A NEW EXACT SOLUTION OF THE EQUATIONS OF VISCOUS MOTION WITH AXIAL SYMMETRY

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Abstract
An exact solution for the motion of viscous fluid flow for axially symmetric motion has been found by Squire (1) in the form ψ = vr f(μ), where (r,θφ) are spherical polar coordinates, μ = cos θ, and ν is the kinematic viscosity. Squire has shown that a special case of his solution gives the flow for a jet emerging from a hole in an infinite plane wall. In the present paper, another exact solution of the Navier-Stokes equations is obtained for the steady flow of a viscous incompressible fluid for the case of axial symmetry in the form ψ = νrnf(θ) provided that n = 1, 2, or 4. For n = 1 the solution becomes that of Squire. For n = 2 we obtain the solution ψ = νr2C1 sin2θ(C1 being a constant) which is well known. The case n= 4 appears to be new.

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