Viscous stresses try to stop relative motion between near by parts of the fluid.
Said differently, whenever there is a strain in the fluid, a stress acts to reduce the strain. In order for the fluid element to be in local equilibrium, it is necessary that these forces exactly balance. As , this is clearly a disaster. Our goal is to figure out the form of these tangential stresses. The stress tensor is a matrix with i , j component which has the property that the stress acting in the direction of the unit vector is just .