EXAMPLES. 49 



38. If the height of the wall be 8 ft, its thickness 6 ft., 

 and each cubic foot weighs 180 Ibs., find whether it will 

 stand or fall when the water is on a level with the top. 



Ans. 



39. The depth AB of the water in the head bay (Fig. 13) 

 is 7 ft., the depth DB of the water in the chamber of the 

 lock is 4 ft., and the width of the lock-chamber is 7.5 ft. ; 

 find (1) the resultant pressure upon the gate AB, and (2) 

 the depth of the point of application of the resultant press- 

 ure below the surface of the water in the head bay. 



Ans. (1) 7734.4 Ibs.; (2) 4.18 ft. 



40. If the vessel (Fig. 15) make 140 turns per minute, 

 find the value of NM. Ans. 1.78 in. 



41. A hollow paraboloid of revolution, with its axis ver- 

 tical and vertex downwards, is half filled with liquid. With 

 what angular velocity must it be made to rotate about its 

 axis, in order that the liquid may just rise to the rim of the 



Ans. If 2p = latus rectum, w 2 = ^ 



42. If the vessel in the last example be filled with liquid, 

 find the angular velocity and the time of rotation that it 

 may just be emptied. 



Ans. If 2jt? = latus rectum, w 2 = "; time = STTA /- 



43. A hemispherical bowl is filled with liquid, which is 

 made to rotate uniformly about the vertical radius of the 



bowl. Find how much runs over. 1 7ra 4 o> 2 



Ans. - - 



4 g 



44. A closed cylindrical vessel, height h and radius , is 

 just filled with liquid, and rotates uniformly about its ver- 

 tical axis. Find the pressures on its upper and lower ends, 

 and the whole pressure on its curved surface. 



9 4w2 ,/a 2 o>2 \ / wV\ 



Ans. ffpna 1 -j , gpnd'i-j h >}, and gprrah (h + ! 



