For section A (clear = 0) 

 z = 4 feet 



1=4^= 0.00943 



2ttz 

 From tables, cosh — — = 1.0017 



IT H '^"^ *■ L ^ ttC10)(1.0017) -, -, ^ ,r ^ 

 ">"ax = — -— 72id7 = - (10)C1.481) =2.12 feet per second 

 sinh(— j^ — ^J 



Component of Uj^g^^^ perpendicular to the pipeline axis is 



"max ^^°^ 20°) = (2.123(0.866) = 1.84 feet per second 



(a) Since the pipe is in contact with the bottom, (clear = 0) , 

 (}) = 0° and k = 0. From Figure 40, Cl = 4.5. 



(b) Maximum positive lift (per unit length) 

 FL(l-k) = -^ Cl P A u^^/ (1-k) 



= ~ (4.5)(2)(8)(1.84)^ (1-0) 



= 121.9 pounds per foot. 



Maximum negative lift (per unit length) 



Since k = 0, there is no negative lift, and the lift force is 

 positive throughout the wave cycle. 



(c) Since (() = 0°, the positive lift forces are maximum at 0° and 180° 

 in the wave cycle (under the crests and troughs) , corresponding to 

 the points of maximum horizontal velocities. 



Tlie lift does not become negative, but diminishes to zero at 90° 

 and 270°, the positions of horizontal flow reversal in the wave 

 cycle. 



(d) At 6 = 120° 



Fl = y Cl P a un^ax' [cos' (6 - C()) - k] 



= J (4.5)(2) (8)(1.84)' [cos' (120° - 0°) - 0] 

 = 30.5 pounds per foot 



115 



