Concept

# Potential flow around a circular cylinder

Summary
In mathematics, potential flow around a circular cylinder is a classical solution for the flow of an inviscid, incompressible fluid around a cylinder that is transverse to the flow. Far from the cylinder, the flow is unidirectional and uniform. The flow has no vorticity and thus the velocity field is irrotational and can be modeled as a potential flow. Unlike a real fluid, this solution indicates a net zero drag on the body, a result known as d'Alembert's paradox. Mathematical solution A cylinder (or disk) of radius R is placed in a two-dimensional, incompressible, inviscid flow. The goal is to find the steady velocity vector V and pressure p in a plane, subject to the condition that far from the cylinder the velocity vector (relative to unit vectors i and j) is: :\mathbf{V}=U\mathbf{i}+0\mathbf{j} ,, where U is a constant, and at the boundary of the cylinder :\mathbf{V}\cdot\mathbf{\hat n}=0 ,, wher
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