wave length for each run was more than 0.075 ft., and in addition the surface 

 tension was reduced to about 40 dynes/cm. j hence, the Equation (2) should be 

 valid. 



In Equation (2) tanh (2?f d/L) approaches unity when d becomes large as compared 

 with L. TShen d/L = 0.25 the wave velocity is 5/& less than that for deep-water 

 waves. For d/L ■ 0.5, tanh (2JT d/L) s, 0,9963 and the error in wave velocity 

 will be negligible using the formula 



G -\fl£" . 5.12T (4) 



N 2-7T 



where tanh (2^"d/i,) is taken as a unity. In most papers the waves in water 

 having a depth greater than half the wave length are considered as deep-water 

 waves, while waves in lesser depths are shallow-water waves. 



If the wave length is very large as compared with the depth, tanh (2 Jt d/L) 

 approaches 2 3Z d/L and Equation (2) takes the form 



<=-^¥"=nF"- 



(5) 



Hun 1 (Figure 3a) represents the oondition for a uniform depth of water d = 

 0.04 ft. and a constant wave period T ■ 0.24 sec. To compute the wave length 

 for the given oondition we have from Equations (l) and (2) the following 

 equation 



L ■ g/27rT2 tanh (2/Td/L) - 5.12 T 2 tanh h (2fniA) ( 6 ) 



In this equation L is in implicit form. To solve it, L in tanh (2«"d/L) should 

 be assumed for the first approximation and the computations repeated until the 

 equation is satisfied. This prooedure is tedious; consequently, tables have 

 been prepared to present various factors as functions of d/L Q and d/L (Ref. 11). 



Making use of Equations (l) and (4) it is found that 



L s 5.12 T 2 (7) 



for Run 1 (Fig. 3a) 



and 



L = 5.12 (0.24) 2 s 0.2949 ft. 



d/Lp » 0.1356 



For this value of &/L in the tables it is found that d/L ■ 0.1713 whioh gives 

 L ■ 0.04/0.1713 ■ 0.234 ft. This is in close agreement with the measured value 

 of 0.24 ft. 



For Run 2 (Figure 3a) the ohannel was divided longitudinally so that, starting 

 from a oertain point, half of the ohannel had a depth of d^ ■ 0.071 ft. while 

 the other half had a depth of d ■ 0.027 ft. The period was the same for both 

 of the sections (T s 0.22 sec). 



L. = 5.12 (0.22) 2 = 0.2478 



