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Thoughts to ponder:

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Thoughts to ponder:

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  1. A fluid is a material in which its molecules may move freely over one another. Thus fluids include gases and liquids. Gases are compressible, while liquids are not.Density = m / V = ρ (kg/m3)Pressure = F / A (N / m2 )Pat = 101 kPa = 14.7 lb/in2 = 1 barPg= Gauge Pressure, Pg= P – PatW = mg = ρVg =ρ (Ah)gP = ρ (Ah)g /A = ρgh

  2. Gauge Pressure:For any depth, h, below the surface of a fluid, P = Pat + ρgh can be applied to any two points within a fluid.Dependence of Pressure on Depth:P2 = P1 + ρgh where P2 is below P1.Ex: P1 = Pat + ρgh = 1.0195x105Pa P2 = P1 + ρgh = 1.03x105 Pa

  3. Pascal’s Principle: P = Pat + ρghP = Pat + ΔP + ρgh = (Pat + ρgh) + ΔPAn external pressure applied to an enclosed fluid is transmitted unchanged to every part of the fluid.For a hydraulic lift with pistons of different areas, A1 and A2 at each side:ΔP1 = ΔP2F1 /A1 = F2 /A2 Let d represent the distance a piston rises or falls,A1d1 = A2d2

  4. Buoyancy:As pressure increases with depth, the force exerted on the bottom of a completely submerged object is greater than the force exerted on the top of the object. This greater upward force is what causes a buoyant force acting on an object immersed in a fluid.Archimede’s Principle:An object completely immersed in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object.Fb = ρfluidgV = mfluid g

  5. Archimede’s PrincipleFb = ρfluidgV = mfluidgW = mobject g = ρobjectgVT = Fapparent = W - Fb

  6. Thoughts to ponder: • Your ice cubes in your cold water drink are melting. When completely melted, will the level of your drink increase, remain the same, or decrease? • While floating on an inflatable raft with your friend during the summer in your backyard pool, you friend slips off the raft into the water. Will the water level consequently rise, fall, or remain the same in your pool? • How is a submarine made to sink or surface?

  7. Fluid Flow and Continuity:As the cross sectional area of a pipe decreases, the speed of the fluid flow increases to pass the same volume of fluid.ΔV = A v ΔtΔm1 = ρ1 ΔV1 = ρ1 A1v1ΔtΔm2 = ρ2 ΔV2 = ρ2 A2v2ΔtΔm1 = Δm2ρ1 A1v1Δt = ρ2 A2v2ΔtEquation of Continuity:ρ1 A1v1 = ρ2 A2v2Equation of Continuity for an incompressible fluid:A1v1 = A2v2

  8. Bernoulli’s Equation:

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