The existing numerical solutions of linear partial differential equations by means of the difference-methods can be applied only to the cases with simple boundary conditions, but not to the cases with complicated boundary conditions. In the present paper, the author tried to obtain a general numerical solution free from such inconvenience, and applying this new solution to the heading problem, examined whether it is of general practical use by comparing the result with that of Ritz's solution of the same problem.

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In the present paper, the author has mentioned a new solution based on Lagrange's Formula of Interpolation as one of the numerical solutions of linear partial differential equations in the case of having a domain surrounded by an arbitrary closed curve, and has examined whether it is of general practical use by obtaining the answer of the heading problem through applying this new solution to it.

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The author deduces some theoretical formulae for the turbulent flow through a fine clearance space (δ) between two parallel walls, one of them being in relative motion to the other at arbitrary angle to the direction of the pressure gradient. Therefore, he applies this formula to the flow through the annular space formed by two concentric pipes in relative rotation, and then obtains an empirical formula for the turbulent flow in such a case using the experimental data of R. J. Cornish. In case of the flow through the concentric double pipes in relative rotation, if we consider the Reynolds number as an important criterion of the state of flow, it is reasonable to adapt [numerical formula] instead of usual [numerical formula], where v is kinematic viscosity, w and v is resultant and axial mean velocity respectively.

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