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Engineering · Mechanical Engineering
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A type of wire-coating die consists of a cylindrical wire of radius R placed vertically along the axis of a cylindrical die of radius Ro. The polymer melt flows through the narrow annular region and may be approximated as a steady-state Newtonian fluid of constant viscosity μ and density ρ. Gravitational acceleration is g. At some distance downstream of the dire exit (see the figure) a uniform coating of thickness δ is formed around the wire When the annulus gap δο-(Ro-R) or the coating thickness dis very small. the flow can be considered as a thin layer liquid film over a flat surface. For example, the flow in the annulus of the dire is equivalent to the flow between two flat plates. Answer the following questions in terms of the given parameters ρ, μ, g, R, Ro, and 8, (a) (30 points) If the pressure in the die is uniform, determine the velocity profile Uz in the annular region of the die and the coating thickness δ (b) (10 points) To increase the coating thickness, one could impose a pressure gradient in the z direction in the annular region of the dire to help the flow move. If the coating thickness δ is increased to δο (the annulus gap), determine the pressure gradient 2 that is needed Air op

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