HYHROnYNAMICS 1\ SHIP Dl.SlGN 



Src. 40.2 



fiiul out whether it will mniiitnin a reasonable 

 tjpitil ill stomiy weather. 



The nuHlerii t^hip designer, with all the methods 

 and data of the twentietli centurj' at his eommand, 

 can »io wontii-rs in this respect, especially with 

 the help of model tests. However, it is not wise 

 to rely so much on nunlel results that analytic 

 ability and prediction procedure sufTer by con- 

 sequence. 



40.2 Useful Formulas Embodied in Theo- 

 retical Hydrodynamics. The amazingly large 

 grouj) of naval architects, engineers, scientists, 

 and mathematicians, manj" of them of great 

 renown, who devoted their thoughts, energies, 

 and talents to a study of the mechanics of fluids, 

 have tackled the problems confronting them 

 along two general lines. Some have conducted 

 experiments, analyzed data, and evolved theories 

 explaining the fluid action obser\'ed. Others have 

 started with certain basic assumptions and 

 premises, like the principles of continuity and 

 conser\'ation of energj- and the laws of mechanics, 

 and have succeeded, bj' reasoning and intuitive 

 processes, in deriving fundamental mathematical 

 expressions for the behavior and flow of ideal 

 liquids. By a judicious combination of the results 

 stemming from these two lines of endeavor, there 

 is aviiilablt! a surpri.sing store of mathematical 

 expressions by which data on the flow of real 

 licjuids can be derived in numerical tenns. 



For example, by the application of the well- 

 known kinetic-energj- formula for solid bodies, 

 where E = ii.bmV^, and by the tlieorem which 

 maintains the sum of the potential and kinetic 

 energies constant, it is possible to deduce the 

 ram pressure at the stagnation point in the center 

 of the nose of a body of revolution. Here the 

 Uquid-strcam velocity is zero, and the ram pres- 

 sure 7 = O.opf/". The modern engineer uses this 

 formula, as he does many others like it, without 

 a moment's hesitation as to its accuracy and 

 certainly without requiring its experimental 

 confirmation. 



In this respect, the everyday formulas derived 

 by the mathematics of classical hydrcxlynaniicsare 

 to the mfKJern naval architect and marine engineer 

 ju.st HO many u.seful tools. This is the reason why 

 the chaptirrs which follow are given over to a 

 presentation of formulas gathered from many 

 .s<jurce«, without including the mathematical 

 proofs or derivations among them. The engineer 

 may continue to |(M)k upon the mathematics as a 

 mearm to an end, without rendering iiimself 



vulnerable, as long as .someone cLso continues to 

 work out new exjircssions, like the ram-pressure 

 formula, that help him in his ilaiiy work. However, 

 to apply these or other formulas intelligently, the 

 engineer shoulii know what the}' mean. 



Furthermore, as the science of ship propulsion 

 and ship motions progresses, more and more new 

 formulas are needed. Many of them can be derived 

 only through mathematical processes. It is not 

 too much to say that many of them can best be 

 derived bj' the naval architect himself. The 

 omi-ssion of the mathematical derivations in this 

 tliird part should not be taken, therefore, as an 

 indication that the ability to derive them or to 

 formulate better ones can be omitted from the 

 knowledge of one who aims to specialize in the 

 hydrodynamics of the ship. 



The reader who wishes to familiarize himself 

 with the mathematical theoiy and processes of 

 hydrodynamics is referred to a number of text- 

 books and other publications. The authors, titles, 

 and other data on these books, listed in Sec. 1.3 

 of the Introduction to Volume I, are repeated 

 here for convenience: 



(1) Binder, R. C, "Fluid Mechanics," Prcntice-llall, 



New York, 1947. A third edition appeareti in 1955. 



(2) Vennard, J. K., "Elementary Fluid Mechanics," 



Wiley, New York, 2nd edition, 1917. A third 

 edition appeared in 1951. 



(3) Rouse, II., and Howe, J. W., "Basic Mechanics of 



Fluids," Wiley, New York, 1953 



(4) Rouse, H., "Elementary Mechanics of Fluids," 



Wiley, New York, 194G 



(5) Prandtl, L., and Tietjens, O. G., "Applied Hydro- 



and Aeromechanics," McGraw-Hill, New York, 



1934 

 (C) Rouse, II., ICtlitor, "Engineering Hydraulics," Wiley, 



New York, 1950 

 (7) Dryden, H. L., Murnaghan, F. D., Bateman, H., 



"Hydrodynamics," National Research Council, 



Wasliington, 1932 

 (S) Slrceter, V. L., "Fluid DynainicM," McGraw-Hill, 



New York, 194S 

 (9) Binder, R. C, "Advance*! Fluid Dynamics and Fluid 



Machinery," Prentice-Hall, New York, 1951 

 (10) Goldstein, S., "Modern Developments in Fluid 



Mechanics," Vols. I and II. Oxford Prcts, 1938 

 (U) Milne-Thomson, L. M., "Theoretical Hydrody- 

 namics," .Macmillan, New York, 2nd edition, 1950 

 (12) Lamb, Sir Horace, "Hydrodynamics," Dover, New 



York, 0th rcvisetl e<iition, 1915. 



40.3 Present Limitations of Mathematical 

 Methods. .Matlicmutical and jiiialytical nicduxis 

 in their present state, even though stretched to the 

 utmost, can by no means .supply all the an.swers 

 wanted l.v llif nindrrn marine nrcliitecl. Thi-y 



