150 



n nuonvNANfics i.\ ship ofsicx 



Sec. 47. f 



, V2Q(hthA-hv) 

 "niis Nomoijroph Represents the E^ootion V '—^ 



Where q i» the Accelerotion Due to Grovity 



h IS the Depth Below the Water Surface 



h/\ is the Equivalent Head Due to the Atmosphere 



Viy is the Head of the Water Vapor, 



about 0.57 ft at 59 de<3 F t- 



V is the Speed of the Body 



cr (siqma) is the Covitatjon Index 



of the Body 



Depth in feet, 

 h 



-200 



m 



it 



To Estimotc the Speed 

 of Incipient Covitotion 

 for a Body. Lou Q 

 Stroiahteaoe on the 

 Given h- and (J-vqIocs. 

 The Resultant Cavitation 

 fifseed is the Intercept 

 on the Speed or V-Scole. 





5i 



or 

 9 : 

 C^^IO 



Fjc. 47.B Nomogram for Relatino Submeroknce 



Depth, Cavitation Index, and Water Speed for 



Incipient Cavitation 



Since incipient cavitation is involved, the cavitation 

 index indicated here is the critical value. From the relation 

 <j " (po. — e)/(0.5pV"), the critical value diminishes as 

 the water s|K'cd incrca.ws. From Sec. 47.5 and Fig. 47. D, 

 the pressure coeflicient En must diminish numerically 

 witli ffc« to avoid cavitation. 



foil scctioim, including many of tluwe u.sed Im- 

 propeller blade.s, and for an infinite span, it is 

 possible to calculate the ratio V lU^ for all part,s 

 of the surface. From this ratio it is pos.siblc to 

 determine the pressure coeflicient or Euler number 

 E, at any point, and hence the absolute pressures 

 at all points for any given set of undisturbed- 

 velocity and initial-pressure conditions. Absolute 

 pressures approaching the vapor pressure c of 

 the liquid are in<licatioiis of incipient cavitation. 

 Calculations for a great number and a wide 

 variety of hydrofoil st;ctions, already made, arc 

 li»l«wj ill \\fA |{i|)(.il H'JI, nfiTciircd in Sec. 

 44. .'5. 



.\iiy liydrufuil .section, no matter how well 

 shaped i( may be for straight-ahead (low, cavi- 

 tates when it makes too great an angle with the 

 incident flow. The excessive angle of attack for a 

 lifting foil may be either i)ositive or negative. 



In general it may be .said that for any hj-drofoil 

 section designed to produce lift, the best shape is 

 one which, under the angle of attack to be 

 expected in service, produces a distribution curve 

 of — Ap on the back that has the maximum spread 

 of the greatest reduced pressure across the chord, 

 without an excessivelj' low depression. 



The technical literature contains data derived 

 from a limited number of cavitation tests made 

 on hydrofoils under 2-diml flow conditions. A 

 typical result, set down graphicall}' in Fig. 47.C 



20 -o 



100 90 80 70 60 50 40 30 ZO 10 O'^cl 

 Angles of Attock a. on Hvjdrofoil 



^^^^ 



-04 -OZ OZ 0.4 0.6 0.8 10 

 Lift Coefficient Cl 



Fig. 47. C Cavitation Limits for Lift Coefficient 

 AND Angle of Attack on a Typical Hydrofoil 



[Uaily, .1. W., ASME, Jour. Ai)pl. .Mcrli., li)l!), 

 Vol. 71, p. 209], shows that at negative angles 

 of attack cavitation generally occurs on the face 

 and at positive angles of attack on the back. 

 'riici;c is usually a single angle of attack at which 

 cavitation occurs simultaneously on both surfaces 

 if the cavitation index is reducetl to a sufficiently 

 low nuniljcr. .\ diagram similar to that referenced, 

 (•X(('l)l that it is tierived by an analytic procedure 

 I'm- a whole screw jiropeller, is given bj' J. F. 

 ShaiiniMi and R. N. Arnold |IFS8. 1!):?S li):?9. 

 Vol. 82, Fig. 18, p. 285|. 



As is the case for the lift, drag, and moment 

 data on hydrofoils, described and presented in 

 Sec. 11. .5, the cavitation test data are of limited 

 design a|)plication unless aconnpanied by section 

 drawings or tables of coordin.'ites of the foil. If it 

 is possible to know also the chcuibvise pressure 



