# 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);
• 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. 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