Wiegel and Delmonte 



DISCUSSION 



Choung M. Lee 



Naval Ship Research and Development Center 

 Bethesda, Mary land 3 U.S.A. 



Perhaps I should direct this question to Keulegan anc Carpenter 

 themselves, but since Professor Wiegel seems to have much expe- 

 rience in Keulegan number, I would like to ask one question. Keulegan 

 number is formed by the maximum fluid velocity which is multiplied 

 by the period of the flow and divided by the diameter of the circular cy- 

 linder. For a periodic fluid motion the maximum velocity can be simp- 

 ly converted into a product of the amplitude and the frequency which is 

 equal to 2 tr times the amplitude over the period. Then the Keulegan 

 number becomes the ratio of the amplitude of the oscillation of fluid to 

 the diameter of the cylinder. This means that the Keulegan number is 

 independent of frequency. It is a puzzle to me that all the forces act- 

 ing on the circular cylinder only depend on the ratio of the amplitude 

 of oscillation of fluid to the diameter of the circular cylinder. I believe 

 that there must be a physical reason for such a phenomenon. I would 

 appreciate Professor Wiegel' s comment on this remark. 



REPLY TO DISCUSSION 



Robert L. Wiegel 



University Of California 

 Berkeley y California, U.S.A. 



One can make use of the wave equation, calculate the actual 

 excursion of the water particle motion, and what one comes up with 

 is a ratio of the distance that the water particle moves to the diameter 

 of the pile. If you have water waves it is very simple to show that the 

 controlling number there is probably only the ratio of wave height to 

 the diameter. You are correct. I hope I put this in my Paper ; if not, 

 I should have, because it is not really the time, it is the distance along 

 the boundary that the fluid must move in order for the boundary layer 

 to form and for the vortices to form, and so forth. So the time is 

 really only used to calculate how far it has moved. I hope that has 

 answered your question and I see that you indicate that it has. 



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