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# Simple shear

Simple shear is a special case of deformation of a fluid where only one component of velocity vectors has a non-zero value:

$V_x=f\left(x,y\right)$

$V_y=V_z=0$

And the gradient of velocity is perpendicular to it:

$frac \left\{partial V_x\right\} \left\{partial y\right\} = dot gamma$,

where $dot gamma$ is the shear rate and:

$frac \left\{partial V_x\right\} \left\{partial x\right\} = frac \left\{partial V_x\right\} \left\{partial z\right\} = 0$

The deformation gradient tensor $Gamma$ for this deformation has only one non-zero term:

Simple shear with the rate $dot gamma$ is the combination of pure shear strain with the rate of $dot gamma over 2$ and rotation with the rate of $dot gamma over 2$:

An important example of simple shear is laminar flow through long channels of constant cross-section (Poiseuille flow).

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