Scaling Chemical Processes

(6.43)

Its determinant is

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