Simple problems of viscous flow

The emphasis in this section has been on viscous behavior but both liquids and amorphous solids can show viscoelastic behavior this will be considered in Section 5.7. 

It is useful to analyze some simple modes of flow in Newtonian fluids. As indicated at the start of this chapter, the analogy between Newton s Law and Hooke s Law can be used to solve some problems of viscous flow. To do this, one assumes the flow is laminar and not turbulent. Laminar flow usually occurs at small flow rates. For simplicity, it will be assumed that the liquid is incompressible and that no slip occurs at the interface between the fluid and its container. 

Consider two plates separated by a Newtonian fluid under the action of a constant shear stress. One can imagine layers in the liquid being sheared past each other, much like a pack of cards. The relative velocity of the plates will depend on the viscosity of the liquid. Indeed, the strain rate is equivalent to the velocity gradient (dv/dx) and, thus, Newton s Law can be written as 

for a constant stress, v=Thlr), where h is the thickness of the fluid. Clearly, this sliding geometry could be used as a technique for measuring viscosity. 

A related problem is the flow of a fluid down a cylindrical tube, length L, under the action of a pressure P, as shown in Fig. 5.4. One can again think of layers of fluid sliding down the tube with velocity v in the x direction. In this case, however, the velocity will be dependent on r. Equation (5.9) is, therefore, written as 

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