^r. Paul Dergarabedian (Communicated by Mr. Go V, Schliestett) 

 Naval Ordnance Test Station, Pasadena, California ' 



The inception of cavitation in terras of the dynamical be- 

 havior of a vapor or gas bubble involves the consideration of the 

 groxvth of such bubbles from an initial etiUilibrium size. This 

 problem has been considered in the Cal, Inst, of Tech, Hydro » 

 Lab. Report No. 21-10, August 1952. In this report calcula- 

 tions are presented for the dynamic stability of vapor and 

 air bubbles in superheated water. These calculations indicate 

 that the values of the bubble radii for which the equilibrium 

 is unstable are restricted to a finite range of radii whose 

 values are governed by the temperature of the water and the 

 initial air content in the bubble o 



In the analysis for the bubble radii it is assumed that 

 the vapor pressure remains constant during the growth and 

 hence the bubble growth is isothermal. This assumption is a 

 reasonable one near the equilibrium point since the rate of 

 growth is very slow initially compared to the subsequent be- 

 havior of the bubble. In addition the assum.ption is made 

 that the diffusion of air across the bubble boundary is negli- 

 gible which means that the air content in the bubble rem.ains 

 constant. With these assumptions it turns out that the range 

 of radii for which the equilibrium is unstable is given by 



^r PAo^ 



v;here Pa^ is the initial pressure of any air in a bubble of 

 radius Kq, Py is the vapor pressure of the v/ater at the 

 appropriate liquid temperature, P^ is the atmospheric pressure, 

 Jl is the surface tension constant for water, and^^P^Py-^ . 



One phase in the cavitation research program of the Naval 

 Ordnance Test Station is to obtain the rate of growth of vapor 

 bubbles near the equilibrium radius by high-speed photography 

 in order to check the theoretical calculations on the equilibrium 

 radii. Such photographs have been obtained in the Cal, Tech. 

 Kept. No, 21-10, but these photographs do not give sufficient 

 detail near the equilibrium sizes of the bubbles. Hence 

 greater magnification of the photographs are needed to record 

 the initial growth of the bubbles « 



