Pulsing Flows of a Viscous Incompressible Liquid in a Pipe with Elastic Walls

As you know, the recent intensive introduction into practice of flexible pipelines made of polymer synthetic materials, pulsating fluid flow in elastic pipes is of great importance. As you know, the recent intensive introduction into practice of flexible pipelines made of polymer synthetic materials, pulsating fluid flow in elastic pipes is of great importance. By solving the problem, the necessary hydrodynamic parameters will be determined, such as pressure distributions, velocities, flow rates, the speed of propagation of the pulse wave pressure and their decay. For the first time in this article, a decrease in hydraulic resistance in a pulsating flow through pipes due to the elasticity of the wall will be determined. The dependence of the dimensionless value of the pressure pulse wave on the vibrational number was investigated .The speed of the pulse wave was compared with the speed of Moens-Korteweg , and significant differences were revealed between them occurring at lower values of the Womersley oscillatory parameter, at large values of which significant differences are not observed. The dependence of the reciprocal damping per wavelength on the vibrational number , was also investigated; it was shown that the damping is free at smaller values of the Womersley vibrational parameter, practically equal to zero, and at large values of which it asymptotically approaches unity.

Study on Natural Vibration Characteristics Based on the Coupled Wave Theory of Spring Supported Elastic Pipes and Fluids

A gradient of a blood flow velocity on the surface of a blood vessel is one of the clinical medicine concerns from the view point of prevention of the arteriosclerosis. In previous study, we formulated a relationship between the pressure and a flow velocity based on the coupled wave theory of elastic pipes and Newtonian fluids [1]. In addition, a flow velocity distribution and a wall shear stress are estimated by using the blood pressure data, which are non-invasively obtained by the tonometry method. This method is quasi-analytical method to apply the coupled wave theory for industrial flow field inside steel pipes proposed by Urata [4] to blood vessel, and has the advantage of systematic estimator compared with the numerical calculation. However, the coupled wave theory has applied to the elastic pipes that were assumed to be infinitely long. In addition, a single wave was assumed to be dominant within the elastic pipes and the Newtonian fluids. Therefore, in order to apply various length vessels in clinical field, the boundary of the blood vessels that varies from site to site, and the natural vibration characteristics that depend on the boundary conditions, could not be reflected in the wall shear stress estimation. In general, in order to solve the forced vibration with the boundary condition, it is necessary to clarify natural frequency and natural mode as natural vibration characteristics of structure. In this study, we introduce the spring supported elastic pipes to the coupled wave theory and formulated a relationship between the natural vibration characteristics and the boundary conditions. In this proposed method, the spring-supported elastic pipe has a feature that can be treated as an arbitrary boundary condition of an artery by giving an appropriate spring coefficients. Therefore, it is easy to apply to various types of blood vessels clinically. By investigating the natural vibration characteristics of blood vessels that varies from site to site, it may be possible to clarify fluctuations of blood flow in response to blood pressure with some frequency-bands. In addition, natural angular frequencies and natural modes of the spring supported elastic pipes and the Newtonian fluids were estimated for general blood vessel based on the coupled wave theory. In the result, the natural angular frequencies and the natural modes that reflect the clinical vibration characteristics to some extent can be estimated. On the other hand, particular modes may not reflect boundary condition, and further examination of the relationship between natural vibration characteristics and boundary condition is needed.