APPENDIX 



DISCUSSION OF CORRECTIONS 



It has been mentioned in the body of the report that the 

 finite size of the sampling tube will have an effect upon the 

 measured values of the dye concentration curves This effect 

 may be estimated as follows if one assumes that the true dye 

 concentration curve is a generator of a circular Gaussian error 

 surface „ Then the true curve will have the equation 



where r is the distance from the axis and A is some constant de- 

 pending upon X, the distance from the injector to the sampler,, 

 If one takes the radius of the opening of the sampler as R, the 

 curve actually obtained by measurement will be 



e 1 °~ 1L aJfclQ 



which can be rewritten as 



where I is the Bessel function of zero order with pure imaginary 

 argument o The procedure described for obtaining a was to com= 

 pute the indefinite integral G(r) a Jfjg(s)ds and determine & from 

 the condition Q(&)/Q(&s) s o 68 o Although this would be correct 

 if the measured curve were f(r) 9 it tends to overestimate sr in 

 the actual casec This correction could be computed from the ex- 

 pression for g(r) without a large amount of labor for a suffi- 

 cient range of values of r/ & and R/c o However, one may sub- 

 stitute for the circular opening of the sampler a square opening 

 of equal area without altering too greatly the correction and 

 with substantially less labor 



For the case of the square sampler of side 2R one replaces 



J 4R Z vV -fl Z7TCr ' 





Za* 



IK V_ K Va7P i 



