Pressure around Spheres in a Viscous Fluid. 



435 



imaoo containino- this ratio to a hioher i)ower than the sixth 

 were neglected ; that is, terms containing a factor less than 

 8*GxlO-^ have been omitted in the computation of the 

 broken-line curves in figs. 11 and 12. 



9. Comparison of the Distribution of Pressure for a Perfect 

 Fluid with the Pressure obtained for a Viscous Fluid. — For a 

 single sj^here moving with constant velocity in a perfect 

 fluid at rest at infinity the curve of distribution of pressure 

 is symmetrical with res])ect to each plane of the three rect- 

 angular axes whose origin is at the centre of the sphere. 

 And hence the resulting force in any direction is zero. For 

 the viscous fluid the curve is asymmetrical with respect to 

 the plane perpendicular to the direction of motion, but svm- 

 metrical with respect to the line of motion ; and the resultant 

 force is such as would tend to bring the sphere to rest. 



For two spheres moving in their line of centres in a perfect 

 fluid the curves of distribution of pressure are asymmetrical 

 with respect to the axial planes which are perpendicular to 

 their direction of motion, the force on the inner hemisphere 

 being the greater. The normal pressure and the resultant 

 component pressures along the line of motion over the inner 

 and outer hemispheres at different points are given in the 

 following table for sphere B. 



Table Y. 



Angle. 



Inner 

 hemisphere. 



Angle. 



Outer 

 hemisphere. 



Dif- 

 ference. 



Resultant 

 eomponeiit. 



1 0° 



•5028 



o 



180 



•499 



•0038 



•0038 



30 



•2940 



1.50 



•220 



•0540 



•0468 



60 



-•2550 



120 



—•320 



•0650 



•0320 



90 



-•5880 



90 



-•5880 



•0000 



•0000 



The resultant force on both spheres is tending to separate 

 the spheres, i. e, gives repulsion. The results for the two 

 spheres in a viscous fluid are exhibited in Table I., and it is 

 evident that the two spheres would have a relative motion 

 such that they would approach each other, /. e. attract. 



For two spheres moving in a perfect fluid perpendicular to 

 their line of centres the curves of distribution of pressure are 

 asymmetrical with respect to a plane perpendicular to the 

 line joining them, the pressure in the outer hemisphere being 

 the greater. 



The following table gives the normal pressures land] the 

 resultant component pressures over the outer and inner 



2 F2 



