Recall from the study of elasticity (Chapter 50) that when a body is placed under transverse (shear) stress \(\sigma=F_{t} / A\), the resulting strain \(\varepsilon\) is the tangential displacement \(...Recall from the study of elasticity (Chapter 50) that when a body is placed under transverse (shear) stress \(\sigma=F_{t} / A\), the resulting strain \(\varepsilon\) is the tangential displacement \(x\) divided by the transverse distance \(l\) : Fluid flow undergoes a similar kind of shear stress; however, with fluids, we find that the stress is not proportional to the strain, but to the rate of change of strain:
As a consequence of the transverse velocity gradient, the liquid below the dashed line will be dragged forward by the tangential force of the faster liquid above it, and the liquid above the dashed li...As a consequence of the transverse velocity gradient, the liquid below the dashed line will be dragged forward by the tangential force of the faster liquid above it, and the liquid above the dashed line will be dragged backward by the tangential force of the more sluggish liquid below it. The ratio of the tangential force per unit area to the transverse velocity gradient is called the coefficient of dynamic viscosity, for which the usual symbol is η.
