In stable equilibrium for completely submerged bodies what is the relation between forces?

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In stable equilibrium for completely submerged bodies what is the relation between forces?

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The floating body is said to be in neutraL equilibrium if the metacentre is above the centre of gravity.

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The floating body is said to be in unstable equilibrium if the metacentre is below the centre of gravity.

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If the magnitude of dimension of a rectangular wooden block is length>breadth>height, then for it to float on the water, it should be immersed in what manner?

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For a completely immersed body, the metacentric height is always zero.

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As a balloon rises in the air its volume increases, at the end it acquires a stable height and cannot rise any further.

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In the manometer given above, 2 immiscible fluids mercury (ρ = 13600 kg/m^3) and water (ρ = 1000 kg/m^3) are used as manometric fluids. The water end is exposed to atmosphere (100 kPa) and the mercury end is exposed to a gas. At this position, the interface between the fluids is at the bottom most point of the manometer. Ignore the width of the manometer tube and the radius of curvature. The value of h is found to be 9.45 m. The height of the mercury column is given to be 75 cm. Find the gauge pressure of the gas. (g = 9.8 m/s^2)

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A rectangular pontoon is 5 m long, 3 m wide and 1.40 m high. The depth of immersion of the pontoon is 0.60 m in seawater. If the centre of gravity is 0.7 m above the bottom of the pontoon, determine the metacentric height. The density for seawater = 1045 kg/m^3.

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Find the position of centre of buoyancy for a wooden block of width 3.5 m and depth 1 m, when it floats horizontally in water. The density of wooden block id 850 kg/m3 and its length 7.0 m.

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Equal volume of two liquids of densities ρ1 and ρ2 are poured into two identical cuboidal beakers. The hydrostatic forces on the respective vertical face of the beakers are F1 and F2 respectively. If ρ1 > ρ2, which one will be the correct relation between F1 and F2?

asked Jan 30, 2022 in Fluid Mechanics by Charlotte (118k points)

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A student wants to find the absolute pressure of water at a point below the surface of water. He has a barometer and a manometer pressure gauge. The barometer reads 1.3152 bar where as the manometer pressure gauge reads 0.3152 bar. What is the absolute pressure? (Assume that pressure at one end of the manometer is atmospheric.)

asked Jan 30, 2022 in Fluid Mechanics by Charlotte (118k points)

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Proper explanation for metacentre is:

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Find the density of metallic body which floats at the interface of mercury of sp.gr 13.6 and water such that 40 % of its volume is sub-merged in mercury and 60% in water.

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In a U-tube mercury manometer, one end is exposed to the atmosphere and the other end is connected to a pressurized gas. The gauge pressure of the gas is found to be 40 kPa. Now, we change the manometric fluid to water. The height difference changes by: (ρmercury = 13600 kg/m^3, ρwater = 1000 kg/m^3).

asked Jan 30, 2022 in Fluid Mechanics by Charlotte (118k points)

In stable equilibrium for completely submerged bodies what is the relation between forces?

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