Shear Stress - Frictional force per area parallel to the surface which it acts. - it has the units of dv Where: = viscosity = shear rate Newton’s Law of Viscocity t = m x yx dy i = direction of the unit normal to the surface on which the force is acting j = direction of the force on the surface. y t yx t Shear stress component is positive when both the vector normal to the surface of action and the force due to shear stress act in the same direction. Normal direction Force direction + + > 0 + - < 0 - + < 0 - - > 0 yz t xy t zy t xz t zx x z

μ>0 Why is shear stress positive or negative? Let’s look at the sign of shear stress  for the region of fluid outlined by the dashed line nT Force due to friction between laminar y >0 x Force due to friction nB The sign of the shear stress depends on the direction of the frictional force and the orientation of the surface. Your text describes the orientation as going from “out to in”. We can also describe the orientation by the normal vector for that surface. The shear stress on the top surface, is positive because the unit normal is in the plus j direction and the force is in the plus i direction. On the bottom surface, the shear stress is also positive because the unit normal is in the minus j direction and the force is in the minus i direction. Notice that is positive since and dv μ>0 t = m x > 0 yx dy

nT Force due to viscosity y < 0 x nB Force due to viscosity The sign of the shear stress in this case is negative because the normal on the top is positive and the force is negative. At the bottom, the normal is negative and the force is positive, so the shear stress is again negative. is negative since and . dv μ>0 < 0 t = m x yx dy