Newtonian fluid: Definition from Answers.com

Continuum mechanics

Laws
Conservation of mass Conservation of momentum Conservation of energy Entropy inequality

Solid mechanics
Solids · Stress · Deformation · Finite strain theory · Infinitesimal strain theory · Elasticity · Linear elasticity · Plasticity · Viscoelasticity · Hooke's law · Rheology

Fluid mechanics
Fluids · Fluid statics Fluid dynamics · Viscosity · Newtonian fluids Non-Newtonian fluids Surface tension

Scientists
Newton · Stokes · Navier · Cauchy· Hooke · Bernoulli

A Newtonian fluid (named after Isaac Newton) is a fluid whose stress versus strain rate curve is linear and passes through the origin. The constant of proportionality is known as the viscosity.

Definition

A simple equation to describe Newtonian fluid behaviour is

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

where

τ

is the shear stress exerted by the fluid ("drag") [Pa]

μ

is the fluid viscosity - a constant of proportionality [Pa·s]

$\frac{du}{dy}$ 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. 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).

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.

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,

τ i j

is the shear stress on the

i t h

face of a fluid element in the

j t h

direction

u i

is the velocity in the

i t h

direction

x j

is the

j t h

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.

	Newtonian viscosity (fluid mechanics)
	apparent viscosity (fluid mechanics)
	laminar flow (fluid mechanics)

	Example for newtonian fluids? Read answer...
	Is blood a newtonian fluid? Read answer...
	Is mercury a non-Newtonian fluid? Read answer...

	Is mercury is anon Newtonian fluid?
	What are some Non-Newtonian fluid?
	Is mineral oil a newtonian fluid?

		Sci-Tech Dictionary. McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved. Read more
		Sci-Tech Encyclopedia. McGraw-Hill Encyclopedia of Science and Technology. Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Read more
		Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Newtonian fluid". Read more

Newtonian fluid

Definition

See also