Newtonian fluid

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.

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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