Newton’s Law of Viscosity

Newton’s Law of Viscosity, Newtonian and Non-Newtonian Fluids

Viscosity is the physical property that characterizes the flow resistance of simple fluids. Newton’s law of viscosity defines the relationship between the shear stress and shear rate of a fluid subjected to a mechanical stress. The ratio of shear stress to shear rate is a constant, for a given temperature and pressure, and is defined as the viscosity or coefficient of viscosity. Newtonian fluids obey Newton’s law of viscosity. The viscosity is independent of the shear rate.

Non-Newtonian fluids do not follow Newton’s law and, thus, their viscosity (ratio of shear stress to shear rate) is not constant and is dependent on the shear rate.

Dynamic viscosity is the coefficient of viscosity as defined in Newton’s law of viscosity. Kinematic viscosity is the dynamic viscosity divided by the density.

Viscosity is the physical property that characterizes the flow resistance of simple fluids.
Viscosity is the property of a fluid by virtue of its offers resistance to the movement of one layer of fluid over an adjacent layer.

Viscosity

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Internal versus External Flow

Internal versus External Flow A fluid flow is classified as being internal or external, depending on whether the fluid flows in a confined space or over a surface. The flow of an unbounded fluid over a surface such as a plate, a wire, or a pipe is external flow. The flow in a pipe or duct is internal flow if the fluid is completely bounded by solid surfaces. Water flow in a pipe, for example, is internal flow, and airflow over a ball or over an exposed pipe during a windy day is external flow (Fig. 1–18). The flow of liquids in a duct is called open-channel flow if the duct is only partially filled with the liquid and there is a free surface. The flows of water in rivers and irrigation ditches are examples of such flows. Internal flows are dominated by the influence of viscosity throughout the flow field. In external flows the viscous effects are limited to boundary layers near solid surfaces and to wake regions downstream of bodies.

Expression for capillary rise and capillary fall - Jurin's law

Expression for capillary rise and capillary fall - Jurin's law Expression for height in Capillary rise Consider a narrow glass tube of diameter of d dipped in a liquid (say water). Water in the tube will rise above the adjacent liquid level. It is called capillary rise. Let σ = Surface tension of liquid. ϴ = Angle of contact between the glass tube and the liquid surface. h = Height of liquid column in glass tube. Under equilibrium, two forces are acting on the water inside. The first one is weight of water column and second is the upward force acting on water due to surface tension. The weight of liquid of height h should be balanced by the force at liquid surface. This force at surface of liquid is due to surface tension. The weight of liquid of height h in the tube = Volume x ρ x g = (π/4)d 2 x h x ρ x g Here ρ = density of liquid g = acceleration due to gravity. The vertical component of surface tensile force = surface tension x circumference x cosϴ = σ x πd x cosϴ At eq...

capillary rise

A liquid of density ρ ρ and surface tension σ σ rises in a capillary of inner radius r r to a height h = 2 σ cos θ ρ g r h = 2 σ cos ⁡ θ ρ g r where θ θ is the contact angle made by the liquid meniscus with the capillary’s surface. The liquid rises due to the forces of adhesion, cohesion, and surface tension. If adhesive force (liquid-capillary) is more than the cohesive force (liquid-liquid) then liquid rises as in case of water rise in a glass capillary. In this case, the contact angle is less than 90 deg and the meniscus is concave. If adhesive force is less than the cohesive force then liquid depresses as in case of mercury in a glass capillary. In this case, the contact angle is greater than 90 deg and the meniscus is convex. The formula for capillary rise can be derived by balancing forces on the liquid column. The weight of the liquid ( π r 2 h ρ g π r 2 h ρ g ) is balanced by the upward force due to surface tension ( 2 π r σ cos θ ...

Fluid mechanics

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