28 IXTEGEATION OF THE EQUATIONS IN SPECIAL CASES. [CHAP. II. 



The maximum velocity of efflux occurs when p t = 0, i.e. when the 

 gas escapes into a vacuum ; it is 



2 \ 



- ) x velocity of sound, 

 &quot; 1 / 



or, for atmospheric air at 32 F., about 2413 feet per second. 



The rate of escape of mass however depends on the value of 

 ?P 2 &amp;gt; or 



2 



which does not continually increase as/&amp;gt; 2 diminishes, but attains a 

 maximum when 



7 + 

 The velocity of efflux is then, by (17), 



// 2 \ 

 q = A / ( - j x velocity of sound, 



or, for atmospheric air at 32 F., about 997 feet per second. 



The reduced velocity, i.e. the velocity of a current of the 

 density p t of the gas in the receiver which would convey matter 

 at the same rate is got by dividing the expression (18) by p lt and 

 is, when a maximum, about 632 feet per second for air at 32 F. 



34. Example 3. A mass of liquid rotates, under the action of 

 gravity only, with constant angular velocity o&amp;gt; about the axis of z 

 supposed drawn vertically upwards. 



By hypothesis, u= coy, v = cox, w ; 

 also Z=0, r=0, Z=-g. 



The equation of continuity is identically satisfied, and the dynamical 

 equations of motion become 



2 1 dp 2 1 dp I dp 



-u? x = ---f, -u?y = ---f- y = --^-or. 

 p djc pay pdz 



These have the common integral 



- = Jo&amp;gt; 2 (a; 2 + 7/ 2 ) gz + const. 



