Document: NRC Regulatory Guide
Document ID: c9ebcbb0-96c4-4d29-be51-5acae9cc858a
Document Type: regulatory_guide
Title: Estimating Aquatic Dispersion of Effluents from Accidental and Routine Reactor Releases for the Purpose of Implementing Appendix I (Rev. 1)
Source: NRC Regulatory Guide Division 1
Source URL: https://www.nrc.gov/docs/ML0037/ML003740390.pdf
Revision Date: 2023-06
Chapter: 
Section ID: RG-1.113
CFR Part: 
CFR Title: 

Content:
, where B is the river width and Q is the total river floe. Substitution of Equation (2) into Equation (1) yields the following transport equation: 2-_ . L-_ -(yu2 IC i C ."(3) In the decay term, the velocity umay be.replaced, to a good approximation, by the sectional mean value u. If this is done, the decay term may be removed through the transformation A x C(xq) - x(x,q)e u (4) The result is the following transport equation for the nondecaying concentration x: S~(s) The quantity Kvud2 is known as the "diffusion factor." Yotsukura and Cobb (Ref. 14) have shown that the variable diffusion factor may be replaced by a constant factor Kyud , where Q 1 Kyud fo Kyud 2dq is the discharge-weighted mean value. Equation (5) may now be written 1.113-5 x - Downstmma y - Aro, Strum z - Verticly Doaumld From Water Surface u(y)- Ve.ocity in x Direction Varying with y S.0 u(y FIGURE 1. MODEL OF AN INFINITESIMAL STREAM TUBE IN A NATURAL STREAM (Rdamwn frmo Yotukua oad Cobb. Ref. 14.) I- (6) ax aq where D a K-- ud a consta-nt diffusion factor y Equation (6) is a standard diffusion equation which has a closed-form analytical solution. Assume a steady vertical line source discharge emitting a constant W Cl/sec is located at x = 0, y = ys. Since there is a one-to-one correspondence between the transverse distance y and the cumulative discharge q, the vertical line source discharge may be located at x a 0, q m qs" A closed-form solution to Equation (6) that satisfies the condition that there be no flux of material across the bounding surfaces is given by X a W +2 nil n2w2Dx e Q Cos n4 ZOS This expression, although of different form, is equivalent to Equation (14) of Reference 14. If the liquid effluent Is injected as an area source perpendicular to the river flow, the solution may be obtained by integration of Equation (7) over the source dimensions. If the source is located in the river between distances ysl and y.2 (cumulative discharges qsl and qs2), the area source solution may be