42 EXAMPLES. 



Therefore, from (7) .and (8), by the principle pf work, we 

 have 



2neTl dr = 2-rrrlp dr, 



i'ss'tt 



~ V ' 



which is the same as (6). 



From (3) and (6) it follows that, to prevent a longi- 

 tudinal rupture, the wall must be made tivice as 

 thick as would be necessary to prevent a transverse 

 one. 



COR. Since p = zw [from (1) of Art. 10], (3) and (6) 

 become, respectively, 



rp rzw rp rzw 



/> ^ inn ^ ^ 



~ 2T~ 2T> ~ T ~ T ' 



that is, the thickness of similar pipes must vary di- 

 rectly as their diameter and as the pressure upon the 

 unit of surface, or in the case of a liquid, as the 

 depth of the pipe below the upper surface of the 

 liquid, and inversely as the strength of each unit of 

 section. 



A pipe which has twice the diameter, and has to sustain 

 four times the pressure of another, must be eight times as 

 thick. (See Weisbach's Mechs., Vol. I., p. 739 ; Bartlett's 

 Mechs., p. 294; Tate's Mechs., p. 268.) 



EXAMPLES. 



1. It is found that the pressure is uniform over a square 

 yard of a plane area in contact with Buid, and that the 

 pressure on the area is 13608 Ibs. ; find the measure of the 

 pressure at any point (Art. 6), (1) when the unit of length 

 is an inch, (2) when it is two inches. 



Ans. (1) 10$ Ibs. ; (2) 43 Ibs, 



