Fluid Dynamics: MDCAT Notes and MCQs
Fluid drag & terminal velocity
- Fluid drag: frictional (resistive) force exerted by a fluid on a body moving through it; depends on speed, size/shape and viscosity. Stokes' law (small sphere, slow speed): F = 6πηrv.
- Terminal velocity: maximum constant velocity reached when drag (+ upthrust) equals weight → net force zero. For a sphere: vt = 2ρgr² / 9η → vt ∝ r². Viscosity η unit: N s m−2 (Pa s); viscosity of liquids decreases with temperature.
Types of flow
- Steady / streamline / laminar: every particle passing a point follows the same path with the same velocity; streamlines never cross.
- Turbulent: irregular, eddies — occurs at high speed (above a critical velocity), and is more common in practice (rivers, air around vehicles). Reynolds number R = ρvd/η: < ≈ 2000 laminar; > ≈ 3000 turbulent.
- Ideal fluid: incompressible (constant density), non-viscous (no internal friction), steady and irrotational flow.
Equation of continuity
A1v1 = A2v2 = constant (volume flow rate) — expresses conservation of mass (ρAv = constant). Narrow pipe → faster flow (e.g. nozzle on a hose; v ∝ 1/r²).
Bernoulli's equation
P + ½ρv² + ρgh = constant — conservation of energy per unit volume. For a horizontal tube: P1 + ½ρv1² = P2 + ½ρv2² → where speed is high, pressure is low (Bernoulli effect).
- Torricelli's theorem: speed of efflux from a hole at depth h: v = √(2gh).
- Applications: venturi meter, carburettor, aeroplane lift, atomizer/spray, swing of a spinning ball, chimney draft.
- Blood physics: in a narrowed artery (plaque/atherosclerosis), blood speeds up and pressure drops → artery may collapse under external pressure (vascular flutter), increasing blockage; turbulence produces sounds heard with a stethoscope. In a sphygmomanometer, the cuff pressure is measured at the level of the heart; systolic ≈ 120 torr, diastolic ≈ 80 torr (first and last Korotkoff sounds from turbulent flow).
PMDC learning outcomes for this unit
- Fluid flow: 5.1 Describe the terminal velocity of an object.
- Fluid flow: 5.2 Define and explain the term fluid drag.
- Fluid flow: 5.3 Define steady (streamline/laminar) flow, incompressible flow and non-viscous flow for an ideal fluid.
- Fluid flow: 5.4 Explain that at sufficiently high velocity, viscous flow changes from laminar to turbulent.
- Fluid flow: 5.5 Describe that most practical examples of fluid flow involve turbulent conditions
- Fluid flow: 5.6 Describe equation of continuity Av = constant and solve problems using it.
- Fluid flow: 5.7 Identify that the equation of continuity is a form of the principle of conservation of mass.
- Fluid flow: 5.8 Interpret and apply Bernoulli's effect in blood physics.
- Fluid flow: 5.9 Derive Bernoulli's equation for the case of horizontal tube of flow
- Fluid flow: 5.10 Describe that a pressure difference can arise from different rates of flow of fluid (Bernoulli effect).