In gas--solid fluidization, it is frequently common to have a wide size distribution of particles present in the system. During fluidization the smaller particles can be entrained from the fluidization column. Sometimes it is useful to know the maximum particle size that could be elutriated from the system. In order to do this the equation for the terminal velocity will be used as shown below.

u_{t} is the terminal velocity (m/s)

d_{p} is the particle diameter (m)

ρ_{p} is the particle density (kg/m^{3})

ρ_{f} is the fluid density (kg/m^{3})

g is the gravitational constant (9.81 m/s^{2})

C_{D} is the drag coefficient.

According to Haider and Levenspiel (1989) a single correlation for the drag coefficient for all flow regimes and non--spherical particles is described as follows.

**Task**

The task for this assignment is to resolve for the particle diameter (dP), in µm, at different terminal gas velocities (ut) between 0 and 1 m/s. The solution should be robust and flexible enough that different parameters (e.g. particle density, sphericity) could be easily modified and a new solution is automatically evaluated. The root finding method could also be able to be easily adapted to handle different nonlinear problems.

For this problem the subsequent parameters will be used.

ρ_{p} 950 kg/m^{3}

Φ 0.77

ρ_{f } 1.184

µ 1.85×10--5 kg/m^{3} kg/m•s

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