# Shear flow

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.

## Definition

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:

where

*q*- the shear flow*V*_{y}- the shear force perpendicular to the neutral axis*x*through the entire cross-section*Q*_{x}- the first moment of area about the neutral axis*x*for a particular web section of the cross-section*I*_{x}- the second moment of area about the neutral axis*x*for the entire cross-section

## Notes

- ↑
^{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

## References

- 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