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Step 1 — Classify the problem. Is it statics (pressure, buoyancy) or dynamics (flow, Bernoulli)? Statics: use $P = P_0 + \rho gh$ and Archimedes'. Dynamics: use continuity + Bernoulli. Viscosity: use Stokes' law or Poiseuille's equation.

Step 2 — For buoyancy problems: draw a free body diagram with weight (down), buoyancy (up), and any other forces. For floating bodies: weight = buoyancy gives fraction submerged = $\rho_{\text{body}}/\rho_{\text{fluid}}$.

Step 3 — For Bernoulli problems: (a) Choose two points on the same streamline. (b) Apply continuity if cross-section varies. (c) Apply Bernoulli. (d) Boundary conditions: at a free surface $P = P_0$ and $v \approx 0$ (for large tanks).

Step 4 — For terminal velocity: set up force balance $mg = F_B + 6\pi\eta rv_T$ and solve.

Common traps: (1) Forgetting atmospheric pressure acts on both sides (it cancels in many problems). (2) Confusing gauge and absolute pressure. (3) In Torricelli's theorem, depth $h$ is measured from the surface, not from the bottom. (4) The Venturi effect — pressure decreases where velocity increases, not vice versa. (5) Terminal velocity scales as $r^2$, not $r$. (6) Poiseuille flow: $Q \propto r^4$ — the fourth power catches many students off guard.