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| Taking the classical steady laminar solution as the first approximation, the critical Reynolds number problem for plane Poiseuille flow is studied by perturbation method. The solution of Navier-Stokes equation is obtained. Then, the critical Reynolds number is expressed by the steady laminar solution. The result shows that, for plane Poiseuille flow, the critical Reynolds number is a function of position. At the wall position, the critical Reynolds number is roughly 1; near the wall position, the critical Reynolds number is very different; for the centre zone of transportation, the critical Reynolds number is a limit value. However, this limit value is very sensitive about initial condition, which is a fact well known for experiment researchers. Except at wall position, the critical Reynolds number is transportation distance dependent. For very long transportation distance, the critical Reynolds number tends to zero. |
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| Keywords:critical Reynolds number, Navier-Stokes equation, plane Poiseuille flow |
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