188 Prof. Osborne Reynolds on 



motion and the intrinsic energy. As the gas acquires energy 

 of motion /it loses intrinsic energy to exactly the same extent. 

 Hence we have an equation between the energy of motion, 

 i. e. the velocity of the gas, and its intrinsic energy. The 

 laws of thermodynamics afford relations between the pressure, 

 temperature, density, and intrinsic energy of the gas at any 

 point, Substituting in the equation of energy, we obtain 

 equations between the velocity and either pressure, temperature, 

 or density of the gas. 



The equation thus obtained between the velocity and pres- 

 sure is that given by Thomson and Joule; this equation holds 

 at all points in the vessel or the effluent stream. If, 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 water. 



Taking no account of friction, the equations of hydrodyna- 

 mics 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 show whether 

 or not this would be the case with an elastic fluid. 



In the case of an elastic fluid, the difficulty of integration 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 cir- 

 cumstance, 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. 



4. To understand this circumstance, it is necessary to con- 

 sider a steady narrow stream of fluid in which the pressure 

 falls and the velocity increases continuously in one direction. 



