Document: NRC Regulatory Guide
Document ID: f4c5fb1d-efb9-4168-9804-5ad3f6f64d06
Document Type: regulatory_guide
Title: Reporting Procedure for Mathematical Models Selected To Predict Heated Effluent Dispersion in Natural Water Bodies
Source: NRC Regulatory Guide Division 4
Source URL: https://www.nrc.gov/docs/ML0037/ML003739535.pdf
Revision Date: 2023-06
Chapter: 
Section ID: RG-4.4
CFR Part: 
CFR Title: 

Content:
pMGacUW situation, however, these quantities are only very sightly tempemture dependent and, with one exception, may be treated a- constants. The one exception is the external force term, pXi, in the momentum equation. Heem, the density cannot be treted as a constant. Its variation, when multiplied by Xi, can produce an acceleration comparable in mgneitude to that of the Inertial term. Hence, ;, cv, a, and k my be treated a consants wherever they appear, and p may be treated a a constant except when it WOWha In the tasdfiorce term. This treatment of the density variation is the Bouainesq approximation. Its physical significance becomes clear upon consideration that, in practical situations, the external force term is the acceleration of gravity. 2Effects of salinity have been ignored for the sake of brevity of diacur•do. The smplest equation of state, including the rdksitywoulidbe ofthe form p a1p ll-(Tr-T o)+p(S-S o)J, whime S = salinity, 0 = coefficient o;?saline contraction. 4.4-10 Under the Bousuneq approximation, the equation for manu conservation becomes which Is the familiar expression of ,ncomPresability. in the light of Eq. (B-S), the momentum equation becomes 'IV, + Uau i= at 2 a9 ktJfk 1 ap PO ax, where V2 is the Laplahcan operator axl 2 + a2 a2 ax 3 2 3. Conervtdon EqtL"one for Turbulent Flow The above equations express the basic conservation principles in terms of the instantaneous fields of velocity, temperature, pressure, and density. In any natural system, the flow is turbulent. Because turbulence is Inherently random, solution of the above equations is impractical for any real problem. The equations must be subjected to an averaging operation that separates the deterministic and stochastic components of the quantities in question. Accordingly, the instantaneous quantities, ui, p, and T, are each written as the sum of an average component (denoted by a bar over the symbol) and an instantaneous fluctuation about the average (denoted by a primed