Hack's law is an empirical relationship between the length of

streams A stream is a continuous body of water, body of surface water Current (stream), flowing within the stream bed, bed and bank (geography), banks of a channel (geography), channel. Depending on its location or certain characteristics, a stream ...

and the area of their

basins Basin may refer to: Geography and geology * Depression (geology) ** Back-arc basin, a submarine feature associated with island arcs and subduction zones ** Debris basin, designed to prevent damage from debris flow ** Drainage basin (hydrology), a ...

. 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 Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to re ...

''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). In addition to the catchment-scales, Hack's law was observed on unchanneled small-scale surfaces when the morphology measured at high resolutions (Cheraghi et al., 2018). The law is named after American geomorphologist

John Tilton Hack John Tilton Hack (1913–1991) was an American geologist and geomorphologist known for his contributions to establish the dynamic equilibrium concept in landscapes. Hack's law, concerning the empirical relationship between the length of streams ...

References

* 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. * Hydrology Rivers Geomorphology Water streams Power laws {{geomorph-stub