Newton's law of viscosity relates to:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2004
Detailed Explanation
Newton's law of viscosity provides the constitutive equation for simple fluids. In fluid kinematics, the rate of shear strain is geometrically identical to the rate of angular deformation.
Newton's law of viscosity:
\[ \tau = \mu \frac{d\theta}{dt} = \mu \frac{du}{dy} \]
Here \(\frac{d\theta}{dt}\) represents the rate of angular deformation (rate of shear strain), and \(\mu\) is the dynamic viscosity. The book's official answer key designates option (b).
Why “viscosity and rate of angular deformation” Is Correct
Newton's law relates shear stress to dynamic viscosity and the rate of angular deformation (\(\tau = \mu \frac{d\theta}{dt}\)). Option (b) is the official key given by the examination commission.
Why the Other Options Are Wrong
- A. intensity of pressure and rate of angular deformation: Pressure is a normal stress and is not part of Newton's viscosity law for laminar shear.
- C. among shear stress, viscosity and temperature: While viscosity varies with temperature, Newton's law does not explicitly incorporate temperature in its relation.
- D. none of these: Option (b) is the accepted key.
Key Point
Newton's law relates shear stress, dynamic viscosity, and rate of angular deformation (τ = μ·dθ/dt).
Key Concepts for Students
- Rate of angular deformation dθ/dt equals velocity gradient du/dy.
- Shear stress is proportional to deformation rate in fluids, unlike solids where stress is proportional to deformation.
- Newtonian fluids have a constant coefficient of viscosity μ.
Practice more: this is question 80 in Properties of Fluid MCQs – Part 6. Try the whole set and check every answer instantly.