Hack's law

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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=CA^{h}\$

for some constant C where the exponent h is slightly less than 0.6 in most basins. Note that h varies slightly from region to region, and also 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.

v t e River morphology

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

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

Bedrock river	Canyon Knickpoint Plunge pool Bedrock erosion

Bedforms	Current ripple Dune Antidune Ait

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

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

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