Table of Contents
What is power law in fluid flow?
The power law is usually used to model shear thinning by making 0 < n < 1, though it can also be used for modelling shear-thickening by making n > 1. A smaller value of n represents a higher shear thinning of the fluids.
What is K in power law?
K is the flow consistency index (SI units Pa sn), ∂u∂y is the shear rate or the velocity gradient perpendicular to the plane of shear (SI unit s−1), and. n is the flow behavior index (dimensionless).
What is a power law function?
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another.
How do you find the K and N in power law?
n and K can be calculated from any two value of shear rate and shear stress. The method of reading shear rate on the rig comes from a V-G meter. Typically, 600 rpm, 300 rpm and 3 rpm are obtained from every mud test and we can use those reading to determine n and K.
Why do we use power law?
Power laws are very important because they reveal an underlying regularity in the properties of systems. Often highly complex systems have properties where the changes between phenomena at different scales is independent of which particular scales we are looking at.
What is power law formula?
A power law is often represented by an equation with an exponent: Y=MX^B. Each letter represents a number. Y is a function (the result); X is the variable (the thing you can change); B is the order of scaling (the exponent), and M is a constant (unchanging). If M is equal to 1, the equation is then Y=X^B.
Can the Navier-Stokes equation be solved analytically?
There are no methods so far or very highly complex methods to solve these non linearity. N-S equations also show such kind of non linearity hence Analytical solution does not exists.
What do the 5 terms in the Navier-Stokes equations each represent?
where u is the fluid velocity, p is the fluid pressure, ρ is the fluid density, and μ is the fluid dynamic viscosity. The different terms correspond to the inertial forces (1), pressure forces (2), viscous forces (3), and the external forces applied to the fluid (4).
What is the difference between Navier Stokes and Euler equations?
The difference between them and the closely related Euler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model only inviscid flow.
What are Navier-Stokes equations in fluid mechanics?
The Navier-Stokes equations in fluid mechanics are the most general description of a fluid’s mechanical behavior. Solving these equations requires applying some approximation to reduce their complexity. Numerical methods are primarily used in engineered systems because analytical solutions to the Navier-Stokes equations do not exist.
What is a power law fluid?
A Power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid for which the shear stress, τ, is given by ∂ u /∂ y is the shear rate or the velocity gradient perpendicular to the plane of shear (SI unit s−1), and
What are the Navier Stokes equations called?
Continuum mechanics. In physics, the Navier–Stokes equations (/nævˈjeɪ stoʊks/), named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances.
What is power law of viscosity?
Power-law fluid. represents an apparent or effective viscosity as a function of the shear rate (SI unit Pa s). Also known as the Ostwald – de Waele power law this mathematical relationship is useful because of its simplicity, but only approximately describes the behaviour of a real non-Newtonian fluid.