Newton’s law of viscosity states that
- AShear stress is directly proportional to the velocity
- BShear stress is directly proportional to the velocity gradientCorrect
- Cshear stress is directly proportional to shear strain
- Dshear stress is directly proportional to the viscosity
Solution
Concept
Definition of Newton's law of viscosity
Formula
τ = μ × (du/dy)
Step-by-step solution
1. Newton's law of viscosity describes the relationship between shear stress and fluid deformation rate. 2. It specifies that shear stress in a fluid is directly proportional to the velocity gradient perpendicular to the direction of flow. 3. Mathematically, shear stress is equal to dynamic viscosity multiplied by velocity gradient. Answer: B
Explanation
Newton's law of viscosity states that the shear stress between adjacent fluid layers is directly proportional to the spatial rate of change of velocity perpendicular to the flow direction, known as the velocity gradient. The constant of proportionality in this relationship is dynamic viscosity. Fluids that follow this linear relationship are classified as Newtonian fluids.
Why the other options are wrong
A) Shear stress is directly proportional to the rate of shear strain (velocity gradient), not velocity alone. C) Shear stress proportional to shear strain defines Hooke's law for elastic solids. D) Viscosity is the constant coefficient of proportionality, not the variable to which shear stress is proportional.
Shortcut
Newton's law of viscosity: Shear stress is directly proportional to velocity gradient.
Common mistake
Confusing velocity gradient with simple velocity or shear strain in Newton's law of viscosity.
Correct answer: B) Shear stress is directly proportional to the velocity gradient