POLYFLOW - evaluation of a typical wall shear rate
Considering a flow rate Q, and some geometric dimensions (width L, half height H, radius R), what is a typical wall shear rate g-dot? The formulae below provide typical values; they assume that the geometry is smooth and that the viscosity is constant. For shear-thinning materials, the actual wall shear rates can be some 50% larger. 2D planar flow (between two plates): - the flow rate Q is given per transverse unit of length [thus e.g. cm^3/s/cm] - the channel has a height 2H - the typical wall shear rate is given by g-dot = 3.Q/(2.H^2) 2D axisymmetric flow (through a circular tube): - the flow rate concerns the whole circular cross section - the cross section has a radius R - the typical wall shear rate is given by g-dot = 4.Q/(pi.R^3) 2D axisymmetric flow (through an annular tube): - the flow rate concerns the whole annular cross section - the cross section has an average radius R and an opening 2e - the typical wall shear rate is given by g-dot = 3.Q/(4.pi.R.e^2) or Q/(4.R.e^2) 3D flow: - the flow rate concerns the actual cross section - the cross section has a length L and a width 2H (with H < L) - the typical wall shear rate is given by g-dot = 3.Q/(2.L.H^2) - for an annular cross section, the actual geometry can be unrolled. |
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