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Fluidized beds, in which a fluid flows through a matrix of particles, are used for a variety of purposes such as enhancing chemical reactions, 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 particles $\backslash ($ 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 the length of the bed as repeating variables to develop a suitable set of pi terms for this problem. The first dimensionless group should contain the pressure drop, the second dimensionless group should contain the diameter of the particles and the third dimensionless group should 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$\}$

$\backslash ]$

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