Viscosity is a property of fluids that measures their resistance to flow. It is influenced by factors such as the surface area of contact, the gradient of flow speed, and the fluid's viscosity constant, called the coefficient of viscosity. The coefficient of viscosity, also known as dynamic viscosity, is denoted by the symbol η. It determines the proportionality between the viscous force and the gradient of flow speed.
Newton's law of viscosity states that the viscous force on a faster-moving fluid is in the opposite direction of its motion.
F = − ηA(dv/dz)
Where, F = viscous force, η = coefficient of viscosity, A = area, and (dv/dz) = velocity gradient
This force tends to slow down the faster-moving fluid and speed up the slower-moving fluid. The law is well obeyed by gases and most liquids under laminar (or streamlined) flow conditions. However, at high flow rates, the law does not hold, and the flow becomes turbulent. Non-Newtonian liquids, deviating from this law, exhibit changes in viscosity coefficient with varying velocity gradients.
The SI unit of viscosity is the Pascal-second or kg m−1 s−1. The non-SI unit is the poise, where 1 poise equals 10−1 kg m−1 s−1, and other common measurements are centipoise and millipoise.
The Reynolds number (NR) is a dimensionless quantity that characterizes the flow of a fluid. It is defined as the ratio of inertial forces to viscous forces in the fluid. The Reynolds number determines whether the flow is laminar or turbulent.
Laminar flow refers to smooth and orderly flow where viscous forces dominate and velocity gradients are stable. On the other hand, turbulent flow is characterized by random fluctuations of velocity and fluid movement in multiple directions. It occurs at high flow rates when Newton's law of viscosity does not hold. Both laminar and turbulent flow are types of bulk (or viscous) flow.
Poiseuille's law, also known as the Poiseuille equation, describes the flow of a viscous fluid through a cylindrical tube. It states that the flow rate is directly proportional to the pressure gradient and the fourth power of the tube radius and inversely proportional to the fluid viscosity. Poiseuille's law is valid for laminar flow in a tube and is widely used in the study of fluid dynamics.
V = [πR4(ΔP)t] / [8ηl]
Viscosity is the internal friction or resistance to flow in a fluid.
Viscosity arises because intermolecular interactions cause adjacent layers to resist sliding, creating a velocity gradient that scales from the stationary surface layer to the faster-moving center.
To maintain this gradient, an external force is applied that is proportional to the area and the velocity gradient described by Newton's law of viscosity, a relationship that connects applied force and flow rate to the fluid's physical properties.
The proportionality constant is the coefficient of viscosity
As temperature increases, the viscosity of a liquid generally decreases, whereas viscosity tends to increase with higher pressure.
The Reynolds number is a dimensionless ratio of inertial to viscous forces in a fluid. It determines flow type. High viscosity promotes laminar flow as viscous forces dominate, while low viscosity favors turbulent flow due to dominant inertial forces.
The volume of liquid in laminar flow is given by Poiseuille’s equation, where R is the pipe radius, p1 and p2 are the inlet and outlet pressures, t is the flow time, η is the viscosity coefficient, and l is the pipe length.
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