Uniform flow, inertial effects

Liu et al. [1] found that an enlarged manifold can deteriorate the lateral flow uniformity, and higher flow rates would appear at the ends of the die. The inertial effect was neglected here and Re = 0. yo was selected to be 0.05 and /3o = 0.5cm. The effect of the power-law index n on the taper function l y) is displayed in Fig. 4. Note that here y=0 refers to the die end and... 

For turbulent flow, with roughly uniform distribution, assuming a constant friction factor, the combined effect of friction and inertial (momentum) pressure recovery is given by... 

The viscosity of polymeric liquids is usually very high, so the inertial force can be neglected. However, for metal extrusion and coating operations, the fluid viscosity can be low and the inertial force cannot be neglected. Leonard [5] and Lee and Liu [6] used the one-dimensional lubrication approach to analyze the effect of inertial force, and their results showed that the inertial force will deteriorate the flow uniformity. To regain perfect flow distribution in Die I, we need to substitute Eq. (14) into Eq. (9) and select Q = y- The... 

The major practical use of Equation 11.1 lies in testing whether a film of uniform initial thickness ho remains stable or eventually become unstable with time. The solution of linearized equations of motion incorporating the effect of intermolecular forces, can be simplified by the lubrication approximation (non-inertial laminar flow in thin films) and admit space periodic solutions for the film thickness h(x, t) = ho + E sin(kx) exp(cof) with ... 

---