Flow of Fractal Fluid in Pipes: Non-Integer Dimensional Space Approach

Abstract

Using a generalization of vector calculus for the case of non-integer dimensional space we consider a Poiseuille flow of an incompressible viscous fractal fluid in the pipe. Fractal fluid is described as a continuum in non-integer dimensional space. A generalization of the Navier-Stokes equations for non-integer dimensional space, its solution for steady flow of fractal fluid in a pipe and corresponding fractal fluid discharge are suggested.

arXiv comment24 pages. LaTeX, 8 figures. arXiv admin note: substantial text overlap with arXiv:1503.02022

References in corpus (11)

• Continuous Medium Model for Fractal Media
• Fractional Hydrodynamic Equations for Fractal Media
• Vector Calculus in Non-Integer Dimensional Space and its Applications to Fractal Media
• Fractional Systems and Fractional Bogoliubov Hierarchy Equations
• Fractional Liouville and BBGKI Equations
• Wave Equation for Fractal Solid String
• Laplace Operators on Fractals and Related Functional Equations
• Quantum mechanics in fractional and other anomalous spacetimes
• Solutions of a particle with fractional $\delta$-potential in a fractional dimensional space
• Dynamics of Fractal Solids
• Deformation of quantum mechanics in fractional-dimensional space

Cited by in corpus (4)

• Anisotropic Fractal Media by Vector Calculus in Non-Integer Dimensional Space
• Large Lattice Fractional Fokker-Planck Equation
• Vanishing in Fractal Space: Thermal Melting and Hydrodynamic Collapse
• Fractatomic Physics: An Invitation with Atomic Stability and Rydberg States in Fractal Spaces