﻿982 Dr. Thomas on Discharge of Air through Small 



For the channels 1 A-5 A of constant length 02789 cm., 

 the value of A' in the empirical formula for the discharge A'e a 

 is given in terms of the diameter d by the linear relation 

 A' = 73i — 2*33. The gradual increase of the index a in the 

 case of channels 1 A-5 A as the diameter of the channel 

 decreases is seen from fig. 5. It will be noticed that at a 

 pressure a little greater than the maximum employed in the 

 construction of fig. 5, the straight lines shown corresponding 

 to the orifices 11 and 5 A of the same diameter intersect 

 (actually the pressure was found to be 33*2 cm. of water). 

 For pressures greater than this, the discharge through the 

 longer channel is actually greater than that through the 

 shorter channel of the same diameter. A similar phenomenon 

 is represented by the points P and Q, in which the straight 

 lines corresponding to channels 8 and 11 in disks of thick- 

 ness 0*0229 cut the line corresponding to channel 4 a, of 

 slightly larger diameter and of about 12 times the length. 

 The phenomenon is clearly attributable to the difference in 

 the form of the issuing jet in the respective cases of discharge 

 through a channel in a thin or thick plate, the existence of 

 the vena contracta in the former case reducing the effective 

 area of the discharge and tending to counterbalance the effect 

 of the greater length of the channel in the latter. Attention 

 has been directed to the existence of a critical length of 

 channel, such that the discharge through an orifice of given 

 size is a maximum, in a recent publication of the Bureau of 

 Standards, Washington *. 



(b) Air Entrainment. — In fig. 6, the respective total 

 volumes of air (reduced to 0° C. and 760 mm. pressure, dry) 

 entrained by the issuing jet in the case of each of the jets 

 nos. 1-10, are plotted as ordinates against the respective 

 pressures as abscissse. The several curves are numbered 

 according to the number of the corresponding orifice. Curves 

 1-7 represent the normal manner in which the volume of 

 air entrained by a jet of air issuing from a given orifice 

 increases as the pressure at the orifice is increased. As 

 the pressure is increased, an initial approximately linear 

 increase of the total volume entrained is followed by a 

 subsequent increase at a continuously decreasing rate, the 

 curve becoming concave to the axis of pressure. This latter 

 is to be anticipated, as the viscous and frictional drag upon 

 the stream of entrained air increases as the velocity of the 

 stream increases. 



The curves corresponding to orifices nos. 8, 9, and 10, 



* Technologic Paper,- No. 193, p. 17 (Sept. 6, 1921). 



