Physics 1B03summer-Lecture 12 1 Fluid Mechanics Pressure Buoyancy.

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Presentation transcript:

Physics 1B03summer-Lecture 12 1 Fluid Mechanics Pressure Buoyancy

Physics 1B03summer-Lecture 12 2 Buoyancy h P1P1 P2P2 The fluid exerts an upward force on the object equal to the weight of fluid displaced. This force is result of pressure differences in the fluid; the pressure is greater at the bottom than at the top. This is why objects can ‘float’: the magnitude of the buoyant force equals that of the force of gravity: B=F g so: B=mg=ρVg

Physics 1B03summer-Lecture 12 3 Archimedes’s Principle: the magnitude of the buoyant force always equals the weight of the fluid displaced by the object. Totally Submerged Object For a submerged object in fluid with ρ f the upward force is B=ρ f V o g (=weight of fluid displaced) and so the net force is: B - F g = ρ f V o g - ρ o V o g = (ρ f – ρ o )V o g Floating Object For a floating object, it displaces a volume of fluid equal to its own volume, and so: B = F g ρ f V f g = ρ o V o g

Physics 1B03summer-Lecture 12 4 Example A giant ice cube (   917 kg/m 3 ) floats in a pail of cold water. If the cube is mm on each side, how far is the top surface of the ice above the water? When the ice melts, does the level of water in the pail rise or fall?

Physics 1B03summer-Lecture 12 5 Example A 10-kg rock (density 2500 kg/m 3 ) is suspended in a large bucket of water by a cord. What is the tension in the cord? tension = ?

Physics 1B03summer-Lecture 12 6 A large bucket half full of water is placed on a scale; the scale reads 500 N. A 10-kg rock (density 2500 kg/m 3 ) is lowered into the bucket by a cord. When the rock is completely underwater, but not touching the sides or bottom of the bucket, what does the scale supporting the bucket read? 500 N??? N

Physics 1B03summer-Lecture 12 7 A boat filled with bricks floats in a swimming pool. If the bricks are dumped overboard does the water level in the pool rise, or fall? ?

Physics 1B03summer-Lecture 12 8 How heavy a balloon can 100 litres of helium lift? Hydrogen has half the density of helium. How heavy a balloon can be lifted by 100 litres of hydrogen?