Which equation relates shear stress and velocity gradient in a Newtonian fluid?
- ABernoulli’s equation
- BNavier-Stokes equation
- CNewton’s law of viscosityCorrect
- DEuler’s equation
Solution
Concept
Relation between shear stress and velocity gradient
Formula
τ = μ du/dy
Step-by-step solution
1. Newtonian fluids obey τ = μ (du/dy). 2. This is called Newton's law of viscosity.
Explanation
Newton's law of viscosity states that the shear stress is directly proportional to the rate of shear strain (velocity gradient), with the dynamic viscosity as constant of proportionality.
Shortcut
τ = μ du/dy.
Common mistake
Choosing Navier–Stokes because it includes viscosity.
Correct answer: C) Newton’s law of viscosity