# Minimum Critical Power Ratio (MCPR) for a BWR

1. Sep 13, 2011

### antony1103

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

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).

2. Sep 13, 2011

### antony1103

I was on the right track and got the answer after a little frustration. Thanks anyway though! I'll have to remember this site when I am having trouble in my NUC E/M E classes this year.

3. Sep 18, 2012

### s14newb

did you ever figure out what to do with the critical bundle power... i know this is an old thread. sorry