196 Prof. Osborne Reynolds on 



9. For air through an orifice, since 7 = 1*408, when the 

 pressure in the receiving vessel is less than '527^, the nume- 

 rical value of U„, the velocity iu the neck of the orifice, is 



. 17^=997 (feet per sec.) A/- 1 ; ... (13) 



and if the temperature is 57° F., as in Mr. Wilde's experi- 

 ments,. . 



U n =1022. (14) 



Reducing this in the ratio of the density at the neck to the 

 density in the discharging vessel, 



ESP 5 } <-> 



We have the reduced velocity 



U n ^ = 650 (feet per sec.) (16) 



Pi 



Therefore the discharge will be given in cubic inches per 

 second, KO being the effective area of the orifice, by 



/ > 1 Q = 12U nPn KO 1 



= 12x650KOJ K } 



Or, since the actual area in square inches 



= -000314 sq. inches, 



Q = 2*44K (cubic inches per sec). . . . (18) 



10. In order to compare the experimental discharges with 

 those calculated, it is necessary to know, besides the size of 

 an orifice and the pressure and temperature of the discharging 

 vessel, the coefficient of contraction or the effective area of 

 the orifice. To obtain this from the equations requires that 

 the terms depending on viscosity should be introduced, which 

 renders the integration so far impossible. The only plan is 

 to obtain this coefficient by comparing the theoretical results 

 with the experimental. Such comparisons have been made 

 by Prof. Weisbach for air; and in the case of short cylin- 

 drical orifices such as that used by Mr. Wilde (a cylindrical 

 hole through a plate having a radius equal to the thickness 

 of the plate) , the value of K, the coefficient of contraction, 

 given by Weisbach (' The Steam Engine/ p. 324, Rankine) 

 is from *73 to *833. Whether these are the real coeffi- 

 cients of contraction may, however, well be doubted, as it is 

 extremely difficult to determine the experimental quantities 



