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<br />The variables considered by Garton to be pertinent in his study are <br />listed below: <br /> <br />Svrnhol <br /> <br />Variables <br /> <br />n <br /> <br />Roughness coefficient----------------- <br />Mean velocity------------------------- <br />Depth of flow------------------------- <br />Slope of channel---------------------- <br />Channel width------------------------- <br />Channel test length------------------- <br />Acceleration due to gravity----------- <br />Shape factor defining type of stem---- <br />Factor denoting roughness pattern----- <br />Average number of stems/row----------- <br /> <br />Density of stem per square foot------- <br />Stem diameter------------------------- <br />Stem length--------------------------- <br /> <br />Stiffness modulus of stem------------- <br /> <br />Stem density per unit length of stem- <br />Fluid density------------------------- <br />Fluid viscosity----------------------- <br /> <br />V <br />D <br />S <br />b <br />L <br />g <br />1:s <br />5 <br />Ns <br />Bd <br />ds <br />ls <br />Ks <br />Ps <br />P <br />Ii <br /> <br />Dimp-n~ions <br /> <br />Ll/6 <br />LT-l <br />L <br /> <br />L <br />L <br />LT-2 <br /> <br />L-2 <br />L <br />L <br />FL2 <br />FL-2T2 <br />FL-4T2 <br />FL-2T <br /> <br />The general functional relations between Garton's variables can be <br />written: <br /> <br />f (n, V, D, S, b, L, g, 1:s, 5, Ns, Bd, ds, ls, Ks, Ps, p, Ii ) = 0 (2S) <br /> <br />Garton (1970) reduced the number of variables and presented the following <br />relation: <br /> <br />n D <br />f ( Rl/6' dsBdD, b' <br /> <br />Nsds <br />b ' S, <br /> <br />V2 <br />gR <br /> <br />(26) <br /> <br />He rearranged equation 26 for convenience as follows, substituting x <br />terms for the above variables: <br /> <br />y Cl + C2Xl + C3X2 + C4X3 + CSX4 + C6XS <br /> 2 2 2 <br />y Cl + C2Xl + C3Xt + C4X2 + CSX2 + C6X3 + C7X3 <br /> 2 2 <br /> + CSX4 + C9X4 + ClOXS + CllXS <br />Itl. Xl = 1t2, X2 ~ 1t3, X3 = 1t4, X4 ItS, XS 1t6, and <br />the experimental coefficients. <br /> <br />Itl <br /> <br />n <br />Rl/6' 1t2 <br /> <br />D <br />dsBctD, 1t3 - b' 1t4 <br /> <br />N~d~ <br />............. ItS ~ S, 1t6 <br />b ' <br /> <br />The polynomial equations developed were of the form: <br /> <br />Linear: <br /> <br />Quadratic: <br /> <br />Where: Y <br />Ci <br /> <br />The exponential model was built from the equation, <br /> <br />Itl =Aa 1t2 sa 1t3 Ca 1t4 Da ItS Ea 1t6 Fa <br /> <br />10 <br /> <br />v2 <br />gR <br />