# Minimum Critical Power Ratio

1. Jan 16, 2007

### daveb

From Todreas & Kazimi, Nuclear Systems I, Problem 2-3
1. The problem statement, all variables and given/known data

Calculate the minimum critical power ratio for a typical 1000 MWe BWR operating at 100% power using the data in Tables 1 – 2, 1 – 3, and 2 – 3. Assume that:

a) The axial linear power shape can be expressed as

q’(z) = q’(ref)e^(-az/L)sin (az/L)

where a = 1.96. Determine q’(ref) such that q’(max) = 44 kW/m

b) The critical bundle power is 9319 kW

2. Relevant equations

Minimum Critical Power Ratio = Critical Power/Operating Power
(unfortunately, the textbook is sparse in its relevant equations and examples)
3. The attempt at a solution

From the referenced table, the efficiency of a BWR is 32.9%, so the operating power is 3039 MWth.

For q’(z) to be a maximum, e^(-a/L)sin (az/L) must be maximum. This maximum occurs when the derivative with respect to z/L is zero (or at the ends). Solving this, I find z = L*tan^(-1)(pi/a)/pi = 0.322L, and q'(ref) = 4685 kW/m. From here I have no clue what to do (especially with the given critical bundle power).

Last edited: Jan 16, 2007