JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV TRANSPORT PHENOMENA Previous Question Paper (September - 2021 - R16)

Newton's law of viscosity states that for a fluid in laminar flow, the shear stress (τ) acting on a fluid layer is directly proportional to the velocity gradient (dv/dy) perpendicular to the direction of flow. Mathematically, this is expressed as:

where μ is the dynamic viscosity of the fluid. The negative sign indicates that momentum is transferred in the direction of decreasing velocity.

The kinetic theory of gases explains viscosity at low density by considering the random molecular motion of gas molecules. In a gas with a velocity gradient, molecules moving between layers carry their momentum with them. When molecules from a faster layer move to a slower layer, they increase the momentum of the slower layer, and vice versa, resulting in a net transfer of momentum that manifests as viscous drag.

Key aspects of the theory include:

• Molecules possess a mean free path (λ), which is the average distance traveled between collisions.
• Viscosity is derived as μ = (1/3)ρvλ, where ρ is the gas density and v is the average molecular speed.
• Since density (ρ) is inversely proportional to the specific volume and the mean free path (λ) is inversely proportional to density, the product ρλ remains independent of pressure at low densities.
• Consequently, the viscosity of a gas at low density is independent of pressure and increases with the square root of the absolute temperature (T^1/2), as the average molecular speed v is proportional to the square root of temperature.