Final answer:
Viscosity is the resistance of a fluid to flow, represented by the coefficient of viscosity (η). It is determined by the internal frictional force, surface area, and velocity gradient. The SI unit of viscosity is Pascal-seconds (Pa·s), derived through dimensional analysis.
Step-by-step explanation:
Viscosity is defined as the resistance of a fluid to flow. This property is akin to internal friction within the fluid and encompasses the interactions between the fluid layers as they move past each other. A fluid with high viscosity, like syrup, flows slowly due to strong internal friction, whereas a fluid with low viscosity, like water, flows more freely. The coefficient of viscosity (η) is a measure of this internal resistance and is defined by the equation η = F / (A * (dv/dx)), where F represents the internal frictional force, A is the surface area through which the liquid is moving, and dv/dx is the velocity gradient perpendicular to the direction of flow.
When considering laminar flow, we find that the flow of liquid is streamlined and smooth, with each layer of liquid sliding past the adjacent layers without mixing. The pressure drop along the flow is directly proportional to the viscosity and velocity gradient, as explained by Poiseuille's law. This law helps us calculate flow and resistance and explains how pressure drops due to the viscous resistance exerted by the fluid.
By dimensional analysis, the units of viscosity in the International System of Units (SI) are derived to be Pascal-seconds (Pa·s), where 1 Pa·s is equivalent to 1 N·m / [(m/s) m²], indicating the force per unit area required to maintain a velocity gradient of one meter per second per meter across the fluid.