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# 3-14 - 3-14 In Figure 3.14 we have illustrated a...

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3-14. In Figure 3.14 we have illustrated a cross-sectional view of a barge loaded with stones. The barge has sprung a lead as indicated, and the volumetric flow rate of the leak is given by o leak flow rate ( ) d i C A g h h = Here is a discharge coefficient equal to 0.6, d C o A is the area of the hole through which the water Figure 3.14 Leaking barge is leaking, h is the height of the external water surface above the bottom of the barge, and h is the internal height of the water above the bottom of the barge. The initial conditions for this problem are i I.C. o , 0 , i h h h t = = 0 = and you are asked to determine when the barge will sink. The length of the barge is L and the space available for water inside the barge is HwL ε . Here ε is usually referred to as the void fraction and for this particular load of stones 0.35 ε = . In order to solve this problem you will need to make use of the fact that the buoyancy force acting on the barge is buoyancy force ( ) gh wL = ρ where is the density of water. This buoyancy force is equal and opposite to the gravitational force acting on the barge, and this is given by ρ gravitational force mg = Here m represents the mass of the barge, the stones, and the water that has leaked into the barge.

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3-14 - 3-14 In Figure 3.14 we have illustrated a...

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