Hack's law is an

empirical relationship In science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural science ...

between the length of

streams A stream is a continuous body of surface water flowing within the bed and banks of a channel. Depending on its location or certain characteristics, a stream may be referred to by a variety of local or regional names. Long, large 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), ...

. 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 In mathematics, exponentiation, denoted , is an operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, i ...

''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.

References

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