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    jons theory

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    m15 jons theory

    مُساهمة من طرف teacher في الإثنين 23 يونيو 2008, 10:55 pm

    John's theory

    Laminar shear, the non-constant gradient, is a result of the geometry the fluid is flowing through (e.g. a pipe).



    In general, in any flow, layers move at different velocities and the fluid's viscosity arises from the shear stress between the layers that ultimately opposes any applied force.
    Laminar shear of fluid between two plates. Friction between the fluid and the moving boundaries causes the fluid to shear. The force required for this action is a measure of the fluid's viscosity. This type of flow is known as a Couette flow.



    Laminar shear, the non-constant gradient, is a result of the geometry the fluid is flowing through (e.g. a pipe).


    In general, in any flow, layers move at different velocities and the fluid's viscosity arises from the shear stress between the layers that ultimately opposes any applied force.




    John Newton postulated that, for straight, parallel and uniform flow, the shear stress, τ, between layers is proportional to the velocity gradient, ∂u/∂y, in the direction perpendicular to the layers.


    .
    Here, the constant η is known as the coefficient of viscosity, the viscosity, the dynamic viscosity, or the Newtonian viscosity. Many fluids, such as water and most gases, satisfy Newton's criterion and are known as Newtonian fluids. Non-Newtonian fluids exhibit a more complicated relationship between shear stress and velocity gradient than simple linearity.
    The relationship between the shear stress and the velocity gradient can also be obtained by considering two plates closely spaced apart at a distance y, and separated by a homogeneous substance. Assuming that the plates are very large, with a large area A, such that edge effects may be ignored, and that the lower plate is fixed, let a force F be applied to the upper plate. If this force causes the substance between the plates to undergo shear flow (as opposed to just shearing elastically until the shear stress in the substance balances the applied force), the substance is called a fluid. The applied force is proportional to the area and velocity of the plate and inversely proportional to the distance between the plates. Combining these three relations results in the equation F = η(Au/y), where η is the proportionality factor called the absolute viscosity (with units Pa·s = kg/(m·s) or slugs/(ft·s)). The absolute viscosity is also known as the dynamic viscosity, and is often shortened to simply viscosity. The equation can be expressed in terms of shear stress; τ = F/A = η(u/y). The rate of shear deformation is u / y and can be also written as a shear velocity, du/dy. Hence, through this method, the relation between the shear stress and the velocity gradient can be obtained.
    James Clerk Maxwell called viscosity fugitive elasticity because of the analogy that elastic deformation opposes shear stress in solids, while in viscous fluids, shear stress is opposed by rate of deformation.





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