ON THE RELATION BETWEEN DRAINAGE AREA AND MAIN STREAM LENGTH

Abstract

Hack (1957) found an empirical equation relating the drainage area (A) to the mainstream length (L) . The equation is L=cA_u^r where the c and r are constants and the suffix u denotes the stream order of the basin concerned. According to results by Hack (1956) and Gray (1961), the values of r are 0.6 and 0.568 respectively. The author derived the Hack's relation from Horton's two laws, equations (2) and (3) in the text. Applying Strahler's stream ordering system (Strahler, 1957), and expressing the length ratio e^D by equation (4) and the drainage area ratio e^H by equation (5) where D and H are constants, the exponent r in Hack's relation may be expressed by r_??_D/H. Using the mean values of e^D and e^H for 14 drainage basins reported by Yang (1971),
_??_
This value agrees quite well with ones obtained by both Hack and Gray.