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Dimensional-and-Model-Analysis

1. A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at base is 1.5 cm long and of specific gravity=6.5. The or part of cylinder is made of material having specific gravity 0.75. State, if it can float vertically in water.


Hint Answer

2. In manometer given above, 2 immiscible fluids mercury (ρ = 13600 kg/m3) and water (ρ = 1000 kg/m3) are used as manometric fluids. The water end is exposed to atmosphere (100 kPa ) and mercury end is exposed to a gas. At this position, interface between fluids is at bottom most point of manometer. Ignore width of manometer tube and radius of curvature. The value of h is found to be 9.45 m. The height of mercury column is given to be 75 cm. Find gauge pressure of gas. (g = 9.8 m/s2)
In manometer given above, 2 immiscible fluids mercury (ρ = 13600 kg/m3) and water (ρ = 1000 kg/m3) are used as manometric fluids. The water end is exposed to atmosphere (100 kPa ) and mercury end is exposed to a gas. At this position, interface between fluids is at bottom most point of manometer. Ignore width of manometer tube and radius of curvature. The value of h is found to be 9.45 m. The height of mercury column is given to be 75 cm. Find gauge pressure of gas. (g = 9.8 m/s2)\r\n \r\n


Hint Answer

3. A block of material of specific gravity 0.45 floats in water. Determine meta-centric height of block if its size is 3 m * 2 m* 0.8 m.


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4. When body is completely or partially immersed in a fluid, how much its weight be distributed for it to be in stable equilibrium.


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5. In unstable equilibrium what is relation between forces?


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6. Find density of metallic body which floats at 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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7. Find 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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8. Meta centre always lies below centre of gravity


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9. In a U-tube manometer, one end is open to atmosphere, or end attached to a pressurized gas of gauge pressure 40 kPa. The height of fluid column in atmospheric side is 60 cm, and that on gas side is 30 cm. The manometic fluid used is: (Take g = 9.8 m/s2).


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10. What happens to buoyant force acting on airship as it rises in air?


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This Chapter Dimensional-and-Model-Analysis consists of the following topics

Buoyancy and Floatation

A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at base is 1.5 cm long and of specific gravity=6.5. The or part of cylinder is made of material having specific gravity 0.75. State, if it can float vertically in water.

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In manometer given above, 2 immiscible fluids mercury (ρ = 13600 kg/m3) and water (ρ = 1000 kg/m3) are used as manometric fluids. The water end is exposed to atmosphere (100 kPa ) and mercury end is exposed to a gas. At this position, interface between fluids is at bottom most point of manometer. Ignore width of manometer tube and radius of curvature. The value of h is found to be 9.45 m. The height of mercury column is given to be 75 cm. Find gauge pressure of gas. (g = 9.8 m/s2)
In manometer given above, 2 immiscible fluids mercury (ρ = 13600 kg/m3) and water (ρ = 1000 kg/m3) are used as manometric fluids. The water end is exposed to atmosphere (100 kPa ) and mercury end is exposed to a gas. At this position, interface between fluids is at bottom most point of manometer. Ignore width of manometer tube and radius of curvature. The value of h is found to be 9.45 m. The height of mercury column is given to be 75 cm. Find gauge pressure of gas. (g = 9.8 m/s2)\r\n \r\n

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A block of material of specific gravity 0.45 floats in water. Determine meta-centric height of block if its size is 3 m * 2 m* 0.8 m.

;

When body is completely or partially immersed in a fluid, how much its weight be distributed for it to be in stable equilibrium.

;

In unstable equilibrium what is relation between forces?

;

Find density of metallic body which floats at 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.

;

Find 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.

;

Meta centre always lies below centre of gravity

;

In a U-tube manometer, one end is open to atmosphere, or end attached to a pressurized gas of gauge pressure 40 kPa. The height of fluid column in atmospheric side is 60 cm, and that on gas side is 30 cm. The manometic fluid used is: (Take g = 9.8 m/s2).

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What happens to buoyant force acting on airship as it rises in air?

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