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Appendix C


Calculation pressure flow rate

Details of notations on page 51
A perfect sphere has a surface area of

(C-1)


The volume per spherical particle is

(C-2)



This means that surface area – volume ratio for a sphere is 1 because:

A nearly spherical shape is desired, so will be assumed to be 0.83. For this, void fraction will vary from 0.4-0.45. Particle diameters evaluated: 0.05, 0.1, 0.2, 0.3, 0.4 and 0.5 mm.


Ergun equation:

(C-3)

Length of bed assumed to be 0.5 m is approximation of how deep into the sand in the 0.915 m high water butt the anchor leg will fluidise. Density is for the water, 998 kg/m3, and superficial velocity is:

(C-4)

Since the water butt is 0.56 m in diameter, maximum fluidised cross-sectional area is:




Maximum flow rate is the flow rate directly from the water source. Measuring this resulted in a bucket of volume 5.767*10-3 m3 filled in 35 seconds. This gives a maximum flow rate of:


Maximum possible superficial velocity for the experiment would therefore be:

Viscosity is 0.001 Ns/m2 for water in room temperature [Eng143]33, so if void fraction of 0.4 is used, then pressure flow rate for a 0.1mm diameter particle is:





Finding out what part dominates in the Ergun equation:



First part with viscosity:



Second part with density:





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