Shear flow

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The term shear flow is used in solid mechanics as well as in fluid dynamics. The expression shear flow is used to indicate:

  • the gradient of a shear stress caused by torsion on a closed, thin-walled tube (in solid mechanics);[1]
  • the flow induced by a force (in a fluid).

This article is about shear flow in solid mechanics. See Viscosity for a fuller treatment about the concept in fluid dynamics.


In solid mechanics, shear flow q in a closed, thin-wall tube is defined as the internal shearing force V per unit of length of the perimeter around a thin section. Shear flow has the dimensions of force per unit of length.[1] This corresponds to units of newtons per meter in the SI system and pound-force per foot in the English Engineering and British Gravitational Systems.

Shear flow in semi-monocoque structures

The equation for shear flow in a particular web section of the cross-section of a semi-monocoque structure is:


q - the shear flow
Vy - the shear force perpendicular to the neutral axis x through the entire cross-section
Qx - the first moment of area about the neutral axis x for a particular web section of the cross-section
Ix - the second moment of area about the neutral axis x for the entire cross-section


  1. 1.0 1.1 Higdon, Ohlsen, Stiles and Weese (1960), Mechanics of Materials, article 4-9 (2nd edition), John Wiley & Sons, Inc., New York. Library of Congress CCN 66-25222


  • Riley, W. F. F., Sturges, L. D. and Morris, D. H. Mechanics of Materials. J. Wiley & Sons, New York, 1998 (5th Ed.), 720 pp. ISBN 0-471-58644-7

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