Abstract
The dimensionless slippage coefficient is measured in the study of velocity distribution of a fluid in a pipe and in precision measurement of the viscosity of the fluid. A precise and efficient method to measure the dimensionless slippage coefficient has not been found.
In this paper, taking into consideration the slippage of fluid over walls, the flow through an annulus is analysed in a dimensionless form.
The fluid flows through two annuluses with a common geometry but with different wall surfaces coated with two kinds of slippery materials. The flow rate will depend on the slippage characterized by the dimensionless slippage coefficient β*. Suppose β* changes to Δβ* while the measuring condition is kept unchanged. The ratio of the original flow rate to the new flow rate may be written as:
φ=1+3β*/1+3Δβ*
The above equation holds in a wide range of the ratio of inner radius to outer radius of the annulus.
In the new method proposed by the author the flow rates are measured to obtain β*. When Δβ* has been obtained by a thrust method, β* is obtainable from the above equation. When Δβ* such as the dimensionless slippage coefficient of water flowing over glass surfaces is neglisible, β* is expressed approximately as a function of φ only and is obtained by a simple computation. By the new method, the dimensionless slippage coefficient is measured more efficiently than by other methods, independent of the viscosity of the fluid.
The outline of the experimental equipment and the discussions for experimental results are described.
