# 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:

• 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).

## 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:

$q = \frac{V_y Q_x}{I_x}$

where

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

## Notes

1. ^ a b 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