380 Hydrodynamics. 



If the aperture be only T i^ of a square inch, or the side T V, the 

 time of completely filling the vessel will be 172" nearly, or a 

 little less than 3'. 



If the experiment be made with an aperture, cut in a thin 

 plate, we shall find-the time greater nearly in the ratio of 62 or 

 479t 63 to 100, as we have already remarked with respect to water 

 flowing through small orifices. 



492. We can find, in like manner, the time necessary for 

 bringing the air in the vessel to any particular density, as of 

 that of air in its ordinary state. For the only variable part of 

 the integral, above found, is \/ D A, which in this case becomes 

 >y/l | rr i, and gives y'o \/D A = J; hence, if the 

 aperture were a square, each side being y 1 ^ of an inch, the time 

 sought would be 172", or 86", nearly. 



493. If the air in the vessel be compressed by a weight 

 acting on the moveable cover AD, the velocity of the expelled 



Fig. 238 air may be determined thus. Let the additional pressure be 

 denoted by q, and the density thence resulting by D' ; we shall 

 then have 



p : p + q : : D : D', 

 and 



P'P + qP :: D : D' D, 

 which gives 



D' D 



Now, since the pressure which expels the air is the difference 

 between the force which compresses the air in the vessel and 

 that which compresses the internal air, the expelling force is q ; 

 whence, the forces being as the quantities of motion, 



D' D 



p : p X -- : : m v : n w, 



m, , being the masses expelled, v the velocity with which air 

 rushes into a void, and u the velocity required. But the masses 

 or number of particles which issue through the same orifice in 



