The increment of area which, during the time interval t to t + dt, 

 has a concentration varying from s - 1/2 ds to s + 1/2 ds, if given by: 



2Tirdr 

 n 



and hence the integral which appears in equation 1 is given by 

 .t .A _t 



r ppc r ppc r ppc r ppc r ppc r 



I j ""' -J I ''-^''-j I 







ppc 



— e-r/Pt drdt 



D(Pt)2 



This integral can be evaluated using equations 5, 7, and 8. The solution 

 is given by 



r 



A 



- ppc 



4 M 

 (9) 9 1 sdAdt = - - t 



9 Q ppc 



The criterion for establishing the number of discharges, N, each 

 of strength M, which may be made into a marine locale of area A during 

 the time interval T is then, from equation 1 



9 DAT^s 



(10) N < PP£- . 



"800 t- ,„ Mt 



1/^ ppc 



The time period T, which must be short compared to a man's life 

 span but long compared to the time required to reduce the maximum 

 concentration resulting from a single release to below^ PPC values, is 

 here taken as 30 days. 



Now consider a harbor having relatively poor mixing character- 

 istics and a low rate of exchange with adjacent coastal waters. A re- 

 view of available data indicates that most marine harbors of the United 

 States have a half life of 30 days or less. Joseph and Sender (1958) 

 found that for a number of phenomena of varying scale in the open sea 

 the diffusion velocity _P was nearly constant at 1 cm/ sec. A conserva- 

 tive estimate of this parameter for inshore tidal waters is taken at 0.5 

 cm/ sec. Further, assume that in this "typical" harbor the depth inter- 

 val within which vertical mixing occurs is at least 6 meters. The 

 boundaries of the harbor are considered to constrain diffusion to within 

 an arc of 30°, both up-channel and down-channel; hence n = 6. 



We take for the volume and surface area of this "typical" small 

 harbor the values 3 x 10^ m^ and 5.4 x 10^ m^ respectively. Letting 

 D = 6 meters, t, /2 = 30 days, and T = 30 days, then for this sample 



34 



