First, we lump a modified Navier-Stokes' equation which includes the eddy viscosity as an unknown time-and space-varying parameter by using the finite element method and derive a finite-dimensional dynamic model. In this paper, we present a model-based method for measurement of the eddy viscosity of unsteady turbulent flow in a pipe. For this reason, it is important to develop a dynamic measurement method of the eddy viscosity of turbulent flow. Therefore, it is hard to say that whether or not the prediction of unsteady turbulent flow by those models describe the real flow. However, the turbulence models derived from the eddy viscosity hypothesis are subject to specified steady flows. In general, the undetermined coefficients take different values if the conditions of the flow are different, and have to be prescribed with the aid of empirical information. It is well known that turbulence models based on the eddy viscosity hypothesis are those to formulate the eddy viscosity and each model involves one or more undetermined coefficients.
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