potentials - 2026 ACF Regionals

Question

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>

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Summary


California (North)	Main Site	Y	3	20.00	100%	100%	0%
California (South)	Main Site	Y	4	17.50	100%	50%	25%
Canada	Main Site	Y	1	10.00	100%	0%	0%
Florida	Main Site	Y	2	10.00	100%	0%	0%
Great Lakes	Main Site	Y	5	14.00	100%	40%	0%
Lower Mid-Atlantic	Main Site	Y	8	11.25	100%	13%	0%
Midwest	Main Site	Y	8	18.75	100%	63%	25%
Northeast	Main Site	Y	3	13.33	100%	33%	0%
Overflow	Main Site	Y	3	13.33	100%	33%	0%
South Central	Main Site	Y	2	15.00	100%	50%	0%
Southeast	Main Site	Y	6	16.67	100%	67%	0%
UK	Main Site	Y	12	15.83	83%	50%	25%
Upper Mid-Atlantic	Main Site	Y	8	11.25	100%	13%	0%
Upstate NY	Main Site	Y	3	16.67	100%	33%	33%

Data


Berkeley B	Stanford B	10	0	10	20
Stanford A	Berkeley C	10	0	10	20
Berkeley A	Berkeley D	10	0	10	20
UCLA B	UC Irvine	10	0	10	20
Arizona State	UCSD B	0	10	10	20
UCSD C	UCLA A	0	0	10	10
UCSD A	UC Santa Barbara	10	0	10	20
Brock	UBC B	0	0	10	10
Florida C	Central Florida B	0	0	10	10
Central Florida A	Florida A	0	0	10	10
Michigan State	CWRU A	0	0	10	10
Michigan A	Ohio State A	0	0	10	10
Pittsburgh	Michigan C	10	0	10	20
Ohio State B	CWRU B	0	0	10	10
Michigan B	Ohio State C	10	0	10	20
William and Mary	James Madison B	0	0	10	10
Liberty A	James Madison A	0	0	10	10
Virginia Tech A	NC State A	0	0	10	10
North Carolina B	South Carolina A	10	0	10	20
North Carolina A	South Carolina B	0	0	10	10
VCU	Duke	0	0	10	10
Virginia	Wake Forest	0	0	10	10
NC State B	Liberty C	0	0	10	10
Chicago C	Chicago E	0	0	10	10
Chicago B	Northwestern D	10	0	10	20
Purdue B	Indiana B	10	10	10	30
Northwestern B	Northwestern C	10	0	10	20
Indiana A	Notre Dame A	10	10	10	30
Notre Dame B	Illinois A	0	0	10	10
Illinois B	Indiana C	10	0	10	20
Illinois C	Purdue A	0	0	10	10
Yale	Bowdoin A	0	0	10	10
Harvard A	Brown	10	0	10	20
Dartmouth A	Dartmouth B	0	0	10	10
Claremont	Minnesota A	10	0	10	20
Washington A	Iowa State	0	0	10	10
Missouri A	Georgia Tech A	0	0	10	10
Murray State A	Texas A&M A	0	0	10	10
Texas A	Texas B	10	0	10	20
Alabama A	WashU B	10	0	10	20
Kentucky	WashU A	10	0	10	20
Tennessee A	Georgia Tech C	10	0	10	20
Georgia Tech B	Louisville A	10	0	10	20
Mississipi State	Georgia Tech D	0	0	10	10
Alabama B	Sewanee	0	0	10	10
Birmingham	Montpellier	0	0	10	10
Cardiff	Southampton B	0	0	0	0
Durham	Edinburgh B	10	10	10	30
Imperial A	Oxford A	10	0	10	20
Imperial B	Southampton A	10	10	10	30
Oxford B	Imperial C	0	10	10	20
UCL	LSE	0	0	10	10
Edinburgh A	Manchester	10	0	10	20
Oxford C	Warwick B	10	0	10	20
Cambridge B	Bristol	0	0	10	10
Cambridge A	Warwick A	10	0	10	20
City St. George's	Cambridge C	0	0	0	0
Catholic	Johns Hopkins B	0	0	10	10
Columbia A	Maryland C	10	0	10	20
Maryland B	Columbia B	0	0	10	10
NYU C	John Jay	0	0	10	10
Rutgers A	Maryland A	0	0	10	10
Georgetown	Rutgers B	0	0	10	10
Swarthmore	Columbia C	0	0	10	10
Vassar	NYU B	0	0	10	10
Cornell B	Binghamton B	0	0	10	10
Cornell C	Penn State	0	0	10	10
RIT	Cornell A	10	10	10	30