H6 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 413 



moving aft past a liwp part of the 30-kl ship, 

 ixpn\sso<I as I'. + AT, can not cxcccti 83.75 ft 

 per sec. Since the ship speed V equals the velocity 

 V . , the augment W can not e.\cee<I 83.75 — 

 50.t»7 = 33.08 ft per sec without the onset of 

 cavitation. For the equator of a 3-{liml sphere 

 the augment ACisO.sr^ ; if r„ iso0.t)7 ft per sec, 

 AC is 25.34 ft per sec. This is less than the limiting 

 value of 33.08 ft per sec, so cavitation would 

 not occur at the equator of the sphere at a depth 

 of 37 ft. For the maximum diameter of a 2-diml 

 nxl, normal to its direction of motion, the aug- 

 ment AT is l.OUa. or 50.G7 ft per sec. This 

 exceeds the critical velocity, so at the given 

 depth cavitation would begin ahead of the 

 midsection of the rod. 



Aeration of the salt water raises its vapor 

 pressure. This has the effect of diminishing 

 numerically the augment of velocity At/ at which 

 some form of cavitation takes place. At shallower 

 depths on a large ship, or at the shallower drafts 

 and greater speeds customary on high-speed 

 vessels, cavitating conditions are readily en- 

 countered on the hull, the appendages, and the 

 propulsion devices. 



Bubble cavitation is hastened by the presence 

 of microscopic or submicroscopic pockets of 

 vapor or air or air and gas bubbles, and of cavita- 

 tion nuclei in the form of impurities, animal or 

 vegetable matter, or entities as yet unknown. The 

 water nearest the .surface of the sea carries the 

 mo.st air in solution; this amount is augmented 

 if the surface is disturbed, as during a storm. 

 There are more minute impurities carried in 

 suspension in waters close to the land but there 

 may be more nuclei of other kinds in waters far 

 from the land. 



From the maimer in wliicli citlici- Idihhlc or 

 Hheet cavitation appears to form in the water in 

 which ships operate, a cavitation criterion must 

 take account of at least six factors: 



(a) The ambient pressure p„ in the water 



(b) The vapor, or the gas-air pressure of the 

 water at the temperature concerned 



(c) The relative .speed U„ of the iinciislurlKd 

 water and the brxly or ship 



(d) The shape and proportions of (he body or .ship 

 (c) The augment of velocity Af/ due to potential 

 and other flow over and around a body, a .ship, 

 or any of it.s parts 



(0 The efTectivc angle of attack «, if the part 

 under conaidcration resembles a hydrofoil. 



Concerning the ambient-pre.ssurc factor, it is 

 not sufficient to consider the mean depth at 

 which a hydrofoil section or other movable body 

 operates, such as the depth to the axis of a screw 

 propeller. It is entirely' po.ssible for a blade 

 element, at the top of its path, to cavitate through 

 an arc or region of low hydrostatic pressure and 

 to set up objectionable vibration or other con- 

 ditions from this cause. At the depth of the .shaft 

 axis, or at the bottom of its path, it might not 

 cavitate at all. 



In real, viscous liquids like water, the over-the- 

 surface litiuid velocities at the inner edge of the 

 boundary layer are less than the ship speed V 

 or the velocity U^ relative to the imdisturbed 

 water. The potential-flow velocities are different 

 than they would be o\-er the same body surface 

 in an ideal liquid, becau.se of the displacement 

 thickness of the boundary la.ver, so that accurate 

 prediction of cavitation is difficult. Fortunately, 

 most appendages liable to cavitation are short, 

 with boundary layers of insignificant thickness. 

 In any case a prediction disregarding the boundary 

 layer is usually on the safe side, if the prediction 

 is to foretell the wor.st that may be expected. 



47.3 Vapor-Pressure Data for Water. The 

 vapor pressure e of water drops rather rapidly 

 with temperature, so much so that appendages 

 and propulsion devices which cavitate in the 

 tropics under a given set of conditions may not 

 do so in the polar regions under the same con- 

 ditions. 



\'alues of c for fresh water, o\'er a temperature 

 range from freezing to boiling at sea level, are 

 graphed in Fig. -17. A. They are listed in Table 



Temperature, deq C 



40 SO SO TO 80 90 



2M 



tio 



s SI 



no ISO 190 170 190 210 



Tempgrotu 



d«<) 



Fifi. 47.A Giurii.s OK VAPon-PiiE.isiTiiB Data kor 

 Krksii Water 



