Fluids & Elasticity
Physics for NEET‑M (Medical)
Aim – Understand the behaviour of fluids (liquids & gases) and the elastic response of solids.
Why it matters – Many clinical problems (blood pressure, respiratory mechanics, tissue elasticity) rely on these fundamentals.
1. Hydrostatics (Behaviour of a fluid at rest)
| Concept | Key Equation | What it means |
|---|---|---|
| Pressure | (P = \frac{F}{A}) | Force per unit area. |
| Pressure in a fluid | (P = P_0 + \rho g h) | (P_0) = pressure at surface, (\rho) = density, (g) = 9.81 m/s², (h) = depth. |
| Archimedes’ Principle | (F_b = \rho V g) | Buoyant force equals weight of displaced fluid. |
| Pascal’s Law | (\Delta P = \rho g \Delta h) | Pressure change at depth is same in all directions. |
Key Points
- Pressure increases linearly with depth in a uniform fluid.
- Surface tension is negligible for most medical applications (e.g., blood vessels).
- Buoyancy explains why objects float or sink (e.g., air-filled lung vs. blood).
Worked Example 1: Buoyant force on a stone
A stone of volume (V = 2.0\times10^{-4},\text{m}^3) is dropped into water ((\rho_{\text{water}} = 1000\ \text{kg/m}^3)). What is the buoyant force?
[ F_b = \rho V g = (1000)(2.0\times10^{-4})(9.81) = 19.6\ \text{N} ]
2. Fluid Dynamics (Behaviour of a fluid in motion)
| Concept | Key Equation | What it means |
|---|---|---|
| Continuity | (A_1 v_1 = A_2 v_2) | Mass conservation in incompressible flow. |
| Bernoulli’s Equation | (P + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}) | Energy conservation along a streamline. |
| Reynolds Number | (Re = \frac{\rho v L}{\mu}) | Ratio of inertial to viscous forces; predicts flow regime (laminar vs. turbulent). |
| Viscosity | (\tau = \mu \frac{dv}{dy}) | Shear stress proportional to velocity gradient. |
Key Points
- Laminar flow: Smooth, orderly, (Re < 2000).
- Turbulent flow: Chaotic, (Re > 4000).
- Surface tension – important in capillary action (e.g., capillaries, ocular fluid).
Worked Example 2: Blood flow in a narrowed artery
Artery diameter narrows from (D_1 = 4,\text{mm}) to (D_2 = 2,\text{mm}). Blood speed upstream is (v_1 = 0.3,\text{m/s}). Find downstream speed (v_2).
[
A_1 = \frac{\pi D_1^2}{4} = \frac{\pi(0.004)^2}{4}=1.26\times10^{-5},\text{m}^2
]
[
A_2 = \frac{\pi(0.002)^2}{4}=3.14\times10^{-6},\text{m}^2
]
Continuity: (A_1 v_1 = A_2 v_2 \Rightarrow v_2 = \frac{A_1}{A_2} v_1 = \frac{1.26\times10^{-5}}{3.14\times10^{-6}}\times0.3 \approx 1.2,\text{m/s}).
3. Elasticity (Solid deformation under load)
| Concept | Key Equation | What it means |
|---|---|---|
| Stress | (\sigma = \frac{F}{A}) | Normal (tensile/compressive) stress. |
| Strain | (\varepsilon = \frac{\Delta L}{L}) | Relative change in length. |
| Hooke’s Law | (\sigma = E \varepsilon) | Linear relationship; (E)=Young’s modulus. |
| Shear Stress & Strain | (\tau = G \gamma) | (G)=Shear modulus, (\gamma)=shear strain. |
| Poisson’s Ratio | (\nu = -\frac{\varepsilon_{\text{transverse}}}{\varepsilon_{\text{longitudinal}}}) | Lateral contraction/expansion ratio. |
| Spring Constant | (k = \frac{EA}{L}) | For a uniform bar. |
| Torsion of a Circular Shaft | (\tau = \frac{T r}{J}) | (T)=torque, (J=\frac{\pi d^4}{32}) = polar moment. |
Key Points
- Most biological tissues (bone, tendon, cartilage) behave elastically within physiological limits.
- Young’s modulus: bone ≈ 10–30 GPa, muscle ≈ 0.5–1 MPa.
- Elastic deformation is reversible; plastic deformation is permanent.
Worked Example 3: Bone bending
*A cortical bone segment (circular cross‑section, diameter (d=10,\text{mm}), length (L=0.1,\text{m})) is compressed by (F = 5,\text{kN}). Young’s modulus (E =