โ Scribed by Singh, S. N.
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The effect of a transverse magnetic field on the steady motion of a conducting, viscous and incompressible liquid through a pipe of circular crosssection, coiled in a circle is studied ill this paper. The solution is obtained by successive approximations in ascending powers of the I-Iartmann number; the first approximation corresponds to the non-magnetic case, formulated and discussed by Deanl). It is assumed that the walls of the pipe are nonconducting and the radius of the cross-section is small in comparison with that of the circle in which the pipe is coiled. The stream-lines in the central plane and the projection of the stream-lines on a normal section are shown graphically and are compared with those of a non-conducting fluid. ยง 1. Introduction. The s t u d y of the flow of conducting fluids in pipes under the influence of a transverse magnetic field is of great practical importance, because of the utility of electromagnetic flowmeters with liquid-metals. The problem mentioned above for the straight pipes of various cross-sections has received considerable a t t e n t i o n in the past. H a r t m a n n 2) found exact solutions of the corresponding p r o b l e m for the flow between two infinite parallel plates. In a series of papers S h e r c l i f f 3 , 4 , 5) not only obtained the velocity distribution for the rectangular channel, b u t also studied the s t e a d y state l a m i n a r flow in a circular pipe theoretically and experimentally when the wails conduct currents and also e x a m i n e d the e n t r y length of conducting and non-conducting fluids in pipes b y means of a Rayleigh approximation. The exact solution to the p r o b l e m of s t e a d y one-dimensional flow t h r o u g h a circular pipe has been obtained b y several authors: U f l y a n d 6 ) , U h l e n b u s c h and F i s c h e r T ) and GoldS). G o l d has shown t h a t
๐ SIMILAR VOLUMES
An exact solution of the ~Yfagnetohydrodynalnic pipe flow equations is found in terms of elementary functions. As the Hartmann number increases from zero reverse motion in tile pipe occurs and eventually separates from the boundary. With further increase in the Hartmann number the vorticity on the b