4.6
Viscosity
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 gradien…
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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Q1: What causes viscosity in fluids?
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.
Q2: How does Newton's law of viscosity relate force to flow?
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.
Q3: How do temperature and pressure affect viscosity?
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.
Q4: What does the Reynolds number tell us about fluid flow?
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.
Q5: What is Poiseuille's equation used for?
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.
Q6: What are the SI and non-SI units of viscosity?
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.
Q7: How do laminar and turbulent flow differ?
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.