55 



p is indicated above, it is clear from the discussion of steady-state cavi- 

 ties that, for such cavities, the pressure p should be replaced by the actual 

 pressure within the cavity. For the small cavities, the question of scaling 

 becomes even more complicated. Although the assumption of vapor pressure is 

 usually adequate, errors may arise when attempting to establish critical cavi- 

 tation numbers from model tests. For complete scaling, it would be necessary 

 to investigate the question of nucleus content and formation on the two scales, 

 and, thus, the thermodynamic parameters in relation to growth of nuclei and 

 heat conduction. Furthermore, additional work must be done on surface tension 

 under dynamic conditions. For most engineering applications, however, it is 

 sufficient to test under reduced pressure, as in the variable-pressure water 

 tunnel, using the vapor pressure corresponding to the temperature of the water. 



In the case of tests of model propellers, discrepancies between mod- 

 el tests and sea trials have led several laboratories to adopt a correction of 

 about 15 percent pressure reduction on the model scale. This discrepancy 

 might be attributed to several causes. These are discussed in the following 

 paragraphs . 



The greater number of air and solid nuclei in sea water than in 

 fresh water raises the pressure for inception. On the basis of his experi- 

 ments in sea water and in the water used in the TMB tunnels, Crump 37 reached 

 the conclusion that the tunnel water should be about 30 percent supersaturated 

 to duplicate inception. However, tests for which the correction is made have 

 almost wholly been on rather small propellers running at low Reynolds numbers. 



The effect of Reynolds number on airfoils is well known — with 

 changes in the maximum lift being observed even over the range of full-scale 

 Reynolds numbers. It is not surprising, therefore, that the characteristics of 

 model propellers should be quite variable with Reynolds numbers. This conclu- 

 sion has been substantiated in part by recent tests* at the David Taylor Model 

 Basin with 8- and 1 6-inch propellers operated under high pressures at speeds 

 of 30 knots, i.e. , at much higher Reynolds numbers than obtained previously. 

 It was found that no corrections are necessary for these results. It should 

 be noted, furthermore, that the difference between the flow about the model 

 and on the prototype, due to absence on model scale of a heterogeneous wake, 

 may be another contributing cause, as has been pointed out many times. 



It is clear that in any model test, the cavitation number and the 

 Reynolds number, which are compatible parameters, should be modelled. Usually, 

 it will not be possible to run at prototype Reynolds number. However, care 



*These results were made available to the writer by Mr. W. Bowers of the water tunnel staff of the 

 David Taylor Model Basin. 



