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Chapter 9 Floating and Flow

Chapter 9 Floating and Flow. Archimedes’ Principle Floating Objects 300,000 ton metal ship floats while a 0.1 g pebble sinks Not weight, but density that matters Archimedes’ Principle Density = mass/volume

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Chapter 9 Floating and Flow

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  1. Chapter 9 Floating and Flow • Archimedes’ Principle • Floating Objects • 300,000 ton metal ship floats while a 0.1 g pebble sinks • Not weight, but density that matters • Archimedes’ Principle • Density = mass/volume • Mass = (volume)(density), so objects with the same volume can have different masses, depending on how dense they are • Buoyant Force = If you push down on a floating piece of wood, it pushes back • Archimedes’ Principle says buoyant force = weight of fluid displaced by the submerged object • Fluid is more dense (water/wood) Buoyant Force > Weight of Wood • Fluid is less dense (water, lead) Buoyant Force < Weight of Lead • Wood Floats because it is less dense than water • Lead Sinks because it is more dense than water

  2. Source of the Buoyant Force (FB) • Like the atmosphere, pressure is greatest at bottom of a fluid (water) • Larger pressure at the bottom produces a larger upward force than the downward force created by the smaller pressure at the top • Buoyant Force = difference between the top/bottom forces • Average Density • Why does a steel ship float? Steel is more dense than water/ • In complex shapes, you must use the Average Density • The steel ship has many air pockets—density is much less than water • Average density of ship (steel + air) is less than water, so it floats > FB

  3. FB • Analyze Forces on a Sumberged Object • Average Density > Fluid Density • WO > FB • Object sinks • Average Density < Fluid Density • WO < FB • Object Floats • Just enough remains submerged so that Wo = FB • Average Density = Fluid Density • WO = FB • Object will stay submerged • Submarine or a fish • Object can sink or rise slowly by slightly changing its density • Submarine takes in water • Fish change air bladder size W

  4. II. Fluids in Motion • Flowing Water • Continuity of Flow: same amount of water entering and exiting the stream or pipe at all times • Speed of the water increases as the stream/pipenarrows • Volume = L x A (A = W x H) • Rate of water flow = Volume/time = LA/t • Velocity of water flow = v = L/t • Rate of water flow = vA • If Area increases, v must decrease to keep rate of flow the same • If Area decreases, v must increase to keep the rate of flow the same

  5. Viscosity and Flow • Flowing fluids can be thought of as having layers • Viscosity = frictional forces between those layers • Large viscosity = large friction (syrup or motor oil) • Small viscosity = small friction (alcohol or air) • Layers near edges move slower than the layers near the center • Low viscosity: speed reaches maximum quickly • High viscosity: speed reaches maximum only slowly • Viscosity of liquids >> Viscosity of gases • When you raise the Temperature, you lower the Viscosity (motor oil, syrup)

  6. Describing Flowing Fluids • Laminar Flow = layers of the fluid move parellel to each other • Turbulent Flow = layers move in disordered directions • Increases the resistance to flow (try to avoid for engineering ) • Higher velocity leads to more turbulence • Lower viscosity leads to more turbulence • Transition between Laminar and Turbulent Flow is focus of research

  7. Bernoulli’s Principle • Apply Conservation of Energy to Flowing Fluids • If fluid is not compressed, work done on it has to result in increased KE • If KE increases, Velocity must increase = acceleration • Must be a net force to cause an acceleration • Difference in pressure between points in the fluid • Fluid is accelerated from high to low pressure • Higher velocity at low pressure area • Bernoulli’s Principle = Pressure + KE = constant for a fluid • Pressure variance in pipes or hoses • Pressure is lower at constricted areas (v, KE are higher) d = density v = velocity If v2 is fast, KE is large h2 = pressure = low If v1 is slow, KE is small h1 = pressure = high

  8. Narrow nozzle on a hose • Pressure is actually lower at the nozzle than back in the hose • Velocity is higher at nozzle, momentum = mv is greater • Dp = FDt, you feel a stronger force because of velocity, not pressure • Airplane Wing • Larger velocity means lower pressure • Blow air above a strip of paper, the larger pressure below pushes the paper up into the low pressure area above it • Air going over the top of an airplane wing moves faster than the air going below the wing • Pressure above is less than the pressure below: Wing (and plane) lifted up • Suspended Ball • Air speed greatest at center (pressure is smallest) • Larger pressures outside keep ball centered • Upward force of blowing air keep it suspended

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