Newtonian fluid

A Newtonian fluid is a fluid in which shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear.

Related Topics:
Fluid - Shear stress - Velocity - Gradient - Perpendicular

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The constant of proportionality is known as the viscosity.

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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.

Related Topics:
Temperature - Pressure

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If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress, in the Cartesian coordinate system, is

Related Topics:
Incompressible - Cartesian coordinate system

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: au_{ij}=muleft(rac{partial v_i}{partial x_j}+rac{partial v_j}{partial x_i}-rac{2}{3}delta_{ij} ablacdotmathbf{v} ight)

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where

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: au_{ij} is the shear stress on the i^{th} face of a fluid element in the j^{th} direction

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:v_i is the velocity in the i^{th} direction

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:x_j is the j^{th} direction coordinate

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:delta_{ij} is the Kronecker delta

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If a fluid does not obey this relation, it is termed a non-Newtonian fluid.

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