Problem-Solving: Waves and Fluids
The same deep patterns govern wildly different systems, from earthquake tremors to aircraft lift. Capstone success is entirely about recognizing which principle is in play.
Before computing, classify your system. Real problems never announce their chapter.
| Domain | Governing Principle | Key Formula | Common Pitfall |
|---|---|---|---|
| Waves | Speed & Harmonics | Missing boundary conditions | |
| Fluids (Static) | Pressure depth | Using gauge pressure in gas laws | |
| Fluids (Flow) | Continuity & Energy | Bernoulli's Eq. | Forgetting to convert to Kelvin |
Strategy: Always identify the system, list knowns with units, and solve algebraically before plugging in numbers.
Thermodynamics & Sanity Checks
Energy ledgers track heat, work, and entropy. Always respect sign conventions for work () and heat ().
| Domain | Governing Principle | Key Formula | Common Pitfall |
|---|---|---|---|
| Heat | Temp & Phase Change | , | Ignoring sign conventions |
| Engines | Efficiency limit | Confusing with | |
| Entropy | Disorder ledger | Non-Kelvin absolute temps |
Dimensional analysis is your ultimate sanity check. If the units do not match your target variable, the algebra failed long before the arithmetic did.