Hack's law

Hack's law is an empirical relationship between the length of streams and the area of their basins. If L is the length of the longest stream in a basin, and A is the area of the basin, then Hack's law may be written as

L = C A^h\

for some constant C where the exponent h is slightly less than 0.6 in most basins. h varies slightly from region to region and slightly decreases for larger basins (>8,000 mi², or 20,720 km²). A theoretical value h = 4/7 ≈ 0.571 for the exponent has been derived (Birnir, 2008).

References

Birnir, B., 2008, "Turbulent rivers", Quart. Appl. Math., 66, 3, pp. 565–594.
Hack, J., 1957, "Studies of longitudinal stream profiles in Virginia and Maryland", U.S. Geological Survey Professional Paper, 294-B.
Rigon, R., et al., 1996, "On Hack's law" Water Resources Research, 32, 11, pp. 3367–3374.
Willemin, J.H., 2000, "Hack’s law: Sinuosity, convexity, elongation". Water Resources Research, 36, 11, pp. 3365–3374.

River morphology

Large-scale features	Drainage basin Drainage system (geomorphology) Estuary Strahler number (stream order) River valley River delta River sinuosity

Alluvial rivers	Anabranch Avulsion (river) Braided river Bar (river morphology) Channel pattern Cut bank Floodplain Meander Meander cutoff Mouth bar Oxbow lake Point bar Riffle Rapids Riparian zone River bifurcation River channel migration Slip-off slope Stream pool Thalweg

Bedrock river	Canyon Knickpoint Plunge pool

Bedforms	Ait Antidune Dune Current ripple

Regional processes	Aggradation Base level Degradation (geology) Erosion and tectonics

Mechanics	Deposition (geology) Water erosion Exner equation Hack's law Helicoidal flow Playfair's law Sediment transport

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