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A Newtonian fluid (named for Isaac Newton) is a fluid that flows like water—its stress versus rate of strain curve is linear and passes through the origin. Continuum mechanics is a branch of Mechanics that deals with the analysis of the Kinematics and mechanical behavior of materials modeled as a continuum e The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov - Lavoisier law says that the Mass of In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product The Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous Fluid substances such Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements FLUID ( F ast L ight '''U'''ser '''I'''nterface D esigner is a graphical editor that is used to produce FLTK Source code Water is a common Chemical substance that is essential for the survival of all known forms of Life. A shear stress, denoted \tau\ ( Tau) is defined as a stress which is applied Parallel or tangential to a face of a material In Mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference The constant of proportionality is known as the viscosity. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress.

## Definition

A simple equation to describe Newtonian fluid behaviour is

$\tau=\mu\frac{du}{dx}$

where

τ is the shear stress exerted by the fluid ("drag") [Pa]
μ is the fluid viscosity - a constant of proportionality [Pa·s]
$\frac{du}{dx}$ is the velocity gradient perpendicular to the direction of shear [s−1]

In common terms, this means the fluid continues to flow, regardless of the forces acting on it. In Fluid dynamics, drag (sometimes called fluid resistance) is the force that resists the movement of a Solid object through a Fluid (a For example, water is Newtonian, because it continues to exemplify fluid properties no matter how fast it is stirred or mixed. Contrast this with a non-Newtonian fluid, in which stirring can leave a "hole" behind (that gradually fills up over time - this behaviour is seen in materials such as pudding, starch in water (oobleck), or, to a less rigorous extent, sand), or cause the fluid to become thinner, the drop in viscosity causing it to flow more (this is seen in non-drip paints, which brush on easily but become more viscous when on walls). A non-Newtonian fluid is a Fluid whose flow properties are not described by a single constant value of Viscosity. Oobleck is a fictional form of green precipitation invented by children's author Dr Paint is any Liquid, liquifiable or mastic composition which after application to a substrate in a thin layer is converted to an opaque Solid

For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure (and also the chemical composition of the fluid if the fluid is not a pure substance), not on the forces acting upon it. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface

If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress, in the Cartesian coordinate system, is

$\tau_{ij}=\mu\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i} \right)$

with comoving stress tensor $\mathbb{P}$ (also written as $\mathbf{\sigma}$)

$\mathbb{P}_{ij}= - p \delta_{ij} + \mu\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i} \right)$

where, by the convention of tensor notation,

τij is the shear stress on the ith face of a fluid element in the jth direction
ui is the velocity in the ith direction
xj is the jth direction coordinate

If a fluid does not obey this relation, it is termed a non-Newtonian fluid, of which there are several types, including polymer solutions, molten polymers, many solid suspensions and most highly viscous fluids. Fluid mechanics is the study of how Fluids move and the Forces on them In Mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually A non-Newtonian fluid is a Fluid whose flow properties are not described by a single constant value of Viscosity. A polymer is a large Molecule ( Macromolecule) composed of repeating Structural units typically connected by Covalent Chemical bonds

## Newtonian fluid

### -noun

1. (physics) a fluid whose stress at each point is linearly proportional to the strain rate at that point
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