Question

Compare Newton's law of viscosity and Hooke's law of elasticity. What is the origin of these "laws"?

Answer 1

Answer:

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.

$\tau\ \alpha \ \frac{\mathrm{d} u}{\mathrm{d} y}$

Or

$\tau\ =\mu \times \frac{\mathrm{d} u}{\mathrm{d} y}$

$\tau\ =Shear\ stress$

$\frac{du}{dy} =$ Rate of shear deformation

$\mu\ =Viscosity$

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.

$\sigma\ \alpha\ \epsilon$

$\sigma=E\ \epsilon$

where E is constant of proportionality known as Young's Modulus and it represents the stiffness of the material.