96 



IIVDRODVNAMKLS IN Mill' DKSIGX 



Sec. -(5.5 



velocities nmy l>e lieteriniiied within 0.002 inch 

 of the inner wall of a tube of circular section. 

 Fig. 3 on page 23 of the reference is a plot of 

 local velocity V on distance from the inner wall, 

 embodying observations taken within 0.0006 inch 

 of the solid surface in a regime which is distinctly 

 laminar in character. 



Despite the difficulties and drawbacks men- 

 tioned, the velocities at a series of normal dis- 

 tances from the hull surface can be and have been 

 measured on both ship and model, and the velocity 

 profiles plottetl. Two sets of typical ship profiles 

 arc reproducctl in Sec. 45.6, and reference data 

 are quoted there on many others. Despite the 

 shortcomings of the observed data, anj' informa- 

 tion at all is considered l)etter than none. 



A designer's need for boundarj'-layer data may 

 be sufficienth' pressing — for instance, in selecting 

 propeller-tip clearances alongside the hull on a 

 large and important passenger liner — to justify a 

 rather extensive model- or ship-measurement 

 project. However, it is well for the designer to 

 know beforehand that, no matter how extensive 

 are the measurements projected, they will almost 

 surely be found insufficient when the time comes 

 to plot, analyze, and use the results. This is not 

 intended to discourage the designer before he 

 begins but to broaden the scope of the measure- 

 ments. 



As an illustrative example there may be men- 

 tioned the investigation carried out on a cruiser 

 model in the early 1940's, to determine the proper 



location for a pitot^type speed log. It was necessary 

 to know the position, both fore and aft and 

 relative to the surface of the underwater hull, of 

 the cloak of the boundary layer where, at the 

 designed speed, the relative water velocity was 

 within one per cent plus or minus of the ship 

 speed through undisturbed water. Although it was 

 expected that the log would be installed under 

 the entrance, as is customary' for these instru- 

 ments, an acceptable pasition was found only 

 after exploring the boundarj' layer under a model 

 of the ship from the stem to a position far aft, 

 under the after engine room. When the isotachyl 

 representing 100 per cent of ship speed was 

 drawn on the outboard profile it was found that, 

 at the position originally proposed for the log, 

 the isotachyl lay more than 6 ft below the keel. 

 This distance was about twice as great as the 

 contemplated log extension beyond the hull. 



On the basis previously' mentioned, that some 

 indication of 6-valucs are better than none. Figs. 

 4o.B and 45.C show plots of boundary-layer 

 thicknesses for laminar and turbulent flow, 

 respectively, derived from the space-velocity 

 relationships of Sec. 5.13 of ^'olume I and Eqs. 

 (o.vii) and (5.viii) for flat, smooth plates. In 

 plotting these graphs, the data have been extra- 

 polated to ranges far beyond those justified by 

 the manner in which the formulas were derived. 

 The plots are therefore to be considered as indi- 

 cators of the 5-values, nothing more. 



A graph illustrating the values of 5 for the 



400 360 960 340 320 300 260 260 240 220 200 180 160 140 120 



I- Distance from Leodinq Edqe, ft 



100 eo 



Fio. 45.C' Vaiuatki.n uv HorsDAnY-LAVKii Thic-knkk.h i with j-1)i.stanck kiu)M Lkadino Kiiok, fxju Trniiiii.ENT 



Flow in Fkuii Watek 



