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104  FLOW  OF  FLUIDS

                                                     /==+*:
                                                          ...........................
                                                         ...........................
                                                         ...........................
                                                        .:::::A:: .................
                                                                ..........
                                                   F+/F/+. ................
                                                                ........
                                                      ......................
                                                     ..........................
                                                            .................
                                                          .....................
                                                          ........................
                                                        ..........................
                                                              :
                                                        .::::::A: : : : : : : : : : : : : :
                                                             :
                                                       .:z::::::::::::::::::::...
                                                      .......................  :.
                                                      .......  ........................   U?
                                                                                                                   7
                                                                                              eBingham plastic
                                                                                                            -----.

                                                                                      E
                                                                                     - 3








                        Deformation  rate Idu/dyl
                              (b)






















                          Shearing stress -

                                  (e)
                Figure 6.2.  Relations between shear stress, deformation rate, and viscosity of several classes of fluids. (a) Distribution of velocities of a fluid
                between two layers of  areas A which are moving relatively to each other at a distance x  under influence of  a force F. In the simplest case,
                F/A = y(du/dx) with y constant. (b) Linear plot of shear stress against deformation. (c) Logarithmic plot of  shear stress against deformation
                rate. (d) Viscosity as a function of shear stress. (e) Time-dependent viscosity behavior of  a rheopectic fluid (thixotropic behavior is shown by
                the dashed line). (f) Hysteresis loops of  time-dependent fluids (arrows show the chronology of imposed shear stress).
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