Viscosity

Viscosity arises from intermolecular interactions that cause adjacent fluid layers to resist sliding against each other. This resistance creates a velocity gradient, scaling from a stationary surface layer to faster-moving fluid at the center. The internal friction between layers opposes flow and requires external force to maintain motion.

Newton's law of viscosity states that viscous force is proportional to both the contact area and the velocity gradient, expressed as F = −ηA(dv/dz). The coefficient of viscosity η is the proportionality constant connecting applied force to flow rate. This relationship holds for gases and most liquids under laminar flow conditions.

As temperature increases, liquid viscosity generally decreases because molecular motion overcomes intermolecular forces. Conversely, higher pressure tends to increase viscosity by compressing the fluid and strengthening intermolecular interactions. These relationships are critical for predicting fluid behavior across different conditions.

The Reynolds number is a dimensionless ratio of inertial to viscous forces that determines whether flow is laminar or turbulent. High viscosity promotes laminar flow with smooth, orderly motion where viscous forces dominate. Low viscosity favors turbulent flow with random velocity fluctuations when inertial forces dominate.

Poiseuille's equation describes the volume flow rate through a cylindrical tube under laminar flow conditions. Flow rate is directly proportional to the pressure gradient and the fourth power of the tube radius, but inversely proportional to fluid viscosity and pipe length. This relationship is fundamental to understanding viscous flow in confined geometries.

The SI unit of viscosity is the Pascal-second (kg m⁻¹ s⁻¹). The non-SI unit is the poise, where 1 poise equals 10⁻¹ kg m⁻¹ s⁻¹. Centipoise and millipoise are also common measurements used in laboratory and industrial applications.

Laminar flow is smooth and orderly with stable velocity gradients where viscous forces dominate. Turbulent flow exhibits random velocity fluctuations and multidirectional fluid movement at high flow rates. Both are types of bulk flow, but turbulent flow occurs when Newton's law of viscosity breaks down and inertial forces become dominant.