Flow of Gases through Helical Capillaries

The isothermal flow rates of H2, He, and N2 through several helically coiled capillaries in the laminar, transition, and turbulent ranges are found to follow the expression y=x(2−axn1)2+x12(1−2−axn2)2, where x is the ratio of the product of the average pressure times the pressure drop in the capillary to the value of pressure times pressure drop which produces the transition from laminar to turbulent flow in a straight capillary of the same length and diameter, and y is the ratio of any observed flow rate to that flow rate which corresponds to the transition in the straight capillary. The experimental value of y corresponding to x=1, called y0, is given by 1−y0=12e−0.044(D/d)1/2, where D is the coil diameter and d is the capillary diameter. n1 and n2 are given by n1≐12+110(Dd)3/8; n2≐12+215(Dd)3/8. The quantity a (<1) is obtained by solving y0=(2−a)2+(1−2−a)2, using the value of y0 obtained from Eq. (ii). The above equations hold for porous media also, when the following values are used: D=0, n1=n2=12, a=1, in which case y0=12 as determined previously. The flow apparently may be stabilized against turbulence by centrifugal forces in tightly wound helices up to Reynolds numbers equal to at least 8000, consistent with previous observations by others with liquids.