indicating that the near -bed boundary layer would not be thoroughly mixed by 

 the effect of grain roughness on an incident laminar flow, so equation (4) 

 may also be considered. Equation (1) gives 



0.35 D0-25(Y'g)0.75 0.35 (0.00033) -^^ [ (1.59) (32.2)] -^^ 



(36.35 cm)/s 

 and equation (5) gives 



(5aj)v 



6 = 2 = 0.96 



1.15 



then equation (4) becomes 



£2(^0)) + 5^(50)) (0.24)2(0.37) + (0.96)2(1.19) 



(Sw)^ = 5 5 = r = 1.14 ft 



^ £2+^2 (0.24)2 + (0.96)2 



(34.94 cm)/s 



For the specified situation, d = 60 ft and g = 32.2 ft (9.81 m)/s2, so 



aj2 d (0.571)2 x 60 „ ^, 



~r '^ 32:2 = °-^^ 



and, taking this as the value of [x(tanh x) ] according to equation (7), the 

 Figure gives the abscissa 



x = ^=0.87 



Also from the Figure, 



sinh(0.87) = 0.98 

 Using the value of iE,(^)^, the minimum wave height for sand motion is 



. ^ 2(5a))j^ sinh(^) 2(0.37) (0.98) 

 («min)m = ^ = 037l = 1-27 ft (0.39 m) 



while using the value of (Cw)^, the minimum wave height for sand motion 

 would be 



. . 2(5w) sinh(^) 2(1.14) (0.98) 

 ^in)t = '- ^ = ^^37^ = 3.9 ft (1.19 m) 



