Figure 2a shows the streamline for the creeping flow around a sphere. Flow Past a Spherical Obstacle Consider the steady flow pattern produced when an impenetrable rigid spherical obstacle is placed in a uniformly flowing, incompressible, inviscid fluid. a) Viscous Flow b) Potential Flow Figure 2. Potential Flow around a Cylinder Superimposing a uniform stream of velocity, U, on the potential flow due a doublet oriented in the x Figure 1: Streamlines in the potential flow of a doublet in a uniform stream. It measures how much the fluid is rotating within a region enclosed by a contour line by summing the velocity components along the contour path. This notebook considers the problem of an inviscid flow past a stationary sphere. Comparing the streamlines of the creeping flow conditions to the potential flow one given by ψ= ∞ θ − 3 3 2 2 r R U r sin 1 2 1 (17) and is plotted in Figure 2 b, it appears that the stream lines are more dispersed. Here, two-dimensional potential flow over a rectangular cylinder of given dimensions is solved with stream function formulation.

Steady potential flow around a stationary sphere. Letting U denote the free-stream velocity of the fluid, it's clear that the potential field is axially symmetrical about the axis through the sphere parallel to the direction of flow, so we need only specify the potential ϕ as a function of the polar coordinates r (the distance from the sphere's center) and θ (the angle from the direction of flow. Steady flow of a viscous fluid at very low Reynolds numbers (“creeping flow”) past a sphere. Circulation is the line integral of the velocity field around a closed contour. INSTANTANEOUS PRESSURE DISTRIBUTION AROUND A SPHERE IN UNSTEADY FLOW C1 Leslie S. G. Kovasznay, Itiro Tani, Masahiko Kawamura and Hajime Fujita Department of Mechanics The Johns Hopkins University December 1971.,DDC Office of Naval Research .11 j) Washington D. C. 20360 D *Ljq 119 B Technical Report: ONR No. Figure 2: Potential vortex with flow in circular patterns around the center. Question: Steady Potential Flow Around A Stationary Sphere. Solutions are obtained using both a potential function and a stream function. Comparing the streamlines of the creeping flow conditions to the potential flow one given by ψ= ∞ θ − 3 3 2 2 r R U r sin 1 2 1 (17) and is plotted in Figure 2 b, it appears that the stream lines are more dispersed. The pressure field around the sphere and the drag, which is 0 (d'Alembert's paradox) are found. Computational fluid dynamics provide an efficient way to solve complex flow problems. A large domain is used together with variable spatial resolution to minimise the influence of the finite domain size. For such a problem, we know that the velocity potential must satisfy Laplace's equation (see text after Eq.