SEAWAY 



V 100 m/s 



V25 m/s 



Fig. 10 (Left) Setup as a function of the square of the wind speed at 100 cm elevation; (right) setup as a 

 function of the square of the wind speed at 2 5 cm elevation (from Van Dorn, 1953) 



.S'l = af'2 (18) 



From Fig. 10 at 100 cm ele\-atioii it tullowis then that, 

 at the wind velocity of 10 mps = 82,8 fps, .S'l = 0.28 cm 

 = 0.0092 ft and a = 0.00000855 sec-/ft. 



For the conditions of Van Doni's otwervations the 

 tangential force per unit area is expressed as 



T = p y h Si L = p g h a U-'L (ID) 



where p is water density, /) the effecti\'e depth and L the 

 distance at the ends of which .S'l is measured. The 

 tangential force or drag coefficient is then 



C\ = 



2ps 



1 



f- 



P'L 



0.0039 



(20) 



where p' is the air density. This is in agreement with 

 Motzfeld's wind-tunnel data given in Table 1. 



When waves are formed, there is an added drag due to 

 wa\'e form, and the total setup *S' becomes 



S ^ Si + S-2 



(21) 



The cur\-e of S coincides with the straight-line plot of 

 Si up to a certain speed V„ i.e.. So = for U < V,. 

 Above this speed So is expressed by Keuligan, and follow- 

 ing him by Van Dorn, as 



So 



h{U - vs- 



(22) 



The foregoing expression contains two unknowns h and 

 Vc- By assuming both of these to be constants, by read- 

 ing from Fig. 10 the values of So = S — Si at G and 8 



mps as (0.140 - 0.100) = 0.040 and (0.890 - 0.180) = 

 0.210 cm, and converting to feet, the unknowns are 

 evaluated as 



b = 0.0000518 secVft 

 T', = 14.()5 fps 



By the same procedure as was used in connection with 

 the coefficient a, the nondimensional dynamic or form- 

 drag coefficient is then evaluated on the basis of the ef- 

 fective velocity U — V, as 



C, = 0.0236 



The foregoing analysis was made for comparison with 

 the other previously described w-ave data. Neither 

 Keuligan nor Van Dorn discussed the details of wave 

 form. They called Vc the "formula velocity," treating 

 it just as an empirical constant, and discus.sed the co- 

 efficient b in equation (22) in terms of the length and 

 depth of the test stretch without any reference to the 

 wave form. However, their distinction between »S', and 

 So gives an idea as to the distribution of the waA-e-form 

 drag and the friction drag which is not obtained from 

 other observations of water-surface inclination. 



Observing that the tangential force is directly propor- 

 tional to the setup, the analogy between equations (14) 

 and (22) is of interest. This analogy permits physical in- 

 terpretation of the "formula velocity" F, as the celerity 

 of the wave components most significant in producing 

 the wave-foi-m drag. 



More accurately it is connected with the horizontal 



