• # question_answer Which of the following is not a dimensionless group? A) $\frac{\Delta \,p}{\rho \,{{N}^{2}}{{D}^{2}}}$                     B) $\frac{g\,H}{{{N}^{2}}\,{{D}^{2}}}$C) $\frac{\rho \,\omega \,{{D}^{2}}}{\mu }$                    D) $\frac{\Delta \,p}{\rho \,{{V}^{3}}}$

Solution :

$\frac{\Delta p}{p{{v}^{3}}}=\frac{m{{L}^{-1}}{{T}^{-2}}}{[M{{L}^{-3}}]\,[L{{T}^{-1}}]}={{M}^{1-1}}\,{{L}^{-1+3+3}}{{T}^{-2+3}}$$={{L}^{-1}}T,$ Which is non-dimensional

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