﻿Orifices, and Entrainment of Air by the Issuing Jet. 1)77 

 which may be further transformed ; and we obtain, finally, 



Wl S'=S'(2 ¥l )-(l-^) W . . (iv.) 



Now it is well known that experimental results are not 

 correctly represented by the assumption of the existence 

 of adiabatic conditions during the discharge of the gas 

 through an orifice in a thin plate *, The procedure 

 followed by Buckingham and Edwards is to modify the 

 adiabatic relation by the introduction of corrections, taking 

 into account effects due to viscosity, heat conduction, and 

 turbulence, such disturbing effects being regarded as re- 

 latively small. We propose to follow a somewhat similar 

 procedure. The adiabatic relation (iv.) failed to represent 

 the experimental results obtained in the present series within 

 the limits of experimental error. The expression {S'(2eyo 1 ) 1/2 

 is commonly employed for calculating the approximate mass 

 discharge through orifices in thin plates. The expression 



(1 — - — — I , in which — is small, is a small correcting 

 \ 2ypJ Pl .. * 



factor. By a suitable slight modification of this factor, 

 a formula may be obtained which represents the present 

 results within the limits of experimental errors. 

 We take f 



M = Wl S'=S'(2 e ^ 1/2 (l-^ • • • (v.) 



w r here the value of k is to be determined from the experi- 

 mental results. We have from (v.), 



d log 10 M _ 1_ fee 

 diog W € ' 2 2pi 



assuming - to be small and S' to be independent of 



the excess pressure. Identifying the left-hand side of this 

 equation with the " best " value of a in (i.) as determined 



from the experimental results, we have a = ^ — - — . The 



appropriate value of k is to be determined from a con- 

 sideration of the "best fitting" value of e in this relation. 

 The observations being approximately uniformly spaced 

 through the range of excess pressures employed, and the 



* See, e. </., Buckingham & Edwards, Sci. Tapers, Bureau of Standards, 

 vol. xv. p. 599 (1919-20). 



t M being the mass discharge, is evidently proportional to the volume 

 discharge measured at 0° C. and 760 mm. pressure. 



