The Stokes flow problem is concerned with fluid motion about an obstacle when the motion is such that inertial effects can be neglected. This problem is considered here for the case in which the obstacle (or configuration of obstacles) has an axis of symmetry, and the flow at distant points is uniform and parallel to this axis. The differential equation for the stream function ψ then assumes the form L2−1ψ = 0, where L−1 is the operator which occurs in axiallysymmetric flows of the incompressible ideal fluid. This is a particular case of the fundamental operator of A. Weinstein's generalized axially symmetric potential theory. Using the results of this theory and theorems regarding representations of the solutions of repeated operator equations, the authors (1) give a general expression for the drag of an axially symmetric configuration in Stokes flow, and (2) indicate a procedure for the determination of the stream function. The stream function is found for the particular case of the lens-shaped body.Explicit calculation of the drag is difficult for the general lens, without recourse to numerical procedures, but is relatively easy in the case of the hemispherical cup. As examples illustrative of their procedures, the authors briefly consider three Stokes flow problems whose solutions have been given previously.

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(Jul y 8, ] 966)Bassali 's ge ne ral th eo ry fo r the fl exure of th e thin c irc ul a r elastic pl a te suppo rted a t a n a rbitrary numbe r of points a nd subj ec ted to tran sverse load ove r a n ecce ntri c circle is spec ialized to th e case of a centrally load ed pla te s upporte d at points equally s paced on a c ircle co nce ntri c with th e ce nte r. Simplified me thod s fo r approximating th e res ults predi cted by th e more complic ated theo re ti cal ex· pressions for defl ec ti o n are prese nted along with th e ex pe rim e ntal res ult s from 138 tes ts . Both th e ex pe rimental res ults a nd th e simplifi ed equati ons a re co mp a red with the th eo ry and agree me nt is fo und to be good. Key Word s: Bassali 's th eo ry, co nce ntri c loading, circ ul a r plates, defl ec ti on, elast ic it y, exp eri · me ntal, fl exure, point supp orts, simplified app roximate soluti ons, thin plates. Introducti onThe de termination of the defl ec tion of a centrally loaded circular plate supported at points equally spaced on a circle concentric with the center has long bee n an important structural analysis proble m. In the past th e analysis of thi s problem was us ually limited by the assumption that th e point s upports were numerou s e nough to co ns titute a simple co ntinuous line support. Nadai [1] J presented a theory for the deformation of a circ ular plate s upported at several points with central point load or uniform load whic h was an improveme nt in that it recognized the errors involved in the afore me ntioned assumption. Unfortunately, Nadai's point s upports were located alon g the circumference of the plate. To some exte nt thi s limited the utility of the theory, as this me thod of support is unus ually diffic ult to realize in practi cal s tru ctures .More recently, Bassali [2] has give n the solution of the problem of fl exure of a thin circ ular elastic plate s upported at an arbitrary numb er of points whic h may b e located anywhere within the pl a te periphery, and loaded over a circular area lying anywhere within the boundary of the plate. Implicit in the work of Bassali is the solution of the problem of the centrally loaded plate supported at points equally spaced on a circle concentric with a central load. It may be noted . that the theory accounts for the cons training effec t of an annular region of the plate which overhangs the support circle and is otherwise free from restraint. This paper deals with the s p ecializ~ti~n of that part of the Bassali theory necessary to s· olve the particular proble m described above, and presents the rather tedious theoretical expressions for the defl ec tion at the ce nter of the plate and at a point midway between s upports locate d along the support circle. Since these expressions require considerable e ffort to e valuate, simplified methods of approximating the center d e flection may b e d esirable for d esign purposes. Therefore simplified expressions for ce nter de fl ection, based on the results of the exact theory, are given. Experim...

In this study, a low cost nano-second pulsed high voltage power system was used to generate plasma on water surface in a water treatment reactor at the expense of electrical energy. E. coli was inoculated as a model bacterial contaminant in the treatment water. The results of the bacterial counts obtained showed a 65% decrease from 244 colony forming units (CFUs) in the control to 89 CFUs in the plasma treated water that is a significant reduction of the bacterial count. In a separate experiment, methylene blue was mixed with the water as a model chemical decontaminant. The significance of an alternative decontamination method, both cost effective and safe will be an answer to the increasing scarcity of clean water all around the world. This method will especially be useful in developing countries.

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