Exact solutions of rotating MHD flows using von-Mises coordinates
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Solutions to flow equations of rotating fluids are obtained using differential geometry. Basic equations are written in Martin’s form. We use von-Mises Coordinates (x, y) that require the use of = x in Martin’s Coordinates. = constant are streamlines of the flow and x=constant are the coordinate lines of a rectangular coordinate net. Exact solutions for velocity and pressure distribution are obtained for a class of flow problems. When the streamline pattern for given flow problem is written in the form of y − f(x)/g(x)= constant, where f(x) and g(x) are differentiable functions. By assuming the angular velocity in different forms, pressure distribution is analyzed graphically.
Abstract
Solutions to flow equations of rotating fluids are obtained using differential geometry. Basic equations are written in Martin’s form. We use von-Mises Coordinates (x, y) that require the use of = x in Martin’s Coordinates. = constant are streamlines of the flow and x=constant are the coordinate lines of a rectangular coordinate net. Exact solutions for velocity and pressure distribution are obtained for a class of flow problems. When the streamline pattern for given flow problem is written in the form of y − f(x)/g(x)= constant, where f(x) and g(x) are differentiable functions. By assuming the angular velocity in different forms, pressure distribution is analyzed graphically.