Viscosity — Friendly Notes

What is viscosity?

• Fluids fight motion because their layers rub against one another. This internal friction is called viscosity. :contentReference[oaicite:0]{index=0}
• Honey needs more push than oil in the same setup, so honey is “thicker” (more viscous). :contentReference[oaicite:1]{index=1}

Seeing the idea

Picture two glass plates with a thin oil film between them. The bottom plate stays still while the top one slides right with speed v. Layers touching each plate match its speed, so the speed climbs smoothly from 0 at the bottom to v at the top. Each layer tugs the one above and below, creating a sideways (shear) force. :contentReference[oaicite:2]{index=2}

Coefficient of viscosity (η)

• Defined as the ratio of shearing stress to strain-rate (speed gradient). :contentReference[oaicite:3]{index=3}
• Equation: $$\eta=\dfrac{\text{shearing stress}}{\text{strain-rate}}$$ :contentReference[oaicite:4]{index=4}
• Units: 1 poiseuille (Pl) = 1 N s m^-2 = 1 Pa s. Dimensions: ML^-1T^-1. :contentReference[oaicite:5]{index=5}
• Thin liquids (water, alcohol) have small η; thick ones (glycerine, honey) have large η. :contentReference[oaicite:6]{index=6}

Laminar flow speed profile

Inside a tube the central layer races fastest, and the speed slides down to zero at the walls, giving the familiar “parabolic” profile. :contentReference[oaicite:7]{index=7}

Temperature effect

• Liquids: η drops as temperature rises.
• Gases: η grows as temperature rises. :contentReference[oaicite:8]{index=8}

Typical η values

Blood stays about three times thicker than water from 0 °C to 37 °C. :contentReference[oaicite:9]{index=9}

Stokes’ law — drag on a sphere

For a sphere radius a moving through a fluid with speed v, the backward drag is

$$F = 6\pi\eta a v$$ :contentReference[oaicite:10]{index=10}

Terminal speed in a fluid

A falling drop speeds up until weight balances drag + buoyancy. The steady speed is

$$v_t = \dfrac{2a^{2}(\rho-\sigma)g}{9\eta}$$ :contentReference[oaicite:11]{index=11}

Bigger, denser drops fall faster; thicker fluids slow them down.

Quick example checks

• Sliding-plate method: 0.10 m² block, 0.085 m/s, 0.30 mm film → η ≈ 3.46 × 10^-3 Pa s. :contentReference[oaicite:12]{index=12}
• Copper ball (2 mm radius) in oil: terminal speed 6.5 cm/s → η ≈ 0.99 kg m^-1s^-1. :contentReference[oaicite:13]{index=13}

High-yield ideas for NEET

1. Stress/strain-rate definition and units of η.
2. Stokes’ drag law $$F = 6\pi\eta a v$$.
3. Terminal speed formula $$v_t = \dfrac{2a^{2}(\rho-\sigma)g}{9\eta}$$.
4. Temperature dependence of η (liquids vs gases).
5. Typical η values (water, blood, glycerine) for quick comparisons.