with and the 

 heads of water run, that a straight-line formula could be deduced that within 

 the range of the experiments gave values quite close to the experimental data. 



" The formula 



Q=3.247LH'*^- ( \^2l''^ )^'''' 



gives discharge values for 1-, 1-5, 2-, 3-, and 4-ft. rectangular notches that 

 agree within a maximum of approximatelj' 1.2 per cent and within an average 

 of 0.28 per cent with the curves plotted from the experimental data. The dis- 

 charges throughout the 0.5-ft. rectangular notch do not follow the same law as 

 those for the longer notches. The formula 



Q=1.593F'«« A+ — \j^') 

 \ 800ff2-V 



gives values consistent with the curve plotted from the experimental data. 



" The Francis formula gives values within approximately 2 per cent of the 

 actual discharges, so long as the head does not exceed one-third the length of 

 the notch. Within the limits of the experiments the formula 



Q = 3.08L'-0« fl-(1.4<HO.0O3I,) 



gives discharge values for the 1-, ISj-, 2-, 3-. and 4-ft. rectangular notches that 

 agree within a maximum of 0.7 per cent, and an average of 0.20 per cent, with 

 the values given in the curves plotted from the experimental data. The 

 formula Q=1.566H"** gives values for the 0.5-ft. rectangular notch that agree 

 within 1 per cent with the curves plotted from the experimental data. The 

 curve-line formula for rectangular notches takes account of the law of variation 

 of the discharge curves better than does the straight-line formula and, con- 

 sequently, it appears that it will give closer values for higher heads and longer 

 notches than those experimented with. 

 " The formula 



Q=3.247Zff»-"-C^:^^^*')H'»+0.609fl'2.« 



gives discharge values for the 1-, 1.5-, 2-, 3-, and 4-ft. CipoUetti notches that 

 agree within 0.5 per cent with the curves plotted from the experimental data, 

 except in the case of the lower heads on the 1-ft. notch, where the maximum 

 divergence is approximately 1.5 per cent. The discharges through the 0.!>ft. 

 CipoUetti notch do not follow the same law as those for longer notches. The 

 formula 



Q=1.593i7'-^-^«(l-fg^^,_^+0.587^». 



represents the discharges through such a notch. 



"The CipoUetti formula gives discharge values within 1.5 per cent of the 

 actual discharges so long as the head does not exceed one-third the length of 

 the crest of the notch. The formula 



Q=3.08i'-<«2fl'('-*6+<'-«»L)4.o.6.ff2-«, 



