Fluidized beds, in which a fluid flows through a matrix of particles, are used for a variety of purposes such as enhancing chemical re combustion, or freezing of a material. The pressure drop $\backslash (\backslash$Delta p $\backslash )$ for the fluid flowing through the bed depends on the diameter of the $\backslash ($ D $\backslash ),$ the flow length of the bed $\backslash ($ l $\backslash ),$ and the velocity $\backslash ($ V $\backslash ),$ density $\backslash (\backslash$rho $\backslash ),$ and viscosity $\backslash (\backslash$mu $\backslash )$ of the fluid. Use the fluid velocity, the fluid density, and length of the bed as repeating variables to develop a suitable set of pi terms for this problem. The first dimensionless group should the pressure drop, the second dimensionless group should contain the diameter of the particles and the third dimensionless group contain viscosity of the fluid.

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

$\backslash$Pi$\_\{1\}=\backslash \backslash$

$\backslash$Pi$\_\{2\}=\backslash \backslash$

$\backslash$Pi$\_\{3\}=$

$\backslash$end$\{$array$\}$

$\backslash ]$