THE FLOW OF WATEE IN" WOOD-STAVE PIPE. 



51 



No. V H 



logV 





logH 





272 5. 942 0. 5144 0. 7739 





9.7133] 





273 6.127 .6426 



.7873 



fSum=4. 7756 



9. 8079 



rSum=58. 8637 



274 6. 190 . 6154 



.7917 



lMean=.7959=b^ 



9.7892 



lMean=9.8106=bH 



275 6.312 .6938 



.8001 



1 Anti-log mean 



9. 8412 



|Anti-log mean 



276 6.436 .7237 



.8086 



[ =6.250 



9. 8595 



[ =0. 6466 



277 6.516 .7155 



. 8140J 





9. 8546 





278 6.693 .7700 



.8256 



fSum=3. 4915 



9. 8865" 



fSum=39. 8249 



279 6.852 .7490 



.8358 



lMean= .8729=av 



9. 8745 



lMean= 9. 9562=aH 



280 8.222 1.061 



.9150 



1 Anti-log mean 



10. 0257 



1 Anti-log mean 



281 8.223 1.092 



. 9151, 



[ =7.463 



Sum= 



10. 0382, 



I =0. 9040 



Sum= 



8.2671 



=98. 6886 





Mean= 



.8267 



=Cv Mean= 



-- 9.8689= 



=Ch 



Anti-log mean= 



6.710 



Anti-log mean 



=0. 7393 





The center of gravity of the whole series thus comes at such a point 

 that there are 4 points below and 6 points above c. Then 



ay — Cv = .0462, and an — Ch = .0873 ; 



whence ; 



Cv - bv = .0308, and Ch - bn = .0583 ; 



0.0462 ^ 0.0873 _ 6 

 0.0308 0.0583 4 



When the above ratios are in inverse proportion to the number of 

 observations in the respective zones the three points found he in the 

 same straight line and approve the mathematical operations. 



The exponent of V in formula 17 is the inchnation of the Hne acb 

 and is equal to the tangent of the angle formed by the curve and the 

 axis of V. Thus 



an— bi 



.1456 



av-bv .0770 



= 1.891 =z. (See No. 51, column 17, Table 3.) 



The intercept m is found as follows: Since log m=log H — z log V 

 (from formula 18, p. 49), by using the coordinates of the center of 

 gravity c 



log m = 9.8689 -1.891 X 0.8267 

 log m = 8.3056, therefore m = 0.02021 



In the same manner the exponent of V for each of the pipes 

 underscored in Plate VII was determined, being foimd to vary from 

 1.53 for No. 36 to 2.31 for No. 42. Any general law of variation in 

 this exponent was not considered in their formulas by Moritz, Wil- 

 hams and Hazen, or the writer, although Hazen sees a tendency for 

 the exponent to increase with the size of the pipe,^ while Wilhams 

 later offered the deductions mentioned on page 11. Simultaneous 

 values of diameter and exponent were plotted on logarithmic paper. 



1 Trans. Amer. Soe. Civ. Engin., 51 (1903), p. 320, 



