﻿976 .Dr. Thomas on Discharge of Air through Small 



the several points. Each has been drawn through the 



"centre o£ gravity" — , — of the respective observations, 



n n 



at an inclination 6 to the axis of logarithms o£ pressure given 



by 



where 



x = — and */ = —£-, 



n u n ' 



x and y being the logarithmic coordinates experimentally 

 determined and n the number ofobservations. 



It follows that the dependence of the discharge Q (measured 

 at 0° C. and 760 mm. pressure) upon the excess pressure € 

 can, within the limits of pressure employed in the present 

 series of experiments, be represented by a relation of the 

 form 



Q = AV (i.) 



The respective values of A' and a are set out later in 

 Table II. 



It is cf interest here to consider the relation of this 

 equation to that deduced for the relation of discharge to 

 pressure on the assumption that the discharge occurs under 

 adiabatic conditions. 



Lamb * gives for the mass discharge under these con- 

 ditions the formula 



«**-(£)"*■{(£)'- (rf s ' : <»•» 



where p 1 and p are the respective pressures outside and 

 inside the vessel from which the discharge occurs. p and c 

 are respectively the density of the gas and the velocity of 

 sound inside the vessel, S' is the area of the vena contracta, 

 ry the ratio of the specific heats, and q x the velocity outside 

 the vessel. 



Writing po=\Pi + 6 5 where e is the excess pressure inside 

 the discharge vessel, this expression becomes after some 

 little algebraic reduction, assuming the expansion to take 



place under adiabatic conditions, and the value of — to 



^■-'^Mcf-'aKV)]" « 



* < Hydrodynamics/ 1906, f, 23. 



