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Fluids Mechanics Carlos Silva December 2 nd 2009

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Why is this possible? Hot air ballon Plane (flying or buoying)

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Fluid Mechanics Study of how fluids move and the forces on them Fluids A fluid is a collection of molecules that are randomly arranged and held together by weak cohesive forces and by forces exerted by the walls of a container. liquids, gases, and plasmas (ionized gas) Fluids statics fluids at rest Fluids dynamics fluids in motion The golden crown Archimedes

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FLUIDS STATICS

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Pressure Fluids do not sustain shearing or tensile stresses like solids they only hold compression stresses from all sides Forces applied by static fluids always perpendicular to objects surface (area) depending on the area (surface) of the object, the force is applied in different ways Pressure force applied to a surface area Pressure is a scalar, not a vector

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Pressure varies with Depth Divers know that… pressure increases with depth In Planes… pressure decreases with height (pressurized cabins) Why? Density: mass by unit of volume (volume/mass) Incompressible fluid: the density is the uniform throughout the liquid

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Pascal Law From the previous… the pressure is the same at all points having the same depth, independent of the shape of the container any increase in pressure at the surface must be transmitted to every other point in the fluid A change in the pressure applied to a fluid is transmitted undiminished to every point of the fluid and to the walls of the container.

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Pressure Measurements Barometer Mercury Aneroid Piezometer Pitot tube sphygmomanometer

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Buoyancy force upward force that keeps things afloat is equal to the magnitude of the weight of fluid displaced by the body Archimedes principle the magnitude of the buoyancy force always equals the weight of the fluid displaced by the object. M is the mass of the displaced fluid and not the mass of the object

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Examples Totally submerged object if the density of the object is higher than the density of the liquid, the object will sink If the density of the object is lower, the object will rise Object floating the fraction of the volume of a floating object that is below the fluid surface is equal to the ratio of the density of the object to that of the fluid

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FLUIDS DYNAMICS

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Laminar and turbulent flow A flow in motion can be laminar or steady – each particle follows a smooth path velocity of fluid particles passing any point remains constant in time turbulent - turbulent flow is irregular flow characterized by small whirlpool-like regions occurs above a certain speed

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Equation of continuity of fluids the product of the area and the fluid speed at all points along a pipe is constant for an incompressible fluid

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Bernoulli principle An increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid´s potential energy

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Torricelli law for an open tank, the speed of liquid coming out through a hole a distance h below the surface is equal to that acquired by an object falling freely through a vertical distance h.

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Nozzle Device designed to control the direction or characteristics of a fluid flow as it exists (or enters) an enclosed chamber jet engine rocket engines Laval nozzle

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Aerodynamics The pressure above the wing is smaller 3 rd Newton law Bernoulli effect

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