Shear Stress Quiz: Test Your Knowledge Of Fluid Forces

Concept: Correct property. Dynamic viscosity directly measures resistance to shearing flow. Density and volume do not measure internal friction.

Concept: Different quantities. Dynamic viscosity (μ) and kinematic viscosity (ν) are related but not identical. They describe different aspects of flow resistance and have different units.

Concept: Viscosity definition (mechanics). Viscosity describes how strongly a fluid resists shearing motion. It is not the same as compressibility or density.

Concept: Linear scaling. In Newtonian fluids, τ scales linearly with dydu​. Doubling the gradient doubles the stress.

Concept: Gradient intuition. Large gradients come from big changes over small distances. Strong relative sliding between neighbouring layers creates high shear.

Concept: Two-factor dependence. Shear stress depends on both μ and dydu​. Even small μ can yield large τ if the gradient is huge.

Concept: Naming the law. This equation defines Newtonian behaviour in shear flow. It states shear stress is proportional to velocity gradient.

Concept: Shear stress meaning. Shear stress acts tangentially and tends to make layers slide. In fluids, it appears when adjacent layers move at different speeds.

Concept: Zero relative motion. With no relative motion, all layers share the same speed. That makes dydu​=0, so Newtonian shear stress becomes zero.

Concept: Couette flow role of viscosity. Maintaining a velocity difference between plates requires shear stress. Higher viscosity means more stress (more force per area) for the same gradient.

Concept: Units of viscosity. Dynamic viscosity has units of Pa·s, consistent with shear stress (Pa) divided by velocity gradient (1/s). The units reflect resistance to shear over time.

Concept: Shear and friction link. A bigger gradient means neighbouring layers differ more in speed. That increases the viscous “dragging” between layers.

Concept: Velocity gradient. A velocity gradient measures how rapidly speed changes across the flow. It captures how strongly layers are trying to slide past each other.

Concept: Newton’s law of viscosity. Newton’s law links shear stress to how quickly velocity changes between layers. This is why larger velocity gradients produce larger shear stresses.

Concept: Shear stress notation. τ represents tangential force per area. It’s the key stress associated with viscous shear in flowing fluids.

Concept: Proportionality. For Newtonian fluids, τ=μdydu​. Increasing μ increases the shear stress required for the same gradient.

Concept: Dynamic viscosity symbol. Dynamic viscosity (μ) quantifies resistance to shearing deformation. It connects shear stress to the velocity gradient for Newtonian fluids.

Concept: Kinematic viscosity symbol. ν is used for kinematic viscosity. It relates dynamic viscosity to density and is useful in flow-regime analysis.

Concept: Kinematic viscosity units. ν behaves like a momentum diffusion coefficient. That’s why its units are area per time.

Concept: ν=μ/ρ. For fixed μ, increasing ρ reduces ν. This changes Reynolds number and how easily momentum spreads.