SPHERES AND CYLINDERS 133 



112. Bursting pressure for thick cylinder. Let u t denote the ulti- 

 mate tensile strength of the material of which the cylinder is com- 

 posed. Then, from equation (79), the maximum allowable internal 

 pressure u\ is obtained from the equation 





m(a a -^) L 

 whence 



(M) .._**- 



If m is assumed to be 3J, this formula becomes 



<"> --:?& 



K<1 nations (81) and (82) give the maximum internal pressure w t 

 which the cylinder can stand without bursting. 



Problem 137. A wrought-iron pipe is 4 in. in external diameter and .25 in. 

 thick. Whut head of water will it stand without bursting? 



Problem 138. 1'nder a water head of 200 ft., what is the factor of safety in 

 the preceding problem ? 



113. Maximum stress in thick cylinder under uniform external 

 pressure. ( 'onsider a thick circular cylinder subjected only to external 

 pressure. In this case w { and equations (77) become 



Since p k is positive, the hoop stress in this case is compression. 

 I "i- a point on the inner surface of the cylinder 



2 wo? 

 r = b, p r = Q, and Ph = ^~^' 



Since the radial stress is zero on the inner surface, the equivalent 

 stress is equal to the hoop stress, that is, 



Problem 139. A wron ^it-iron cylinder is 8 in. in external diameter and 1 in. 

 thii-k. How great an external pressure can it withstand ? 



