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(6.43)

Its determinant is

$|R|=|\begin{array}{rrrrr}2& 1& -1& 0& -3\\ 1& 1& 0& 0& 0\\ -2& -3& -2& 0& 0\\ -1& -1& 0& 1& 0\\ 0& 0& 0& 0& 1\end{array}|=-2$ (6.44)

(6.44)

Thus the Rank of this Dimension matrix is 5. The number of dimensionless parameters is

${N}_{\mathrm{P}}={N}_{\mathrm{Var}}–R=19–5=14$ (6.45)

(6.45)

Table 6.3

Dimension Table for First-Order, Homogenous Batch Reaction With Agitation

 Variable V ASurf D B Δt kS ω P E/R ΔTWF CF μ h ρ CP k CSΔHR TS CS Dimension L 3 2 1 1 0 0 0 2 0 0 −3 −1 0 −3 2 1 −1 0 −3 M 0 0 0 0 0 0 0 1 0 0 0 1 1

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