EFFLUX OF MOVING AIR. 247 



Neglecting all powers of above the second, we have 



Pi 



If h be the height of a homogeneous fluid, of the same 

 density as the air, which is necessary to produce the pressure 

 Pi Ps> then j9j jt> 2 = wh, which in (12) gives 



v = $Vh. (14) 



It will be observed that (8), (9), (12), (13), (14) are true 

 only when the pressures jt^ and p z are nearly equal to each 

 other. 



130. Efflux of Moving Air. To find the velocity of 

 efflux when the pressure of the air is given in the 

 pipe through which it flows. 



The formulae for efflux found in Art. 129, are based upon 

 the supposition that the pressure p, or the height h, of the 

 manometer is measured at a place where the air is at rest, 

 or moving very slowly. If the pressure be measured at a 

 point where the air is in motion, in determining the 

 velocity of efflux, we must take into account the kinetic 

 energy of the moving air. 



Let p l be the pressure of the air in the pipe A, as indi- 

 cated by the manometer M, and 

 v l the velocity of the air passing 

 the orifice of the manometer; p z 

 the pressure of the air at efflux, 

 and v z its velocity; a l the area 

 of the section of the pipe A, and 

 2 the area of the orifice ; w the 

 weight of a cubic foot of the air, and Q the volume dis- 

 charged per second. 



Then the work stored in the air while passing from the 

 pipe A to the orifice 



