Hydrostatics: Fluids at Rest. applying Newtonian principles to fluids hydrostatics—the study...

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Transcript of Hydrostatics: Fluids at Rest. applying Newtonian principles to fluids hydrostatics—the study...

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Hydrostatics: Fluids at Restapplying Newtonian principles to fluidshydrostaticsthe study of stationary fluids in which all forces are in equilibriumFluid Mechanicshydrodynamicsthe study of fluids in motionFluid Mechanicsabbreviation: mass per unit volumeg/cm is commonly usedSI unit: kg/mDensityspecific gravity: density relative to waterdimensionless numbernumerically equal to the density of the substance in g/cmDensityPressure is defined as the force exerted perpendicular to a unit area.When a fluid is at rest, the pressure is uniform throughout the fluid in all directions.Units of PressureAt the boundaries of a fluid, the container exerts a pressure on the fluid identical to the pressure the fluid exerts on the container.Units of PressureSI unit: Pascal (Pa)Earliest: atmosphere (atm)1 atm = 1.013 105 Patorrbars and millibars (mb)1 atm = 1.013 bar = 1013 mbUnits of Pressuregauge pressure (Pg) often used with piping systemsabsolute pressure (P)Units of Pressurepressure changes with depthdensity is usually assumed to be constant throughout depthy = d2 = d1 + dF = 0 NIncompressible FluidsFy = Fd1 + Fd2 + Fw = 0 Nto calculate the pressure at any depth d:Incompressible FluidsPd = Pref + gdIncompressible Fluidsd is expressed as a negative scalar distanceg = -9.81 m/sPref is atmospheric pressure if the liquids container is open to the atmospherePd = Pref + gdusually referring to gases, since their density is not constant with height/depthCompressible FluidsP = Pref ePrefref- |g|hmust remember that temperature also affects the pressure of a gasCompressible FluidsPascals principle: the external pressure applied to a completely enclosed incompressible fluid is distributed in all directions throughout the fluidHydraulic Devicesmachines that transmit forces via enclosed liquidssmall input forces can generate large output forcesHydraulic Devicesnote the cross-sectional areas of eachFout = nFinHydraulic Devices

note the distance each piston travelsHydraulic Devices

manometerbarometerfirst instrument to accurately measure atmospheric pressureused mercuryPressure Indicatorsfamous problem: Archimedes and the crownWhat happens when an object is placed in a fluid?Buoyancyfor object in fluid:Fw-o: gravitational force on object in fluidFb: buoyant force on objectFb = |g|VBuoyancyFb = |g|V is the density of the displaced fluidBuoyancyArchimedes principle: any system that is submerged or floats in a fluid is acted on by an upward buoyant force equal in magnitude to the weight of the fluid it displacesBuoyancyIf the buoyant force is equal to the systems weight, the forces are balanced and no acceleration occurs.requires object and fluid to have equal densityBuoyancyIf the weight of a system is greater than that of the displaced fluid, its density is greater than the fluids. Since weight exceeds the buoyant force, the object will sink.BuoyancyIf the weight of a system is less than that of the displaced fluid, its density is less than the fluids. Since buoyant force is greater than weight, the object will accelerate up.BuoyancyWhen the object rises to the surface of the liquid, its volume remaining beneath the surface changes the buoyant force until they are in equilibrium.BuoyancyThis is also true with gases.The density of a gas changes with altitude and temperature.The object may respond to a change in pressure.BuoyancyEvery object submerged in a fluid has both a center of mass and a center of buoyancy.These are the same for objects of uniform density that are completely submerged.Center of Buoyancydefined: the center of mass of the fluid that would occupy the submerged space that the object occupiesCenter of BuoyancyIf the center of mass and center of buoyancy are not the same, the object will experience a torque and rotate.The center of buoyancy will be directly above the center of gravity.Center of Buoyancyinstrument used to measure densityhas many uses HydrometerHydrodynamics: Fluids in Motionassumptions:the fluid flows smoothlythe velocity of the fluid does not change with time at a fixed location in the fluid pathIdeal Fluidsassumptions:the density of the fluid is constant (incompressible)friction has no effect on fluid flowIdeal FluidsStreamlinesnot a physical realitylaminarturbulentflow tubeIdeal FluidsThe rate of volume and mass flow into a segment of a flow tube equals the rate of volume and mass flow out of the flow tube segment.Ideal Fluidsequation of flow continuity:Flow ContinuityA1v1 = A2v2 requires tubes with smaller cross-sectional areas to have higher fluid velocitiesbackground equations:Bernoullis PrincipleK = Vv22 Vv12 U = V|g|h2 V|g|h1 Equation 17.12Equation 17.13background equations:Bernoullis PrincipleWncf = K + UWncf = P1V P2VEquation 17.14Equation 17.15Bernoullis Equation:Bernoullis PrincipleP1 + v12 + |g|h1 =P2 + v22 + |g|h2if the velocity does not change: v1 = v2 Bernoullis PrincipleP1 + v12 + |g|h1 =P2 + v22 + |g|h2P1 + |g|h1 = P2 + |g|h2 if the elevation of the fluid does not change: h1 = h2 Bernoullis PrincipleP1 + v12 + |g|h1 =P2 + v22 + |g|h2P1 + v12 = P2 + v22 A faster-flowing fluid will have streamlines that are closer together.A lower-pressure fluid will have streamlines that are closer together.Bernoullis Principleairfoil: any device that generates lift as air flows along its surfacehydrofoil: object that creates lift in liquidLiftBernoulli principleConad effectTheories of Liftviscosity: a measure of the resistance of fluid to a flowcaused by cohesive forces between particles of a fluida type of internal frictioncoefficient of viscosity ()Real Fluidslower coefficients of viscosity indicate that the fluids flow more easilyviscosity is sometimes referred to as the thickness of a fluidReal Fluidsparticles closest to the walls move more slowly than those farther from the wallsReal Fluids