«M 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 45.2 



in which the friction resistance can be segregated 

 with reasonahle accuracy. 



Adequate nielliotls are not yet avaihible for 

 ninking accurate prwHctions of the effects of 

 transverse and longitudinal curvature and of 

 pressure gradients, when making the transition 

 from the flat, smooth plate to the niotlel or ship 

 surface. 



Limited full-scale data derived from thrust 

 measurements enalile a reasonably reliable assess- 

 ment of combined smooth-plate and rough-ship 

 friction resistances for certain types and condi- 

 tions of ship-bottom surface. 



45.2 Reference Data on Mass Density, Dy- 

 namic Viscosity, and Kinematic Viscosity. Tables 

 X3.d thri)Uij;h X:^.i of Api)x. 3 of this volume give 

 values of the ma.ss density p(rho) and the kine- 

 matic vi.scosity v(\\n) of "standard" fresh and 

 salt water, the latter of 3.5 per cent salinity, for 

 a range of latitudes and temperatures sufficient 

 to meet the usual needs of the ship designer and 

 marine architect. 



Tables X3.j and X3.k of Appx. 3 give values of 

 these characteristics, plus values of the dynamic 

 viscositj' M(niu), over a rather wide range in 

 temperature, for a number of well-known li((uids 

 encountered at times in ship-design work. The 

 original data, from which these tables were 

 adapted, are listed .somewhat differently in: 



(a) Rouse, IT., EMF, 1940, Appx., pp. 3.J7-3G.5 



(b) Rouse, H., EH, 19.50, Appx., pp. KIUI 1013, 



including the references listed 



(c) Rouse, n., and Howe, J. W., BMF, 1953, 



Appx., PI). 231-238. 



45.3 Representative Internal Shearing Stresses 

 in Water Alongside Models and Ships. From the 

 rcl:itionsliii)S given in Chap. 5 of Volume I, 

 particularly in Fig. o.R, the shearing stress r(tau) 

 at any point in a li(|uid undergoing viscous action 

 i.s T = nidU/dy) where y is measured normal to 

 the flow, in the direction in which U is varying. 

 At a solid surface under a viscous liquid flow the 

 shearing stress at the wall is [Rouse, H., KMF, 

 HUG, pp. 185-180] 



'• ■ '(f) L. - '^"(i)"- - '^"'" 



where to ha.s the dimensions of a force per unit 

 area or a pressure, namely in/Li'. The local 

 specific friction resistance coefficient Cir is as 

 given in the wvcral formulas of Figs. 5.R and 

 •t.')..\, for the condilions existing or assumed. 



A calculateii average t„ for a whole solid surface 

 is found simply by dividing the wetted area S 

 into the calculated friction drag Rr • Its local 

 value for any designated point along the solid 

 surface may be found by the formulas of J'ig. 

 45.A and of the preceding paragraph. The 

 numerical examples of Sees. 5.12 and 45.15 give 

 the following representative values for "standard" 

 Siilt water: 



(a) Ship 500 ft long, speed 20.72 kt, 5 = 45,000 

 ft^. To = 1.797 lb per ft' as an average value for 

 the whole ship, calculated at the end of Sec. 5.12 



(b) Ship 400 ft long, speed 30 kt, but basing 

 calculations on a point 200 ft abaft the FP, 

 To = 2.504 lb per ft" at that point 



(c) Ship 190.5 ft long, speed 12 kt, to = 0.485 

 lb per ft' for a point at the stern 



(d) Slup 510 ft long, speed 20.5 kt, t„ = 1.051 

 lb per ft' for a jioint near the stern, TjOO ft from 

 the bow 



(c) Model 20 ft long, speed 10 kt, but basing 

 calculations on a point 10 ft abaft the FP, 

 To = 0.G093 lb per ft' at that point. 



45.4 Tables of Reynolds Numbers for Various 

 Ship Lengths and Speeds. It is pointed out in 

 Sec. 2.22 of X'olume 1 and in many of the standard 

 reference works on hj-drodynainics, that the 

 Reynolds number is a logical and a practical 

 parameter for representing quantitatively the 

 analytical and experimental evidence on viscous 

 flow, involving friction resistance. This is regard- 

 less of the type of viscous flow, whether laminar 

 or turbulent, or of the degree to which surface 

 roughness effects enter into the picture. In the 

 latter case there are, however, certain (|ualifica- 

 tions as to the separate influences of liquid 

 velocity and distance from the leading edge. As 

 such the Reynolds number enters into many of 

 the present-day calculations and predictions, not 

 only with the space dimension x representing 

 length from the leading edge, as in a ship form, 

 but with the space dimension representing the 

 width b or the diameter i) of a body. 



To facilitate calculations involving its wide- 

 spread use. Tables 45. a and 45. b give calculatecl 

 values of /f„ = VL/v for both "standard" fresh 

 and "standard" sjilt water, as defined in .Vppx. 3. 

 The range of lengths L, or j:-<listances, is large 

 enough to span both model and ship sizes, as is 

 the range of speed, expressed in both ft per .sec 

 and kt. 



The <lat;i in Table l.").!i are caiculatrd bv the 



