# 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).

## In solid mechanics

In solid mechanics, the 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

## In fluid mechanics

Main article: Viscosity

In fluid mechanics, the term shear flow (or shearing flow) refers to a type of fluid flow which is caused by forces, rather than to the forces themselves. In a shearing flow, adjacent layers of fluid move parallel to each other with different speeds. Viscous fluids resist this shearing motion. For a Newtonian fluid, the stress exerted by the fluid in resistance to the shear is proportional to the strain rate or shear rate.

A simple example of a shear flow is Couette flow, in which a fluid is trapped between two large parallel plates, and one plate is moved with some relative velocity to the other. Here, the strain rate is simply the relative velocity divided by the distance between the plates.

Shear flows in fluids tend to be unstable at high Reynolds numbers, when fluid viscosity is not strong enough to dampen out perturbations to the flow. For example, when two layers of fluid shear against each other with relative velocity, the Kelvin–Helmholtz instability may occur. Thus,

## 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