Covers Newton's law of internal friction, explaining viscosity as a force that depends on dynamic viscosity and the velocity gradient between fluid layers, with its formula and symbols. Goes on to Poiseuille's law for steady flow through a straight pipe, giving the flow-rate formula with units, then viscosimetry as a timed capillary measurement. Ends with Newtonian versus non-Newtonian fluids, shear-thinning and shear-thickening examples, a short infusion and breathing section linking to Boyle's law.
Topic 7 of 42 in the MU Sofia syllabus for Physics (Dental Medicine, Year 1). The free AceMed note covers it in 1 section, about 701 words (5 min of reading), with 12 flashcards.
In this note
Introduction
Introduction
Newton's Law for Internal Friction:
Inner friction, also known as viscosity, emerges from interactions between molecules of adjacent layers of laminar fluid motion.
It is caused by the gradient of velocity within the fluid.
2. Formula:
F = η * (dv/dy) * A
Where:
F = Force due to internal friction
η (eta) = Dynamic viscosity of the fluid
(dv/dy) = Velocity gradient, representing the rate of change of velocity with respect to distance (y)
A = Surface area
Newton's law for internal friction quantifies the force experienced by a fluid due to its viscosity. The force is directly proportional to the dynamic viscosity of the fluid and the velocity gradient across its layers. A higher viscosity or steeper velocity gradient results in greater internal frictional forces within the fluid.
Poiseulle's law
Poiseuille's Law:
Poiseuille's law describes the flow of non-turbulent, non-pulsatile fluid through a uniform straight pipe.
It quantifies the relationship between pressure difference (∆p), tube length (l), dynamic viscosity (η), tube radius (r), and the volume flow rate (Φ).
Formula:
Φ = (π * ∆p * r^4) / (8 * η * l)
Where:
Φ = Volume flow rate (in cubic meters per second, m^3/s)
∆p = Pressure difference (in pascals, Pa)
l = Length of the tube (in meters, m)
η (eta) = Dynamic viscosity of the fluid (in pascal-seconds, Pa·s)
r = Radius of the tube (in meters, m)
Poiseuille's law helps engineers calculate the required pressure difference or tube dimensions to achieve a specific flow rate in fluid systems.
Viscosimetry.
Viscosimetry (also known as viscometry) involves the measurement and study of the viscosity or internal friction of a fluid. Viscosity is essentially the measure of a fluid’s resistance to gradual deformation or flow. This measurement is performed using an instrument called a viscometery.
It is done by measuring the time taken for a defined quantity of fluid to flow through a capillary with a known diameter and length.
Instrument: The viscometer is used to carry out this measurement.
Non-Newtonian behaviour and microrheological processes.
Newtonian vs. Non-Newtonian Fluids: How They Respond to Shear
The above diagram categorizes fluids based on their viscosity, which is a measure of a fluid's resistance to flow. Specifically, it focuses on how viscosity changes with applied shear stress (force per unit area causing deformation).
Newtonian Fluids:
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