Packet E: Bonus 17
An irrotational fluid can be equivalently expressed as a fluid characterized by one of these functions defined from the velocity field. For 10 points each:
[10m] Name these scalar functions. Generically, they are defined from a vector field such that their negative gradient equals the vector field.
ANSWER: potentials [accept scalar potentials or velocity potential; reject “vector potential”; reject “potential energy”]
[10h] A fluid’s velocity potential and stream function together satisfies these equations. A handy mathematical trick in physics relies on the fact that the pairs of functions that satisfy these equations also individually satisfy Laplace’s equation.
ANSWER: Cauchy–Riemann equations [prompt on CR equations]
[10e] The Joukowsky transform is a conformal map from the unit circle into the cross-section of an idealized one of these structures. The motion of these structures through air generates lift.
ANSWER: wings [or airfoils or aerofoils]
<GC, Physics> | Packet E - Chicago A, Toronto B, Brandeis B, JHU A
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 68 | 14.85 | 97% | 41% | 10% |
Conversion
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| California (North) | Main Site | ✓ | 3 | 20.00 | 100% | 100% | 0% |
| California (South) | Main Site | ✓ | 4 | 17.50 | 100% | 50% | 25% |
| Canada | Main Site | ✓ | 1 | 10.00 | 100% | 0% | 0% |
| Florida | Main Site | ✓ | 2 | 10.00 | 100% | 0% | 0% |
| Great Lakes | Main Site | ✓ | 5 | 14.00 | 100% | 40% | 0% |
| Lower Mid-Atlantic | Main Site | ✓ | 8 | 11.25 | 100% | 13% | 0% |
| Midwest | Main Site | ✓ | 8 | 18.75 | 100% | 63% | 25% |
| Northeast | Main Site | ✓ | 3 | 13.33 | 100% | 33% | 0% |
| Overflow | Main Site | ✓ | 3 | 13.33 | 100% | 33% | 0% |
| South Central | Main Site | ✓ | 2 | 15.00 | 100% | 50% | 0% |
| Southeast | Main Site | ✓ | 6 | 16.67 | 100% | 67% | 0% |
| UK | Main Site | ✓ | 12 | 15.83 | 83% | 50% | 25% |
| Upper Mid-Atlantic | Main Site | ✓ | 8 | 11.25 | 100% | 13% | 0% |
| Upstate NY | Main Site | ✓ | 3 | 16.67 | 100% | 33% | 33% |