168 PROF. OSBORNE REYNOLDS ON 



holds at all points in the vessel or the effluent stream. 

 If J then^ the pressure at the orifice is known^ as well as 

 the pressure well within the vessel where the gas has no 

 energy of motion, we have the velocity of gas at the 

 orifice ; and obtaining the density at the orifice from the 

 thermodynamic relation between density and pressure, 

 we have the weight discharged per second by multiplying 

 the product of velocity with density by the effective area 

 of the orifice. This is Thomson and Joule^'s equation for 

 the flow through an orifice. And so far the logic is 

 perfect, and there are no assumptions but those involved 

 in the general theories of thermodynamics and of fluid 

 motion. 



But in order to apply this equation, it is necessary to 

 know the pressure at the orifice ; and here comes the 

 assumption that has been tacitly made : that the pressure 

 at the orifice is the pressure in the receiving vessel at a 

 distance from the orifice. 



3. The origin of this assumption is that it holds, when 

 a denser liquid like water flows into a light fluid like air, 

 and approximately when water flows into watei. 



Taking no account of friction, the equations of hydro- 

 dynamics show that this is the only condition under which 

 the ideal liquid can flow steadily from a drowned orifice. 

 But they have not been hitherto integrated so far as to 

 sbow whether or not this would be the case Avith an elastic 

 fluid. 



In the case of an elastic fluid, the difficulty of inte- 

 gration is enhanced. But on examination it appears that 

 there is an important circumstance connected with the 

 steady motion of gases which does not exist in the case of 

 liquid. This circumstance, which may be inferred from 

 integrations already effected, determines the pressure at 

 the orifice irrespective of the pressure in the receiving 

 vessel when this is below a certain point. 



