vd.th 



and 



z = rij, 2 = ■•" 0*602 m (2.48 ft) 



HgT cosh[2Tr(z + d)/L] 



t,2 2L cosh(2TTd/L) 



3 /TrH\2 cosh[4ir(z + d)/L] 



4 V L/ sinh'+(2Trd/L) 



with 



z = 



= nt,2 = ~ 0.398 m (1.52 ft) 



Entering Table C-2 with d/L = 0.10, find tanh (2Trd/L) = 0.5569. 



From equation (2-3) which is true for both first- and second-order theories, 



, gL , /2Trd\ (9.8)(60)(0.5569) , ^ , , ,, 



C2 = .S_ tanh = -^ — — — = 52.12 m/s^ (571 ft/s^) 



2Tr \ L / 2tv 



or 



As a consequence. 



C = 7.22 m/s (23.68 ft/s) 



T 1 



- = - = 0.1385 s/m (0.0422 s/ft) 



L C 



Referring again to Table C-2, it is found that when 



z = 



cosh 



2Tr(z + d) 



and when 



cosh 



2ti(z + d) 



= cosh [2Tr(0.108)] = 1.241 



H 



z = 



2 



= cosh [2Tr(0.092)] = 1.171 



Thus, the value of u at a crest and trough, respectively, according to 

 first-order theory is 



2-41 



