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PHYS16 – Lecture 31 Ch. 14 Fluid Mechanics

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This Week Fluid Statics – Pressure and Pascal’s Principle – Buoyant Force and Archimedes’ Principle Fluid Dynamics – Equation of Continuity – Bernoulli’s Equation

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Fluids pre-question Salt water has a greater density than freshwater. A boat floats in both freshwater and salt water. The buoyant force on the boat in salt water is _________ that in freshwater. A)Equal to B)Smaller than C)Larger than D)Not enough information

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Fluids pre-question You are in a boat filled with large rocks in the middle of a small pond. You begin to drop the rocks into the water. What happens to the water level of the pond? A)It rises. B)It falls. C)It doesn’t change. D)It rises momentarily and then falls when the rocks hit bottom. E)Not enough information

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Fluid Statics: Pressure

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Pressure Pressure- quantity that relates force per area, force is perpendicular to area – Scalar – Units = Pa = N/m 2 – Atmospheric pressure = 1E5 Pa = 760 torr

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Discussion: Bed of Nails Why would you want to lay on a bed of nails instead of just one nail? Why might it be easier for a 20-kg child to lay on a bed of nails than a slightly larger 60-kg adult?

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Water Pressure – constant density Find the pressure difference across a cube of water Would the pressure change be larger in salt water or fresh water?

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Example: Container Height If I start filling the following container with water, where will the highest water level be? Manoharan Lectures, Harvard University, Fall 2010

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Example: Submarines A submarine is submerged to a depth of 960 m. What air pressure is needed to blow water out of the ballast tanks? (density = 1024 kg/m 3 )

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Air Pressure – Not constant density As height increases pressure decreases and density decreases

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Example Question: Pistons Given that the density of air is proportional to pressure, how does the air pressure inside a confined volume change if the volume decreases by half? Changes by 2…

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Fluid Statics: Buoyant Force

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Archimedes’ Principle Buoyant force = the weight of the water displaced Density water = 1E3 kg/m^3 Density air = 1 kg/m^3

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Discussion: Bathtub physics If the object is floating, is the buoyant force greater than the force of gravity on the object? Is there a buoyant force for a sunken object? Can the buoyant force ever cause an object to go down instead of up?

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Example: Buoyant force on objects 1)Buoyant force on brick in water Volume= 0.2 m X 0.08 m X 0.05 m F B =8 N 2)Buoyant force on ball in water Volume= (4/3)pi(0.025)^2 F B =0.6 N 3)Buoyant force on Diet Coke vs. Coke Volume= same in both cases F B =same Coke sinks more than Diet Coke bec. Coke more dense (F gravity is more for Coke!)

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Main Points Pressure = Force/Area Pressure varies with height – Water – density is constant – Air – density is not constant Buoyant force is equivalent to the weight of the water displaced

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