A submarine has a total mass of 2.10 106 kg, including crew and equipment. The v

Question

A submarine has a total mass of 2.10 106 kg, including crew and equipment. The vessel consists of two parts, the pressure hull, which has a volume of 1.90 103 m3, and the ballast tanks, which have a volume of 5.15 102 m3. When the boat cruises on the surface, the ballast tanks are filled with air at atmospheric pressure; to cruise below the surface, seawater must be admitted into the tanks. (Neglect the mass of air in the tanks and use 1.025 as the specific gravity of seawater.) (a) What fraction of the submarine's volume is above the water surface when the tanks are filled with air? Answer- 15.2 % (b) How much water must be admitted into the tanks to give the submarine neutral buoyancy? Answer- 366 m3

Explanation / Answer

a) Buoyant Force = Weight of liquid displaced

2.10 *10^6*9.8 = (1.025*1000)*9.8*V

V= 2.10 *10^6*9.8/ (1025*9.8) = 2049 m^3

% immersed = 2049*100/[1900+515] = 84.8 %

volume above water surface = 100-84.8 = 15.2 %

b) volume added = Total volume - volume displaced

                           = [1900+515] - 2049 = 366 m^3

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