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Newton's law of viscosity
It relates shear stress in a fluid flow to velocity gradient in the direction perpendicular to the flow of fluid.
[tex]\tau\ \alpha \ \frac{\mathrm{d} u}{\mathrm{d} y}[/tex]
Or
[tex]\tau\ =\mu \times \frac{\mathrm{d} u}{\mathrm{d} y}[/tex]
[tex]\tau\ =Shear\ stress[/tex]
[tex]\frac{du}{dy} =[/tex] Rate of shear deformation
[tex]\mu\ =Viscosity[/tex]
Hooke's Law
It states that within the limit of elasticity, the stress-induced (σ ) in the solid due to some external force is always in proportion with the strain (ε ). In other words, the force causing stress in a solid is directly proportional to the solid's deformation.
[tex]\sigma\ \alpha\ \epsilon[/tex]
[tex]\sigma=E\ \epsilon[/tex]
where E is constant of proportionality known as Young's Modulus and it represents the stiffness of the material.
The type of matter is different in both Newton's and Hook's laws.
Comparison between Newton's law of viscosity and Hooke's law of elasticity
Newton's law of viscous deformation deals with deformation of fluids that is subjected to a load. This law states that shears stress is proportional to shear strain.
While on the other hand, Hooke's law of elasticity deals with deformation in solids which are subjected to a load so we can conclude that the type of matter is different in both Newton's and Hook's laws.
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