-11- 



Table 1 contains those values of the whole number n for the above given 

 values of a// and for intervals equal to 0,002 of the ratio h/a, which give the 

 least critical pressure. The table is made from direct readings from Figs. 3 and 7- 



Further, Table 2 also contains the magnitudes of the least critical 

 pressures, for the same values of a// and h/a. Equation (D) is the basis for 

 calculations, but improvements are taken into consideration with regard to the 

 more exact equations (A) and (B). The values of p given in the table are valid 

 for an elastic modulus of E = 2,000,000 kg/cm^ (28 x 10 lbs. per sq. in.) and can 

 be changed for metals with another modulus E* in the ratio E'/E. 



In both tables those values are cut off at the lower right hand side 

 which correspond to stress of more than l800 kg/cm^ (25,600 lbs. per sq.in. ) 





1 





/4 



A' 



/' 













1 / 



1 ' 



-7 

 / 



/ 





v 



r^'J^ 



-^ 



M 







hi 



w 















"/ 



li 



y 



y^ 













1 



y 





/ 



.J^ 



^ 



--^ 



Jo' 





k 



S- 



^^ 







O.OOOOi- 







> 



Fig. 7* Fig. 3 to a larger scale. 



lOOh 



0.2 



0.4 



0.6 



0.8 



1.0 



1.2 



1.4 



1.6 



1-0 



0.1 

 0.2 



0.; 

 0.4 

 0.5 



2 



5 

 6 

 7 

 8 



2 



5 



4 

 5 

 6 

 5 



2 



3 

 4 

 5 

 5 



6 



2 

 5 

 4 

 4 

 5 



2 



2 



3 

 4 



2 

 2 



5 



2 

 2 



3 



2 

 2 



4 

 4 

 4 



4 

 4 

 5 



4 

 4 

 5 



5 

 5 



5 



TEble 1. 

 The number of lobes n around the circmuTerence for various 

 wall thicknesses 2h and tube lengths 1, 





lOOh 



" 0.2 



0.4 



0.6 



0.8 



1.0 



1.2 



1.4 



1.6 



r- 







0.1 



0.2 



0.3 

 0.4 

 C.5 



0.055 

 o.i8 

 0.37 

 0.56 

 0.76 

 0.97 



0.28 

 1.0 

 2.1 

 3-2 

 4.5 

 5.5 



0.95 



2.9 



5.9 

 9.5 



11.6 

 15 



2.25 

 6.6 



13 



18 



25 



4.4 



12.3 



21 



32 



7.6 

 17 

 32 



12 



23 

 47 



18 

 31 



66 

 111 

 140 

 190 



51 



70 



87 



76 

 101 



132 



45 

 55 



32 



Efj- ^ 1800 (21) 



In the same way, a dotted line is 

 drawn in Fig, 5» which corresponds 

 to eq. (21), namely 

 y = p 



Table 2. 

 Critical proasure p in kg. per aq. 

 neaaes 21i and tube lengtha 1 for E 



.19 T 10-* 



We will return to the significance 

 of this demarcation immediately. 



If the values of h, a, and / 

 are such that the tables are not 

 sufficient, we must determine the 

 pressure p for various values of n 

 from eq. (D), The determinative val- 

 ue is then the least of these values^ 

 In Fig. 8 are represented on the co- 

 ordinates a/1 and 100 h/a the lim- 

 iting lines that separate, for ex- 

 ample, the region in which n = 3 

 gives the smallest value of p from 

 the region in which n = 2 or 4 is de- 

 terminative. The use of Fig. 8 saves 

 many trials. 



