A submarine submerges by admitting seawater (S = 1.03)into its ballast tanks. The amount

Chapter 2, Problem 2.11

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A submarine submerges by admitting seawater (S = 1.03)into its ballast tanks. The amount of water admitted is controlledby air pressure, because seawater will cease to flow into the tankwhen the internal pressure (at the hull penetration) is equal to thehydrostatic pressure at the depth of the submarine. Consider a ballasttank, which can be modeled as a vertical half-cylinder (R = 8 ft,L = 20 ft) for which the air pressure control valve has failed shut.The failure occurred at the beginning of a dive from 60 ft to 1000 ft.The tank was initially filled with seawater to a depth of 2 ft andthe air was at a temperature of 40 F. As the weight of water in thetank is important in maintaining the boats attitude, determine theweight of water in the tank as a function of depth during the dive.You may assume that tank internal pressure is always in equilibriumwith the oceans hydrostatic pressure and that the inlet pipe tothe tank is at the bottom of the tank and penetrates the hull at thedepth of the submarine.