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Newtonian fluid

 
Sci-Tech Dictionary: Newtonian fluid
 
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(′nü′tō·nē·ən ′flü·əd)

(fluid mechanics) A simple fluid in which the state of stress at any point is proportional to the time rate of strain at that point; the proportionality factor is the viscosity coefficient.

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Sci-Tech Encyclopedia: Newtonian fluid
 
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A fluid whose stress at each point is linearly proportional to its strain rate at that point. The concept was first deduced by Isaac Newton and is directly analogous to Hooke's law for a solid. All gases are newtonian, as are most common liquids such as water, hydrocarbons, and oils. See also Hooke's law; Stress and strain.

A simple example, often used for measuring fluid deformation properties, is the steady one-dimensional flow u(y) between a fixed and a moving wall (see illustration). The no-slip condition at each wall forces the fluid into a uniform shear strain rate ε, given by Eq. (1),
1. \varepsilon = \frac{\partial u}{\partial y} = \frac{V}{H}
which is induced by a uniform shear stress τ. Here V is the speed of the moving wall, H is the perpendicular distance between the walls, and u is the fluid velocity at distance y from the fixed wall.

A fluid sheared between two plates. The resulting strain rate equals <i>V/H</i>.
A fluid sheared between two plates. The resulting strain rate equals V/H.

If the fluid is newtonian, the experimental plot of τ versus ε will be a straight line. The constant of proportionality is called the viscosity μ of the fluid, as stated in Eq. (2).
2. \tau = \mu\varepsilon
The viscosity coefficients of common fluids vary by several orders of magnitude. See also Fluid flow; Fluids; Viscosity.

 
Wikipedia: Newtonian fluid
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Navier–Stokes equations
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A Newtonian fluid (named for Isaac Newton) is a fluid whose stress versus rate of strain 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,

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.

See also

Non-newtonian fluid

External links

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General subfields within physics

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

 
 

 

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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 GNU Free Documentation License. It uses material from the Wikipedia article "Newtonian fluid".  Read more

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