August 2014 Mission Statement Background
Discussion 5.1 Comments on the Experiments
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- 5.2 Further Calculations from Experiment Results
- 5.2.2 Creating Boundary Conditions for the Real-Life Model
- 5.2.3 Stokes Law
5. Discussion5.1 Comments on the ExperimentsThe results indicate that the concept for the sand anchor works. The seabed was able to be fluidised by the use of water jets and enable the anchor leg to embed itself. Furthermore, pulling a vacuum created a strong grip in relation to the model. The gripping force had a general pattern of increasing until 20 minutes of pulling a partial vacuum and then decline slightly to finally become more constant. This suggests that the anchor at sea would after some time have a constant gripping force. With highest force achieved at approximately 391 N and lowest at 124 N, the forces varied but remained high in comparison to the model. It is clear from Graph 2 that for every test carried out, the force curve for one hour decreased slightly. This may be due to smaller sand particles getting through the filter and gradually blocking the hose-system more every experiment. This assumption is due to noticing that the water appeared cleaner for every new test, suggesting less small particles floating in the water. The flow rates from the experiments were very high, and lower flow is preferred for the real-life model. However, over time, the anchor would gradually get seaweed, plankton and other fine sediment, blocking holes, which would help reducing the water flow. It was seen from Graph 6 that including a plastic sheet to force the pressure of the water to spread out changed the suction flow rates. They became more constant in relation to test 3 and on average reduced slightly compared to test 2. However, increasing the amount of holes led to relatively constant, but higher, suction flow rates. The friction tests suggested a minimum friction coefficient of roughly 0.4, which was the reading for inside of the anchor leg for dry silica sand. Although the lower coefficients were expected to be outside the anchor leg due to shape, the finger nail scratching investigation explained in 4.2.3 informs why this was not the case due to surface smoothness. Another important observation was that the anchor leg sucked water too fast during the 10 minute testing for Test 2, leading to air getting into the system. This was both evident in the water butt, where there was too little water, and in the collecting beaker where very large air bubbles started appearing. This is likely the cause of the ‘dip’ seen in Graph 4 for Test 2. The air in the system had a negative impact on the gripping force since the partial vacuum reduced. 5.2 Further Calculations from Experiment Results5.2.1 Size Related ForceThe force on the anchor leg model could be calculated by using the equation:  (5-1)
Through derivation of this equation found in Appendix K, the force on the anchor leg while pulling a vacuum could be defined as:  (5-2)
Using the equation for the 0.74 m long, 0.056 m diameter model leg, the maximum possible gripping force was 10.4 kN for wet sand friction coefficient and 8.1 kN for dry sand friction coefficient. These values are high but the assumption is that there is a perfect vacuum, hence 0 Pa for absolute vacuum pressure. The anchor leg would realistically be in partial vacuum; hence the force would be lower. Force depending on scaling must also be considered as mentioned in section 2.3.3, where for a model being the inverse of a scale, force is found by cube of the scale. By evaluating equation (5-2), this is seen to be true since height H is scale to the power of one, and  resulting in the anchor leg’s surface area is the square of the scale. The model anchor leg is roughly one hundredth of scale; therefore if the gripping force were 164 N as found in test 4, then the full-scaled anchor leg would hold 164 MN. Calculations found on Appendix K.
5.2.2 Creating Boundary Conditions for the Real-Life ModelFrom the slamming tests carried out in [Wav78]18, it was found that the maximum force was roughly 1 MN per metre of the device. Therefore, a 5 m long anchor leg, for example, would at most experience 5 MN force. This is significantly lower than the 100-year Atlantic wave of 40 MN, which must be considered when choosing both size of anchor and its concrete grade. One of the main requirements of the anchor legs of the final design is that they would be able to float when filled with air. For a cylinder to float, then the following equation must be satisfied:  (5-3) [Edi78]30
For concrete, specific gravity is 2.4, giving a wall thickness to be 0.12 of the outer diameter to enable floating [Edi78]30. See Appendix L for details. For a 40 MN force produced by a 100-year Atlantic wave, the outer diameter should be at roughly 3 m minimum. This is assuming grade 55 MPa concrete used, post-tensioned to 20% and that the cylinder is buoyant. Calculations found in Appendix L. Furthermore, the depth of seabed will roughly be 40 m where the desalination device will be anchored. Therefore, a length of approximately 12 m would be good for the anchor legs. This is considering practical issues with towing and handling it, which will be easier if it does not touch the seabed before embedment. 5.2.3 Stokes LawThe sand particles may be investigated further to see what velocity they move in naturally in the water. This is achieved using Stokes law, which mathematically describes the force for a spherical particle to move through a fluid and is as follows:  (5-4) [Tem53]31
It has already been established that the Kiln sand has nearly spherical particles. Equation (5-4) may therefore be used, assuming they are spheres. From drawing a free body diagram of the sphere in water, an equation for the velocity of the particle in water was derived: With Kiln sand diameter being max 0.5 mm and silica crystal density 2600 kg/m3, the velocity becomes 0.218 m/s when the particle is in water. This leads to a Reynolds number of about 109 referred to diameter [Sch79]32. See details of these calculations in Appendix M. As H. Schlichting shows in his graph for drag coefficient for spheres as a function of Reynolds number, 109 suggest a drag coefficient of 1 as seen in Graph 8. This is quite a high Reynolds number, but since the sand particles are nearly spherical, the drag coefficient would not be 1. In reality, Reynolds number may be lower. 
Graph 8 Drag coefficient of sphere depending on Reynolds number from [Sch79]32 Directory: shs shs -> Stonelaw Mathematics Department Green Course Revision Sheets Block E shs -> Core Classes Offered by Department Indicates ncaa clearinghouse Approved Core Class english shs -> Identify the prepositional phrases in the following sentences. Write them on a separate piece of paper shs -> Smart Phone Class Security and Safety shs -> Bordon Luciano shs -> 1 Week before Scheduled Contact shs -> Informative Research Essay Assignment shs -> 10th Daily “Fix It” Sentences shs -> The story of Perseus as told by Diodorus Download 11.38 Mb. Share with your friends:
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