ISSN:
1573-8507
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
Notes:
Abstract We show the applicability of Stokes' approximation at large distances from the vertex of a cone. We discuss the statement of the problem and formulate new asymptotic representations of the solution, which replace the paradoxical solution of Harrison for cone vertex angles α≥120°. A solution of the problem concerning the axially symmetric Stokes' flow of a viscous liquid in a conical diffuser was first obtained by Harrison [1] (see also [2, 3]). The velocity field of this flow has the form $$\upsilon _R = \frac{{3Q}}{{2\pi R^2 }}\frac{{\cos ^2 - \cos ^2 \alpha }}{{\left( {1 - \cos \alpha } \right)^2 \left( {1 + 2\cos \alpha } \right)}}, \upsilon _\theta = 0$$ where R and Θ are spherical coordinates, Θ=0 and Θ=α correspond, respectively, to the axis and to the wall of the diffuser, and Q is the volumetric outflow rate of the liquid. We note that the values of the velocity in this purely radial flow become infinite when the angle α approaches 120°.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01186462
Permalink
