Sec. 45.5 



FRICTION-RESISTANCE CALCULATIONS 



95 



usual formula 72„ = VL/v, where V is the ship 

 speed in ft per sec, L is the length or space 

 dimension in ft, and v is the kinematic viscosity 

 for standard fresh water at a temperature of 

 59 deg F, 15 deg C, namely 1.2285(10"') ft' per sec. 



The data in Table 45. b are calculated in the 

 same way for standard salt water, having a 3.5 

 per cent salinity and a temperature of 59 deg F, 

 15 deg C. Under these conditions the kinematic 

 viscosity v is 1.2817(10"'^) ft' per sec. 



Values of x~ or d-Reynolds numbers are taken 

 from these tables simply by substituting x or D 

 forL. 



Values of /?„ are in millions, or /?„(10"°). 



To facilitate calculations of R^ for speeds and 

 lengths not covered by these tables: 



(a) Speeds in ft per sec corresponding to integral 

 values of kt, from 1 through 100 kt, are given in 

 Table X4.b 



(b) The reciprocal of 1.2285(10^') is 0.8140(10') 

 or 0.08140(10') 



(c) The reciprocal of 1.2817(10"') is 0.7802(10') 

 or 0.07802(10'). 



G. S. Baker gives a small table of R„ for a 

 y-value of 1.29(10"') for speeds of 2 to 35 kt, and 

 for lengths of 50 to 1000 ft [INA, Apr 1952, p. 61]. 



4S.5 Data on and Prediction of Ship Boundary- 

 Layer Characteristics. A number of detail ship- 

 design problems require, for their proper solution, 

 a good estimate of the boundary-layer thickness 

 5 (delta) at any given point around the underwater 



hull, long before the ship is in the water. This 

 applies to both clean, new surfaces and those 

 roughened by uneven paint coatings and by 

 fouling in service. 



A velocity traverse with a cylindrical pitot tube 

 at a given point on a model of the ship gives some 

 indication of the thickness but this method is 

 tedious and uncertain, at least in the present state 

 of the art. The principal reasons for the uncer- 

 tainties are: 



(a) The boundary-layer thickness at a given 

 point on a model is greater in proportion than at 

 the corresponding point on a hydrodynamically 

 smooth ship, for the reasons explained in Sec. 6.8 

 of Volume I and illustrated in Fig. 6.E of that 

 section 



(b) Existing uncertainty (in 1955) as to the 

 effective roughness of the actual ship surface, and 

 its action in thickening the boundary layer, over 

 and above what it would be on a hydrodynami- 

 cally smooth surface 



(c) The difficulties in making accurate velocity 

 traverses in the vicinity of the laminar sublayer 

 on a model, or on a ship, at distances from the 

 surface of the order of a few thousandths of an 

 inch. 



F. M. Richardson, J. K. Ferrell, H. A. Lamonds, 

 and K. 0. Beatty, Jr., in a paper entitled "How 

 Radiotracers are Used in Measuring Fluid Velocity 

 Profiles" [Nucleonics, Jul 1955, pp. 221-223], 

 describe new tracer techniques by which liquid 



6=5xRx,"'° for Laminar Flov 



in Standard Fresh Water 



,R^= 8.14(1 0*") 



Broken Lines Indicate Regions of Extrapolation for the Formula Given 



0.09.: 

 0.08ii 



0.03IQ 



30 £8 26 24 22 20 18 16 14 le 10 8 6 4 2 0""" 

 x-Distonce from Leadino Edae, ft 



Fig. 45.B Vaeiation of Boundary-Layer Thickness 6 with s-Distance from Leading Edge, for Laminar 



Flow in Fresh Water 



