Desai and Lieber 



isopercentage surface, we can obtain an isomagnitude surface on which, in gen- 

 eral, the percentages are different. 



When we want to say that a disturbance has died out in a domain of the fluid, 

 we have two alternatives. We can say that beyond a certain isopercentage sur- 

 face the disturbance is insignificant. Or we might say that beyond a certain iso- 

 magnitude surface the disturbance is insignificant. Now the construction of an 

 isomagnitude surface involves measurement only at points in the flow field, and 

 no knowledge of the disturbance at the source is required except insofar as the 

 suitable selection of a system of units is concerned. On the other hand, the con- 

 struction of isopercentage surfaces involves a detailed measurement and knowl- 

 edge of the disturbance at the source, in addition to the measurement at points 

 in the flow field. From the point of view of measurement, then, the isomagnitude 

 surfaces are more appropriate. More significantly, however, the magnitudes 

 and not the percentages based on the magnitude of the disturbance at the source 

 represent the actual disturbance at a point. Hence, physically also, the isomag- v 

 nitude surfaces are more appropriate to delineate the domains of the disturbed ' 

 and the undisturbed field. For mathematical convenience, we may construct a 

 spherical envelope which would enclose the isomagnitude surface within it, by 

 taking the largest distance between the source and the isomagnitude surface as 

 the radius of the envelope, and then using it in place of the isomagnitude surface. 



Now we introduce the idea of a Physically Infinite Distance. 



Definition: Physically Infinite Distance in a certain direction is 

 that smallest distance away from an obstacle at which the flow 

 field is not significantly affected by the presence or absence of 

 the obstacle. The word "significantly" is to be interpreted in re- 

 lation to the degree of accuracy with which the field variables are 

 measured. 



Evidently, a change in the field variables in the dynamical category repre- 

 sents a disturbance. The magnitude of this change is the magnitude of the dis- 

 turbance. It is a matter of convention to decide when a certain magnitude of this 

 disturbance is negligible. Any magnitude which falls within the limits of accu- 

 racy of a measuring instrument, which is judiciously chosen so that the meas- 

 urements made with it describe the physical conditions properly, may be consid- 

 ered negligible. Then this magnitude may be used to construct an isomagnitude 

 surface. The smallest distance in a certain direction from the obstacle to this 

 surface is the Physically Infinite Distance in that direction. 



The Physically Infinite Distance will depend on the following: 



1. The physical nature of the fluid 



2. The intensity of the disturbance 



3. The direction in which it is reckoned 



4. The degree of accuracy of the measuring instruments. 



510 



