# Shear flow

The term shear flow is used in solid mechanics as well as in fluid dynamics. Loosely speaking, shear flow is defined as:

• the gradient of a shear stress force through the body (in solid mechanics);
• the flow induced by such a force gradient (in a fluid).

In this article the first definition from solid mechanics is used. See Viscosity for a fuller treatment about the term from fluid dynamics.

## Dimensions

In solid mechanics, shear flow is given in dimensions of force per 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