5. Kern E. Kenyon, Reaction Forces of Fluid Flows on Solid Boundaries

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Volume 19: Pages 507-516, 2006

Reaction Forces of Fluid Flows on Solid Boundaries

Kern E. Kenyon 1

14632 North Lane, Del Mar, California 920144134 U.S.A.

Laminar inviscid flows moving by solid boundaries cause a reaction force on these boundaries when the fluid accelerates next to the boundary, as predicted by Newton's third law, assuming there are no external forces acting parallel to the mean flow. The reaction force points opposite to the fluid acceleration. For a thin bump on an otherwise flat wall in a twodimensional configuration there are two horizontal reaction forces, one on either side of the bump, that point outward from the center of the bump and parallel to the flat wall. Exactly the same reaction forces occur for either direction of the mean flow relative to the bump. Calculation by an elementary method shows that in magnitude the reaction force is directly proportional to the density of the fluid, to the square of the mean flow speed, and to the maximum thickness to horizontal length ratio of the bump. When the bump is symmetric front to back, there is no net horizontal reaction force on the bump. An asymmetric bump has a net horizontal reaction force that points away from the face of the bump that has the greater mean slope to its profile and parallel to the flat wall, and its characteristics are independent of the direction of mean flow. Vertical reaction forces on bumps are mentioned. Comparison of the horizontal reaction force on a bump in a wall with the frictional drag force on the bump is made difficult by the uncertainties in the magnitude of the friction force, but when these two forces are opposed, the reaction force can partially offset friction and make it effectively smaller than it would be in the absence of the reaction force.

Keywords: fluidsolid interaction, Newton's third law, reaction forces

Received: November 8, 2004; Published Online: December 15, 2008