16 



innuoDNA \Mi(.s i\ Mill' ni su.x 



Srr. l/.f, 



(lAstinml as ft. 07 ft prr sec or l.l.i kt, aiid u as Ci'A) 

 rpm or 10. S.} t\)!>. 'I'lic liladr-Ht-ynolds lumilitT for 

 a J-value of l'^/ (nD) = 0.80 works out as 



^^_ \Vl+[2M0.7R)]r\c...,) ...^ 



f 



^ 1(6.97)' + |6.2832( 10.83)0.28151' I ° '(0.2235) 

 1.228,5(10-*) 



= 0.371(10') 



41.6 Application of the Strouhal Number. 

 For tlio rc'triU'taliif .sound m'ar .show II in {'"ig. I I.I), 



M I |-^ 



Direction of Motion] I I I Ke el of Vesse j^ 



Fio. 41. D Definition Sketch a.vd Foiimi i.a hhi 

 Eddy Fiu:giEN'cv in a Vortex Tkaii. 



having a cylindrical neck of diameter D, ami a 

 cylindrical liead of diameter D^ , .separation 

 occurs around the after sides of both the neck 

 and the head, ^'ortex trails of eddie.s having fore- 

 and-aft spacings of b, and bj on each side are left 

 behind the two parts of the device. 



Vibration of the neck and head in a transverse 

 plane is certain to be encountered at some speed, 

 and the Strouhal number .S'„ is of interest in this 

 phenomenon. Tlu; situation depicted in Fig. 

 4 1 .D is complicated by a neck and head of dilTerent 

 diameter, so for the jiurpose of this example it is 

 assumed that the head diameter A>, is reduce<l 

 to the neck diameter /->, . This is taken as O.'JO ft. 



The value of the (/-Reynolds number lij is then, 

 at Hay 14 kt or 23.04 ft per sec in standard fresh 

 water. 



H. - 



UD 



23.64(0.96) 



1.228.5(10 ') 



1.8.5(10") 



It Hum been found by experiment that I here is a 

 n-lutiuiMihip between the HeynoIdH iiumber /{j 



and the Strouhal numi)er S, ; this is available for 

 a sonu'wiiat lower range of fi^ in the left-hand 

 diagram of Fig. 4().('i [House. H., EH, 19.50, Fig. 

 94, p. i:U); Landweber, L., TMIJ Rep. 485, Jul 

 1942, Fig. 8, p. 17). Assuming that the corre- 

 sponding S, value is 0.0, and using Kq. (2.xxiii) 

 of See. 2.22, 



S, = ^ = 0.0 = y 



wlicrc the ciidy frc(|uency 



r 23 01 



/ = O.G J- = (0.0) ■' = 14.8 cycles per sec. 



D 



0.90 



If the frequency of resonant transverse vibra- 

 tion of the cylindrical sound-gear assemblj', 

 taking the added ma.ss of the entrained water into 

 account, is close to this value, the vibration caused 

 by the periodic alternating transverse force 

 accompanying the eddy pattern in the vortex 

 trail will be greatly magnified. To avoid resonance 

 without a change in diameter of the .sound gear, 

 the extension below the hull may have to be 

 diminished, or the maximum speed reduced. 



41.7 The Planing, Boussinesq, and Weber 

 Numbers. Tlie planing number /-"„ is of liniilcd 

 application. It is expressed, as described in Sec. 

 2.22, as the ratio between (1) the total drag Dt 

 (or total resistance Rr) of a planing fonn and 

 (2) the dynamic lift Lg produced by that form. 

 When, as usually occurs at full planing speed, 

 the buoyancy B is zero and the entire displace- 

 ment A (delta) or weight IT is supported l\v the 

 dj'namic lift, the expression becomes P„ = 

 Dt/^ = Dr;]V. Expressing the planing nunil)er 

 in numerical values for a given case harilly 

 reciuires an illustrative example here. 



The Houssinesci number, similar to the Froude 

 number with tlu> hydraulic radius Ri, of a conlined 

 waterway as its length dimension, is expressed by 



R. = 



\ <jR„ 



u__ 



(2.XXV) 



The method of calculating the hydraulic 

 radius is described and illustrated in See. 01.14. 



The Weber number \\\ is described in Sec. 2.22. 

 As it is not employed in anj' of the chapters in 

 this volvmie, an illustrative example of the metho<l 

 of computing and applying it is omitted. 



It is again emphasi/ed that, although normal 

 engineering computations of the various dimen- 

 sionle.ss numbers would not take account of all 

 tlu! signilicant ligurcs in the preceding examples, 



