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A UNIVERSAL THEORY OF THE STEADY INCOMPRESSIBLE COUETTE FLOW WITH ZERO SHEAR-STRESS PLANE

Shaoshan Rong

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Abstract

A new universal method is proposed for the calculation of the steady incompressible Couette flow with a zero shear-stress plane. This method applies the kinetic analogy of the Couette flow to the channel flow and six parameter equations of the Couette flow are derived, i.e. two wall-surface shear stresses, the extremal velocities and their coordinates, with which the distribution of velocity and shear stress can be easily obtained. Neither the mixing length hypothesis nor the turbulent adhesive coefficient assumption is needed in this method, but skin friction coefficients and the velocity profiles of a channel flow are required. A new criterion of the Couette flow P is proposed.

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What this paper is about

A new universal method is proposed for the calculation of the steady incompressible Couette flow with a zero shear-stress plane. This method applies the kinetic analogy of the Couette flow to the channel flow and six parameter equations of the Couette flow are derived, i.e. two wall-surface shear stresses, the extremal velocities and their coordinates, with which the distribution of velocity and shear stress can be easily obtained. Neither the mixing length hypothesis nor the turbulent adhesive coefficient assumption is needed in this method, but skin friction coefficients and the velocity profiles of a channel flow are required. A new criterion of the Couette flow P is proposed.

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Available abstract

A new universal method is proposed for the calculation of the steady incompressible Couette flow with a zero shear-stress plane. This method applies the kinetic analogy of the Couette flow to the channel flow and six parameter equations of the Couette flow are derived, i.e. two wall-surface shear stresses, the extremal velocities and their coordinates, with which the distribution of velocity and shear stress can be easily obtained. Neither the mixing length hypothesis nor the turbulent adhesive coefficient assumption is needed in this method, but skin friction coefficients and the velocity profiles of a channel flow are required. A new criterion of the Couette flow P is proposed.

Key concepts: Couette flow, Mechanics, Taylor–Couette flow, Shear stress, Shear flow, Classical mechanics, Shear velocity, Open-channel flow

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