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<br /> <br />20 <br /> <br />PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS <br /> <br />1000 <br /> <br /> <br />100 <br /> <br />10 <br /> <br />~ <br />~ <br />~ <br />~ <br />~ <br />~ <br />< <br />~ <br />0-1 <br />~ <br /> <br />~ <br /> <br />;5 <br />~ <br />< <br />~ <br />" <br />< <br />Z <br />" <br />~ <br />" <br /> <br />.1 <br /> <br />.01 <br /> <br />.001 <br /> <br />52 <br /> <br />4 5 6 7 8 9 10 11 12 <br />STREAM ORDER <br /> <br />FIGURE 16.-Relation of drainage area to stream order lor ephemeral channels in <br />central New Mexico. ::-.rumber beside point is serial identification kC)'ed to dl\ta <br />in appendix. <br /> <br />It follows, then, that there must exist a power-function <br />relation between each two of these variables other than <br />order, in the form <br /> <br />IccA~, BocA:, secl" <br /> <br />where k is some exponent having a particular value in <br />each equation. .\loreover, because it is known that <br /> <br />discharge, Q, bears a relation to drainage area of the <br />form <br /> <br />Qcx:A: <br /> <br />(5) <br /> <br />then discharge must be related to stream order according <br />to <br /> <br />Ocx:log Q <br /> <br />(6) <br /> <br />Reiterating some of the hydraulic relations discussed <br />ea.rlier: <br /> <br />wcx:Q' (7) <br />dcx:Qf (8) <br />vcx:Qm (9) <br />Lcx:QJ (10) <br />scx:Q' (11) <br />n'cx:Q' (12) <br /> <br />Where <br /> <br />Q=discharge <br />w=width <br />d=depth <br />v=veloeit,y <br />L=suspended load <br />s=slope <br />n' = a roughness parameter <br />b, j, m, j, z, and yare numerical exponents <br /> <br />It follows from equation (6) and equations (7) to <br />(12) that there defiuitely is a relation between stream <br />order and width, depth, velocity, suspended load, <br />slope, and roughness of the form <br /> <br />Ocx: log (width, depth, etc.) <br /> <br />Also, therc are several interrelations among variables <br />in equations (1) to (4), and among those in equations <br />(7) to (12). An example of such a relation is that <br />which would exist between sediment load, L, and <br />drainage area, Ad. <br /> <br />Because <br />and <br />then <br /> <br />Lcx:QJ <br />Qcx:A: <br />LccA~k <br /> <br />Thus, it can bc seen that a whole series of hydraulic <br />and drainage-network factors are interrelated in the <br />form of power or exponential functions. These equa- <br />tions can be added to thc several others derived by <br />