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3.2 Pressure Flow RatesVoid fraction, also known as porosity, is calculated by using total volume of a substance and the volume taken by either gas or liquid between the solid particles. The void fraction varies depending on material, shape and size of particles, where nearly spherical particles would lead to a void fraction in the range of 0.40-0.45 [Sub14]19. To simplify calculations and fluidisation, nearly spherical particles are easier to evaluate theoretically, so sand with void fraction within this range would be favoured. Referring back to Ergun equation (2-5) in section 2.2 for fluidised bed, the change in pressure may be considered for this project to see how it is affected by the void fraction and help deciding on sand grain size. Since nearly spherical sand grains are preferred, this was considered for surface area – volume ratio, which is 1 for a perfect sphere. The change of pressure depending on void fraction was plotted for various sand grain sizes seen in Graph 2 and Graph 3 where the surface area - volume ratio is first assumed to be 0.83 and then 0.6 for comparison. 0.83 was chosen from [McC93]14 since it is the sphericity of rounded sand. The calculations are found in Appendix C. It may also be seen in Appendix C that the first part of the Ergun equation, which is in terms of viscosity, is the dominant part of the final pressure flow rate. 
Graph 2 Change of pressure for surface area - volume ratio=0.83 
Graph 3 Change of pressure for surface area - volume ratio=0.6 It was clear, especially for particle size of 0.05 mm, that the change on surface area - volume ratio has a big impact on the change in pressure. The values are nearly doubled at void fraction of 0.4 when the ratio is 0.6. The larger diameters result in more constant pressure flow rates. This makes these grain sizes better for the experiments if it is difficult to get a precise value for the void fraction. Superficial velocity was however calculated from assuming maximum possible cross-sectional area of fluidisation, so the entire cross-section of the water butt and the flow rate directly from the water tap. This was due to difficulty of knowing these exact numbers and therefore the maximum possible values had to be used. Note that superficial velocity is the hypothetical fluid velocity assuming there is only one flowing phase in the cross-sectional area.
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