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Buoyancy

Learn about atmospheric pressure measurement with barometers, Pascal's Law, Archimedes' Principle, and how objects sink or rise in fluids due to buoyant force. Also discover the concept of the Center of Buoyancy and stability in fluid dynamics.

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Buoyancy

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  1. Buoyancy

  2. Barometer • Atmospheric pressure can be measured by balancing weight pressure against air pressure. • A device that uses this is a barometer. This barometer uses the weight of a column of liquid mercury. The meter measures the height in inches (or mm). 1 atm = 29.92 inHg 1 atm = 760 mmHg

  3. Manometer • A manometer compares two different pressures. • Gas compared to air (tire gauge) • Liquid compared to air Gauge pressure is defined as the pressure minus atmospheric pressure.

  4. Pascal’s Law • A change in pressure in a fluid is transmitted to all parts of the fluid equally. Equal pressures, different forces

  5. Fluid Volume • Within a fluid, any volume is at equilibrium. • The pressure force on the sides of the volume balances the weight. Fg = -mg

  6. Buoyant Force • The force remains even without the original fluid. • It must balance the weight that would have been there. • This is the buoyant force. • Equals the fluid weight • Directed upward • Acts on the volume Fb = mg

  7. Sinking and Rising • An object in a fluid displaces a volume that had some mass. • If the object is heavier than the fluid it sinks. • If the object is lighter it rises. Fb = rVg Fb = rVg W= mg W= mg

  8. Archimedes’ Principle • An object suspended in a fluid has less apparent weight due to buoyancy. FT = mg - rVg Fb = rVg W= mg

  9. An iceberg has an average density of 86% of seawater. What fraction of the iceberg is underwater? The buoyant force is the weight of water displaced by the iceberg: Fb = rwaterVsubg. The weight is the total weight of the ice: Wi = riceViceg. Find the ratio of Vsub/Vice We know the ratio rice/rwater rwaterVsubg = riceViceg Vsub/Vice = rice/rwater = 0.86 Iceberg

  10. Center of Buoyancy • The force of buoyancy acts at the center of mass of the missing fluid. • The displacing object has a center of gravity at its center of mass. • The two forces may not act at the same point.

  11. Tippy Canoe • If a forces on an object act at different points there is a torque. • Buoyant force above the center of mass is stable. • The torque moves it back to the center • Buoyant force below the center of mass is unstable. • The torque moves it away from the center

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