Viscosity, Shear Stress, and Flow Regime
For a Newtonian fluid, dynamic viscosity is the proportionality between shear stress and the transverse velocity gradient; Reynolds number compares inertial and viscous effects.
Why this shows up in the exam
Lubricant selection · Estimating shear in rivers and channels · Judging laminar versus turbulent pipe flow
Learn the idea
Viscosity links shear stress to velocity gradient, while Reynolds number indicates whether inertia or viscosity dominates. Neighbouring fluid layers resist sliding past one another. Thick, slow, small-scale flows are viscosity-dominated; fast, large-scale flows are more vulnerable to turbulence.
🧠 Memory hook: Viscosity resists velocity gradients, not uniform translation.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- tau = eta dv/dy — Newtonian shear law for local parallel-layer flow, with sign supplied by the chosen direction
- F = eta A Delta v/Delta y — uniform-gradient approximation over sheared area A
- Re = rho v L/eta — dimensionless inertia-to-viscosity ratio using the characteristic length appropriate to the flow
How to approach it
- 1Identify the sheared area and normal separation
- 2Use SI viscosity consistently
- 3Check the assumed regime before applying a laminar-flow law
Common slip-ups that cost marks
- •Using speed itself instead of a speed gradient
- •Confusing dynamic viscosity with kinematic viscosity
- •Treating one critical Reynolds number as universal for every geometry
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
More from Properties of Bulk Matter
Mechanical properties of solids
Study of how solids respond to applied forces, including stress, strain, elastic moduli (Young's modulus, bulk modulus), and breaking stress.
Fluid dynamics and Bernoulli's theorem
Covers the motion of fluids, including Bernoulli's theorem, Torricelli's law, dynamic lift, and viscous flow.
Surface tension and surface energy
Examines the molecular forces at liquid surfaces, including surface tension, surface energy, and related equations.
Capillarity and contact angle
Focuses on capillary action, meniscus formation, and the role of contact angle in wetting phenomena.
Thermal properties of matter
Deals with heat transfer, thermal conductivity, calorimetry, specific heat, and thermal expansion of solids.
Pressure in fluids and hydrostatics
Explores how pressure is transmitted in fluids, including hydrostatic pressure, Pascal's law, and related phenomena.