Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8263Research ArticleInvestigation of Potential Flow of Fluid in Porous Medium Taking Account of Darcy Law and Variable Diffusion CoefficientRybakovYu PDepartment of Theoretical Physicssoliton4@mail.ruSviridovaO DDepartment of Theoretical Physicsoxanaswiridowa@yandex.ruShikinG NDepartment of Theoretical Physics-Peoples’ Friendship University of Russian15012014114815208092016Copyright © 2014,2014We have considered the potential ﬂow of the ﬂuid in the porous medium taking into account Darcy low and diﬀerent types of the diﬀusion coeﬃcient in a tube with radius a. The ﬂow is supposed to be stationary and cylindrically-symmetric and the Darcy force is a linear function of the velocity. We have established that a result of the potential ﬂow is identity ∂2P∕∂r∂z ≡ ∂2P∕∂z∂r, where ∂P∕∂r and vz = ∂Φ∕∂z are deﬁned from Euler equation for two components of the velocity: vr = ∂Φ∕∂r and vz = ∂Φ∕∂z, where Φ(r,z) is velocity potential. It means that Euler equation system is compatible and integrable, and the solution is reduced to the solution of the continuity equation. Continuity equation is linear diﬀerential equation for the potential Φ(r,z) and one assumes solution in divided variable: Φ(r,z) = U(r)W(z). For U(z) we have Bessel equation of zero order. This solution depends on the choice of the diﬀusion coeﬃcient in the continuity equation. In all the occasions we have exact solution and established that component of the velocity vz descreases like exponent with increase of z.potential flowstationary flowporous mediumdiffusionDarcy lowпотенциальное течениестационарное течениепористая средадиффузиязакон ДарсиШейдеггер А.Э. Физика течения жидкостей через пористые среды. — М.: Институт компьютерных исследований. НИЦ «Регулярная и хаотическая динамика», 2008.Рыбаков Ю.П., Шикин Г.Н. Течение в трубе с зернистой загрузкой: пристеночный эффект // XVI Межд. научн. конф «Мат. методы в технике и технологиях». — 2003. — С. 138–139.Ландау Л.Д., Лифшиц Е.М. Гидродинамика. — М.: Наука, 1988.Никифоров А.Ф., Уваров В.В. Специальные функции математической физики. — М.: Наука, 1978.