Introduction.A number of known families of probability distributions can be derived from requirements that are physical in the sense that they describe the random behavior of the event under consideration. The Poisson process is typical of these: If X{t) is equal to the number of occurrences of a specified event in the interval [0, t), then one can show that X (t) has, for each t, a Poisson distribution, if the probabilistic behavior of the event satisfies a few very simple physical requirements [1], The normal distribution may also be derived from a few physical requirements.In this note we shall employ a simple model and statistical-mechanical methods to derive the three-parameter generalized gamma distribution. The history of this family of distributions was reviewed and further properties were discussed in 1962 by Stacy [2], Subsequent work on statistical problems associated with the distribution has been done by Bain and Weeks [3]. Special cases of the generalized gamma distribution include the Weibull, gamma, Rayleigh, exponential and Maxwell velocity distributions. Another special case is a distribution recently derived on a statistical-mechanical basis to describe rainfall run-off from a watershed [4], The model. We shall consider the following situation: The occurrence of an event, such as the failure of a component or system, depends on some variable such as the stress to which the part has been subjected or the time during which it has been subjected to a given level of stress or use. This variable (be it stress or time) will be designated by t and the number of occurrences of the event during the interval , t,) will be designated by N{ , where t, -i,_i = At and t0 is the arbitrary origin.** The requirements that we shall impose upon the iV.'s are as follows:

Since Zuber made a hydrodynamic prediction of the peak pool-boiling heat flux on an infinite flat plate, his general concept has been used to predict the peak heat flux in two finite heater configurations. These latter predictions have differed from Zuber’s in the introduction of a largely empirical variable—the thickness of the vapor escape path around the body. The present study shows how measurements of this thickness can be combined with the hypothesis that the vapor velocity within the vapor blanket must match the vapor velocity in the escaping jet above the heater. The result is a more exact description of the hydrodynamics of vapor removal. This idea is used to suggest the possibility of a universal value for the ratio of the cross-sectional area of escaping jets to the heater area for large finite heaters and for long slender heaters. A set of general ground rules is developed for predicting the peak heat fluxes on both large and small heaters. These rules are used in turn to predict the peak heat flux from horizontal ribbons. They are also used to correct the traditional prediction for infinite-flat-plate heaters. The predictions are supported with new data.

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A method is devised for correlating the extent that the pressure of a system undershoots the saturation pressure during a rapid depressurization in water. The dependent variables in the correlation are the initial water temperature and the depressurization rate. The correlation is motivated by classical nucleation theory, and based on data from a variety of sources. The probable error of pressure undershoots predicted by the correlation is ±10.4 percent.

Experimental data obtained at both earth-normal and elevated gravity, in a variety of organic liquids and water, are used to verify the hydrodynamic theory for the peak pool boiling heat flux on flat plates. A modification of Zuber’s formula, which gives a 14 percent higher peak heat flux, is verified as long as the flat plate is more than three Taylor wavelengths across. For smaller heaters, the hydrodynamic theory requires a wide variation in heat flux owing to discontinuities in the number of escaping jets. Data for smaller plates bear out this predicted variation with heat fluxes that range between 40 percent and 235 percent of Zuber’s predicted value. Finally, a method is suggested for augmenting the peak heat flux on large heaters, and shown experimentally to be viable.