# Since this logarithmic function fits data for many different flow rates, we

want to investigate if there is a systematic relationship for the spacing between

these curves. Taking one velocity from the plot in figure 8, we can make a plot of

force vs. the gas flow rate. This gives us a plot (figure 9) that diverges to a certain

critical gas flow rate. Using the velocity of 0.038 m/sec, the plot (seen in figure

9) reaches a critical flow rate of 78. This plot gives us an equation, (W) = 2.3

# ((W-Wcrit)/Wcrit) ^{–1}, where W is the gas flow rate and Wcrit is the critical gas

flow rate. This approach was inspired by similarities of figure 10 to that of heat

capacity near a second order phase transition. The critical flow rate of 78 is close

to the point where we measured the sand to become a solid in figure 6. By

looking at this plot (figure 10), it shows how well the sand becomes fluidized with

different gas flows. The line seems to be a phase transition line where to the left

of this line it is a solid and to the right it is a liquid.

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## Gas Flow

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