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Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

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INTERNAL RADIATION SAFETY 629<br />

a = cost per unit electricity,<br />

b = units electricity used <strong>to</strong> move a unit volume of air in the ventilation<br />

system, and<br />

xi = installation cost of the ventilation system.<br />

The <strong>to</strong>tal cost U is<br />

U = x + y (11.30)<br />

U = abfTQ + xi + αNfTF G<br />

.<br />

Q<br />

(11.31)<br />

The optimum ventilation rate Q0 is the value of Q when U is minimized by setting<br />

dU/dQ = 0:<br />

dU<br />

dQ<br />

Q0 =<br />

1<br />

= abfT − αNfTFG × = 0,<br />

Q2 (11.32)<br />

<br />

αNFG<br />

.<br />

ab<br />

(11.33)<br />

If QL is the ventilation rate needed <strong>to</strong> meet a design criterion, such as the DAC,<br />

then the multiplying fac<strong>to</strong>r for increasing the ventilation rate needed <strong>to</strong> achieve the<br />

optimum rate is<br />

But<br />

r = Q0<br />

. (11.34)<br />

QL<br />

QL = G<br />

C<br />

G<br />

= . (11.35)<br />

DAC<br />

Substituting Eqs. (11.33) and (11.35) in<strong>to</strong> Eq. (11.34), we get<br />

<br />

αNFG<br />

ab<br />

r =<br />

G<br />

DAC<br />

<br />

αNF<br />

ab<br />

= √<br />

G<br />

√<br />

G<br />

× √G × DAC (11.36)<br />

<br />

αNF<br />

r = × DAC.<br />

abG<br />

(11.37)<br />

W Example 11.10<br />

For the radiopharmaceutical labora<strong>to</strong>ry in Example 11.9, determine the optimum<br />

ventilation rate if

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