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Code Manual for CONTAIN 2.0 - Federation of American Scientists

Code Manual for CONTAIN 2.0 - Federation of American Scientists

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—= dx —<br />

dt F Pq<br />

1<br />

2[pd - ‘w + g PI(I + ~)x] 1/2<br />

[<br />

where F is equal to ~2- 1 + (1-~)2 + IQW.<br />

By defining<br />

the integration <strong>of</strong> Equation (11-18) is carried out in the <strong>for</strong>m<br />

(11-18)<br />

(11-19)<br />

where XOis the initial value <strong>of</strong> x at the beginning <strong>of</strong> the timestep, ~ is the time at the beginning <strong>of</strong><br />

the timestep, Xq is the (non-isobaric) equilibrium position, and tw is the time to attain such an<br />

equilibrium position from the initial position. Note that equilibrium may not be attainable in the ~<br />

present timestep.<br />

There<strong>for</strong>e, the time to attain equilibrium tw from a non-equilibrium position XOis<br />

P ‘1P<br />

tq<br />

Pd-Pw<br />

= 2F<br />

+ gpt(l + p)xo ‘2<br />

-<br />

Pd-Pw<br />

2F<br />

+ gpl(l + fl)xq n<br />

P&32(1 +102 P& 2(1 + P)2 ‘1<br />

At equilibrium ptg Hd + Pd = plg Hw + Pw and there<strong>for</strong>e<br />

Pw - Pd<br />

Xq = (1 + P)Pjg<br />

(1 1-20)<br />

(11-21)<br />

By applying Equation (11-21) to the second term <strong>of</strong> Equation (11-20), the time to attain equilibrium<br />

tq becomes<br />

2F[pd - pW + g Pt(l + b)xO] 112<br />

tq = (1 1-22)<br />

[ P@2(1 + P)z 1<br />

Rev O 11 12 6/30/97

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