ENGINEERING STRUCTURES 133 



and a cross-sectional area ' a ' square feet. Let this com- 

 municate at its inner end directly with the surface of the 

 enclosed water, and imagine a frictionless piston to form a 

 definite boundary between the entrapped air and the impinging 

 column of water. Let ' x ' be the distance to which this 

 column penetrates on its first impact. 



If the column loses no energy during its entry to, and passage 

 up, the joint, the energy given up by it when it has come to 



v 2 



rest equals 62*4ax foot Ibs. 1 

 2*7 



Equating this to the work done on the air during com- 

 pression, and assuming this, because of the rapidity with 

 which it takes place, to be adiabatic we have 



; 2 

 '2g' aX 



where p a is the initial atmospheric pressure (2120 Ibs. per 

 square foot) and p is the final air pressure. Substituting for 

 p l in terms of p a we finally get 



62-4,. -^{(4- 

 2(7 -4 (Mi 



and if ^-=100 this simplifies to 



62-4 



x 



The value of the ratio x-l, which satisfies this equation is 

 independent of Z, and is equal to *81, in which case 



(1 V' 4 

 ^JQ) =10*25 atmospheres, 



=21,700 Ib. per square foot, 

 =9 ! 7 tons per square foot. 



1 This assumes fresh water of weight 62'4 Ibs. per cubic foot. As fresh water was 

 used in the author's experiments this value has been adopted in these calculations. 



M* 



In the case of sea water the value would be 64aa; foot Ibs. 



2<7 



