g8 KANSAS UNIVERSITY QUARTERLY. 



plane surface whose area equals that of the projection of the curved 

 surface. This would make the value of K=i.73. 

 Substituting for K this value in (13) we have 



Lg:=.oo4ic3 (14) 



Substituting for c the values 8, 10 and 12 miles per hour, we 

 have for Lg the values 6.7, 13.0 and 22.4 ft. lbs. of work per sec- 

 ond respectively. 



Case II. 

 Fans rectangular and x constant. 



Making these substitutions in (6 ) we have 



/\L=:K— ^ ^ COS X c-^rsin2xR3AR— 24','-sinxcosxR2/\R + 

 g Rn Rn L CR„ 



Making A L andAR infinitesimal and integrating between limits 



we have 



r V r R - R ~ V R 3 R 3 



1-. nnc; v r •' I 'iin^x -7 sm X COS X ^ 



C 3Rn' 



L'r=K 1)„ — ^cos X C'"^ sin^x — - — — — — — 2 "sinx cos x 

 c L 2R„ 



I I cos^x =, I 



Substituting t=-:|y^* and multiplying In' n to get the power of the 

 Iv,, 



wheel wc have 



L^=K -n "cos X c-*R„ - sin-x — 2--^sin x cos x( | + 



L 2 c V 3 / 



c 



(v)M"r')] '- 



Cask III. 



The fans witli warped surfaces. 



We may find an approximate vahu,' of the poAver by dividing the 

 fans into strips, x, R and v being variable, and applying (12) or 

 (15), as the case may be to each strip, and adding the results. If 

 the fans are rectangular we have 



L, =:=Kn cos x,c-^R, ' sin-x, — 2 — !-sm x^ cos x, ' + 



] gc '^L2 'c ^ 3 



,. r v., .^^ fi^t! . „ v., . /I — tin 



Kn -cos x.,c-^Rol 'sm-x., — 2 — =sin x., cos x„( - " j 



g c - "L 2 - c - 'V 3 / 



Then L=L,-fL2 + L, (16) 



L2 



g c 



Lg^ etc. 



