Question 8.9: Repeat problem [8] in the absence of the reflector...

Part a. From Eq. (8.3) we may write

V=F_{q}P/P_{\mathrm{max}}^{\prime\prime \prime}

and with a height to diameter ratio of one  V = 2πR³. For a bare cylindrical F_{q}=3.63 (see Eq. (7.30)) From the above equation we may write

R^{3}=\frac{P}{2\pi P_{\operatorname*{max}}^{\prime\prime \prime}}\,F_{q}=\frac{2000\cdot10^{6}}{2\pi450}3.63=2.57

The radius is​

R = 1.37 m

The core volume is

V=2\pi R^{3}=16.1\,\mathrm{m}^{3}

1=\frac{ k_{\infty}}{1+M^{2}B^{2}}

k_{∞}=1+M^{2}B^{2}=1+M^{2}33.0\ /D^{2}=1+0.18^{2}\cdot33.0\ /(2\cdot1.37)^{2}

k_{∞}=1.142

Part b. The earlier equation becomes

R^{3}=\frac{P}{2\pi P_{\mathrm{max}}^{\prime\prime \prime}\cdot\left(0.90\right)}F_{q}=\frac{1}{0.90}2.57=2.86

The radius is

R = 1.42 m

% change = 100(1.42-1.37)/1.37= 3.65 %

The core volume is

V=2\pi R^{3}=18.0\,\mathrm{m}^{3}

% change = 100(18.0-16.1)/16.1= 11.8 %

k_{\infty}=1+M^{2}B^{2}=1+M^{2}33.0\ /D^{2}=1+0.18^{2}\cdot33.0\ /(2\cdot1.42)^{2}

k_{\infty}= 1.133

% change = 100(1.133-1.142)/1.142= -0.79 %