Use the Ergun$$s equation and a force balance to derive the following dimensionless form

of the equation used to define the minimum fluidization Reynold$$s number$\frac{1\mathrm{.}75}{{}_{mf}^3}(\frac{d_p{u}_{mf}{}_g}{})+\frac{150(1-{}_{mf})}{{}_{mf}^3}(\frac{d_p{u}_{mf}{}_g}{})=\frac{d_p^3{}_g(|{}_s-{}_g|)g}{{}^2}$