Pth_{f}V3.12 x 10^{10}fissionswatt secReactor Theory (Neutron Characteristics)DOE-HDBK-1019/1-93REACTION RATESRev. 0Page 21NP-02The power released in a reactor can be calculated based on Equation (2-6). Multiplying thereaction rate by the volume of the reactor results in the total fission rate for the entire reactor.Dividing by the number of fissions per watt-sec results in the power released by fission in thereactor in units of watts. This relationship is shown mathematically in Equation (2-7) below.(2-7)where:P= power (watts)= thermal neutron flux (neutrons/cm -sec)th2= macroscopic cross section for fission (cm )f-1V= volume of core (cm )^{3}RelationshipBetweenNeutronFluxandReactorPowerIn an operating reactor the volume of the reactor is constant. Over a relatively short period oftime (days or weeks), the number density of the fuel atoms is also relatively constant. Since theatom density and microscopic cross section are constant, the macroscopic cross section must alsobe constant. Examining Equation (2-7), it is apparent that if the reactor volume and macroscopiccross section are constant, then the reactor power and the neutron flux are directly proportional.This is true for day-to-day operation. The neutron flux for a given power level will increase veryslowly over a period of months due to the burnup of the fuel and resulting decrease in atomdensity and macroscopic cross section.