DoWLiNG — Steady and Turhulent 3Ioiion in Gases. 395 



couditious wliicli are not closely approximated to in the experiment. Again, 

 the law obeyed by this " critical " velocity seems to hold equally well for 

 wide tubes, where it occurs after turbulent motion of tlie ordinary kind has 

 set in. It is of interest, however, inasmuch as it seems to connect the proper- 

 ties of the gas with the phenomenon we are considering. We have shown 



that it would follow from equation (9) that for all tubes -- would have a con- 

 stant value at the surface of the tube for a velocity just below the "critical" 

 velocitj'. Now i; — represents rate of shearing, so to speak, of the gas at the 



surface layers. Again, >; — for a given tube is proportional to tlie distance 



from the centre, so that the sliearing is greatest in the layers of fluid nearest 

 the walls. If we grant that beyond a certain point "sliearing" becomes 

 unstable and tends to give rise to something, say, in the nature of " rolling," 

 we should expect that this instability sliould depend on a " critical " value 



of the expression — . „-. That is, for a given gas, it would depend on the 



p or 



velocity-slo2)e ; for different gases it would depend directly on the vmosity, 

 and inversely on the density. Unfortunately we have few numbers to check 

 these deductions. However, in column S of Table V are given the values 



-rr 



of the quantity -j-. The simple |^theory we have given would require this 



to be a constant ; but such is hardly the case. The numbers, however, seem 

 to tend to a constant limit for the wider tubes. One fact, liowever, they 

 appear to bring out, and that is the dependence of V on jj/p, for the numbers 

 for CO2 and the CO2 mixture agree quite well with those of the corresponding 

 size tubes for air. 



In a recent paper Stanton' has shown that, even when turbulent motion 

 obtains in a tube, the air flowing very close to the walls continues probably 

 in linear flow — or, at least, that the factor governing the flow is the ordinary 



coefficient of viscosity (ij) and not the ' dynamic viscosity ' ( - ). This thi'ows 



some light on what we are now considering. Since the ' Reynolds ' critical 

 point occurs at a velocity inverse/// proportional to tlie radius, while the 

 second effect occurs at a velocity proportional thereto, for the smaller size 

 tubes the second effect occurs during stream-line flow, while for larger 

 tubes it occurs during turbulence. It is clear, therefore, that with Stanton's 

 result, it becomes less diflicult to imagine how our second effect could obey 



Stautou, Pioo. Hoy. Soc, vol. Ixxxv, lull, p. 366. 



