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Engineering · Mechanical Engineering
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Stokes first problem is very important in engineering. It can be extended to the heat transfer. An infinitely long plate filled with Newtonian viscous fluid. It starts with stationary case. When, the plate suddenly be moved. The flow field is assumed to be fully developed, incompressible, unsteady, laminar, constant viscosity coefficient and ignore pressure and gravitation. The conditions and schematic are shown as the following fig.2 plate ug is constant fig.2 Please, write the Navier-Stoke equation in detail, and use a few words to describe each term assume the flow is incompressible. (15%) (a) (b) In this problem, put your simplified given-conditions to some terms in (c) The dimensionless velocity is which into (b) simplified equation can be (d) Use into dimensionless equation, and adopt chain rule (ex: etc.) and to Navier-Stoke equation with a slash line and notation, then simplify equations.( 1 5%) observed. Apply the Buckingham pi theorem to rewrite in dimensionless form. (10%) Hint: you can get solve the problem. The dimensionless conditions are and . Find the velocity profile .(10%)

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