# 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),

*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.

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