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Appendix HCalculating factor of safety for water butt Details of notations on page 51 For thin-walled cylinder, hoop stress is:  (H-1) [Eng142]25
We know that: Assuming the water butt will be filled ¾ up with sand, volume by sand in water butt is: 
 (H-3)
Calculating mass of the sand in the water butt knowing the density of dry sand=1602 kg/m3 [Eng14]26: 
 = Volume of sand (m3)
Density of the dry sand is different to the density of wet sand, since the gaps between the sand grains are either filled with air or water, changing the density. Calculating actual volume of the sand grains alone lets us find out the volume between grains. Density of silica/silicon dioxide without space in-between is 2600 kg/m3[Kol09]27. Mass of air between sand particles is assumed negligible compared to mass of sand. Mas of dry sand may therefore be used to find volume occupied by sand grains alone.  (H-5)
Volume of voids between sand grains is therefore volume of sand crystals subtracted from total volume of dry sand: 
 is the volume filled with water during the experiments. Density of water from the tap is assumed to be 998 kg/m3 [Eng141]28. As earlier, calculating the mass from density and volume:
Density of the sand and water mixture filling three quarters of the water butt is therefore: 
Therefore: 
 
For worst-case scenario, water may be filled up to the top. Occurs if the anchor leg and the water outlet fail. The mass of the water will be the mass of water between the sand grains and the mass of the extra water filling the remaining quarter of the water butt. 
Density of water and sand mixture when the container is completely filled is then: 
H is the total height of the water butt, which is 0.915 m 
Tensile strength of HDPE is 32 MPa [Azo14]29. For worst-case scenario, factor of safety is: 
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(H-2) 
(H-4)
(H-6)
(H-7) 
(H-8) 
(H-8)