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Unformatted text preview: Phys. 7268 Assignment 1 Due: 2/3/11 Problem 1 Applications of the Reynolds Number. For problems in which an isothermal fluid flows through a pipe or past an object like a cylinder, an analysis of the Navier-Stokes equations reveals a dimensionless stress parameter called the Reynolds number R , R = vL ν , where v is a characteristic magnitude of the fluid’s velocity field (say the maximum speed of the fluid before it encounters some obstacle), L is the size of the object with which the fluid interacts (e.g., the diameter of the pipe or of the cylinder), and ν is the kinematic viscosity of the fluid, the same parameter that appears in the Rayleigh number (see lecture notes). For small flow speeds corresponding to R < 1, the fluid is usually laminar, i.e., time independent and without an interesting spatial structure (the stream lines are approximately parallel). For Reynolds numbers larger than about 1, laminar flows usually become unstable and some new kind of patterns or dynamics occur. Whenlarger than about 1, laminar flows usually become unstable and some new kind of patterns or dynamics occur....
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- Spring '11