C;11A1'1LR IJ 



Viscx)us-Fl()\v Data and Friction-Resistance 

 Calculations 



45 1 General 80 45.13 



45 2 Refcnnice Data on Mass Density, Dynamic 



Viseosity, anil Kinematic Viscosity ... 94 

 45 3 Representative Internal Shearing Stresses in 45. 14 



Water Alongside Models and Ships ... 94 45.15 



45.4 Tables of Reynolds Numbers for Various 



Ship Lengths and Speeds 94 45.10 



45 5 Data on and Prediction of Ship Boundary- 45.17 



I.,ayer Characteristics 95 45.18 



45.0 Typical Velocity Profiles in Ship Boundary 



layers 97 45.19 



45.7 The Development of Formulas for Calculat- 

 ing Ship Friction Resistance 99 45.20 



45. 5 List of Principal Friction-Resistance Form- 



ulas for a Flat, Smooth Plate in Turbulent 15 21 



Flow 102 



45.9 Specific Friction Coefficients for the Schoen- 45.22 



herr or ATTC 1947 MeanHne 104 



45. 10 I.aminar Sublayer Thicknesses in Turbulent 45.23 



Flow 104 



45.11 Friction Data for Water Flow in Internal 45.24 



Passages 105 45.25 



45.12 Computation of the Wetted Surface of a Ship 100 45.20 



Wetted-Surfaco and Boundary-Layer Calcu- 

 lations for the Transom-vStern ABC Ship 



of Part 4 109 



Estimating the .MIowanccs for Curvature . . 110 

 Criterion for a Mydrodynamically Smooth 



Surface 112 



E(|uivalent Sand Roughness 113 



Practical Definitions of Surface Roughness . 1 14 

 Determination of the Allowances for Rough- 

 ness 115 



Factors Affecting Fouling Resistance on Ship 



Surfaces 117 



The Prediction of Fouling Effects on Ship 



Resistance 120 



References Relating to Fouling as Affecting 



Ship Propulsion 125 



The Calculation of the Friction Drag of a 



Ship 120 



Allowances for Friction Drag on Straight- 

 Element and Discontinuous-Section Hulls 127 

 The Friction Resistance of a Planing Hull . 128 

 Friction Drag of a Craft Moored in a Stream 128 

 Selected Bibliography on Friction Resistance 128 



45.1 GeneraL Cliap.s. 5, G, and 22 of \'olume rccniircd for (■.stiinatiiig or [jrodiftiiig various 



I give a general physical picture of the viscous features of the viscous flow around bodies and 



flow in a real liquid along flat and curved plate ships, including the friction resistance. Fig. 45.A 



surfaces, and around the e.xternal boundaries of summarizes these data for convenience and the 



an underwater ship hull. The reader who may subsequent sections of this chapter explain how 



find useful a somewhat different exposition of they are used to derive numerical answers for a 



friction is referred to a paper by Senor M. L. ship and some of its parts. 



Acevedo, .Superintendent of the M(k1c1 Basin at 

 E\ Pardo, near Madrid, Spain, entitled "Shii) 

 Friction Resistance." This is an am()li(ied version 

 (in KnglLsh; of tlur contribution actually presented 

 by Senor Acevedo at the Fifth International Con- 

 ference of Shiji Tank Superintendents, lield in 

 London in September, 1948. It gives a brief 

 re.sumd of the development of the various friction 

 formulas, a most elaborate comi)ari.son of the 

 re.Hultw obtained from each, and a set of re(|uire- 

 mcnt.s for u satisfactory and acceptable f rid ion 

 formulation. A cojjy of this pajjer o' available in 

 Ihr- '1MB library. 



'IhcTc are a«s<?mbli«! in the present cimptcr I lie 

 furnuilaM, c(|untiunH, and other qnanlitalivc data 



The method of calculating and using the 

 Hej'nolds inunber antl it*! several variations is 

 described in Sec. 41..") and in subseciuent .sections 

 of the present chapter. The Reynolds number 

 .serves not only as a flow parameter but as an 

 indicator of the type of viscous flow which may 

 be exi)ected aroimd a IkkIv imder a given set of 

 conditions. This latter feature is of inti-rest in 

 model rather than in ship work, becau.se most of 

 the Rej'nolds nmnbers for minlels are in the 

 low ranges. 



One other fcaliu'e invohing the u.se of the 

 Reynolds number in practice does require men- 

 tion. It is cuslomary in many (juarters, when 

 cnnsidcring only the visctnis-flow situation for 



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