Newtonian Fluid

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Newtonian fluid

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.

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)
which is induced by a uniform shear stress &tgr;. 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

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

Newtonian Fluid

a fluid that obeys Newton’s law of viscous friction. For rectilinear laminar flow, this law states that the shear stress τ in the planes of contact of layers of the fluid is directly proportional to the derivative of the rate of flow ν in the direction of the normal n to these planes; that is, τ = η(∂ν/∂n) where η is the coefficient of viscosity. In the general case of a three-dimensional flow, for a Newtonian fluid a linear relation holds between the stress tensor and the tensor of the rates of strain. Most liquids, including water and lubricating oil, and all gases have the properties of a Newtonian fluid. The flow of Newtonian fluids is studied in hydrodynamics and aerodynamics.

Non-Newtonian fluids are fluids for which the relations indicated above are not linear, for example, for the rectilinear flow

where k ≠ 1. Examples are a number of suspensions and solutions of polymers. Rheology is the study of such flows.

S. M. TARG

Newtonian fluid

[′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.
References in periodicals archive ?
8: (a) capsule shapes for difference power-law indices (the dashed line is for the Newtonian fluid case where n = 1.
These solutions were chosen as model Newtonian fluids (18) and exhibited constant shear viscosities up to a shear rate of [10.
Let us consider an incompressible Newtonian fluid between eccentric rotating porous disks.
The generalized Newtonian fluid includes Newtonian fluid and inelastic non-Newtonian fluid, and the constitutive equation is as follows:
24) This analytical solution is only used for the estimation of final film thickness for Newtonian fluid and was not accurate for the prediction of non-Newtonian coating film thickness for 0.
In both of the figures, the enhancement of viscoelasticity modifies the primary fluid velocity u and secondary fluid velocity w in comparison with Newtonian fluid flow phenomenon.
Water is an example of the Newtonian fluid which means that it will not change its original fluid state when force acting on it.
Elbashbeshy [5] studied the heat transfer over a stretching surface immersed in an incompressible Newtonian fluid when the surface is subjected to a variable heat flux.
Using a bipolar coordinate system and Green's function, Heyda [14] presented analytical solutions for Newtonian fluid flow in an eccentric annulus in the form of an infinite series.
For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity: [([[eta].

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