Fluid Mechanics

Key points

1. 01

   Ideal fluids are inviscid and incompressible (a hypothetical simplification); real fluids are viscous — compressibility is a separate, independent property.

2. 02

   Newton's law of viscosity ($\tau = \mu\dot\gamma$) only holds for Newtonian fluids, where $\mu$ is constant; non-Newtonian fluids need an apparent viscosity ($\mu_a = K\dot\gamma^{\,n-1}$) that varies with shear rate instead.

3. 03

   Flow behaviour index $n$ classifies non-Newtonian fluids: $n < 1$ pseudoplastic (shear-thinning), $n > 1$ dilatant (shear-thickening).

4. 04

   Bingham plastics need a yield stress $\tau_y$ before they flow at all; Casson and Herschel–Bulkley fluids combine a yield stress with shear-thinning/power-law behaviour above it.

5. 05

   Non-Newtonian fluids also split by time-dependence: Bingham, pseudoplastic, dilatant, Casson, and Herschel–Bulkley are all time-independent (viscosity depends only on instantaneous shear rate); thixotropic fluids thin over time at constant shear rate, rheopectic fluids thicken over time at constant shear rate.

6. 06

   Reynolds number thresholds differ by system: stirred tank is laminar below $Re = 10$ and turbulent above $Re = 10{,}000$; straight pipe is laminar below $Re = 2{,}100$ and turbulent above $Re = 4{,}000$ — don't cross-apply the two.

7. 07

   Turbulent flow (with eddies) is needed for mixing; laminar flow is not, and neither is a vortex — a vortex is easy to mistake for turbulence but actually promotes settling, not mixing.

8. 08

   Laminar pipe flow gives a parabolic velocity profile (peak at centreline, zero at wall); turbulent pipe flow flattens it into a near-plug flow shape, with the steep drop confined to a thin near-wall layer.

9. 09

   Human blood's Casson-type yield stress comes from rouleaux formation — red blood cells stacking at low shear rates — not from a generic "blood is thick" explanation.