Hydrodynamics* 



of the pressure of the atmosphere, and it is the excess of this 

 pressure only which constitutes the moving force, the matter to 

 be moved being the same as before. Let D be the natural den- 

 sity of the atmosphere, and A the density of that which opposes 

 itself to the motion in question. Let p be the pressure of the 

 atmosphere, or the force which impels it into a void, and -or the 

 force with which this rarer air would rush into a void ; from the 

 proportion 



D : A : : p : & = , 

 D 



we shall have for the moving* force sought p - Again, let 



v be the velocity of air rushing into a void under the pressure p, 

 and u the velocity of air under the same pressure rushing into 

 rarefied air of the density A. Since the pressures are as the 

 heights producing them, the fluid being supposed of a uniform 

 density through, we shall have 



*:::v^: HZ^ : : 1 : I73F. 



\ l D \ D 



whence it = v X 11 , no allowance being made for the 



*J D 



inertia of the rarer air, which being displaced must oppose a 

 certain resistance. 



490. Let it be proposed to determine the time t in seconds in 

 which the air will flow into a given exhausted vessel, until the 

 air shall have acquired in the vessel a certain density A. 



Suppose h the height due to the velocity v, b the bulk or 

 capacity of the vessel, and 6 the area of the aperture, the meas- 

 ure in each case being in feet. Since the quantity of air neces- 

 sary to fill the vessel will depend upon the size of the vessel, and 

 also upon the density of the air, b A will represent this quantity, 

 the differential of which is b d A. The velocity of influx at the 

 first instant is v = \/2 g h ; and when the air in the vessel has 

 acquired the density A, that is, at the end of the time <, the 

 velocity is 



u = \/2gh 



