Shear Stress at Wall

If the polymer flow is steady, the sum of all the forces acting on the fluid element is zero  

Fj = (surface area) x (diag/unit surface) = surface area x shear stress 

Since the flow pattern is constant along the pipe length, dPIdz is constant and Eqnation 8.16 can be rewritten as  

From Equation 8. 17, it can be concluded the shear stress r has a linear relationship with the element radius r, and it increases from zero at the pipe center linearly with r to a maximum (r ) at the wall. The shear stress at the wall is then given by  

Therefore, when a polymer fluid flows through a pipe with known dimensions (i.e., L and R), the shear stress at the pipe wall can be easily obtained from the pressure drop between the ends of the pipe. In addition, the shear stress at an arbitrary point in the pipe can be obtained by  

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B Ratio of vertical shear stress at wall to vertical normal stress at wall... 

For the two parallel plates where = 4 yo, the shear stress at wall is constant and is written as... 

In the simplified case of a Newtonian fluid, the material viscosity is not changed by shearing in the nip (i.e. n = n in Figure 3) and the following relationships are established for the maximum shear rate ( Y ) and shear stress ( ) at wall (of the... 

Capillary length, L Shear stress at wall End effect... 

CTrw radial stress at wall due to particle slug. Pa CTsw normal wall stress due to material weight. Pa (Tw wall stress, i.e. total normal wall stress. Pa axial stress in particle slug. Pa tw shear stress at wall. Pa... 

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