# Hack's law

From Infogalactic: the planetary knowledge core

**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

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.