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  REVIEW IN FLUID MECHANICS FLUID MECHANICS – the branch of applied mechanicsconcerned with the stacs and dynamics – both liquid andgases. The analysis of the behavior of uids is based on thefundamental laws of mechanics which relate connuity of mass and energy with force and momentum together withthe familiar solid mechanics properes. FLUID – any substance that fows  or deforms connuouslywhen subjected to shearing forces.LIQUID – incompressible uid, constant volume, variabledensityGAS – compressible uid, variable volume, variable densityDENSITY – quanty of maer contained in a unit volume of substance.TYPES OF DENSITY:  Mass Density  Specic Weight (Unit Weight)  Relave Density (Specic Gravity) ACCELERATION DUE TO GRAVITY  g = 32.2/s^2 = 9.81m/s^2DENSITY OF WATER AT STANDARD TEMPERATURE   = 1000kg/m^3  NEWTON’S LAW OF VISCOSITY – in a uid, shear strain (φ)increases for as long as shear stress (  ) is applied.Therefore, the uid ows. VISCOSITY – is the property of a uid, due to cohesion andinteracon between molecules, which oers resistance toshear deformaon.  Dynamic viscosity  Kinemac Viscosity FLUID STATICS – study of uids at rest in stable equilibriumHYDROSTATICS – the study of liquids at rest and the forcesexerted on them or by them.PRINCIPLES:  There are no shear stresses  Pressure exists at every point in astac uid  Pressure at a point is same in alldirecons (Pascal’s Law).  Pressure acts normal to allboundary surfaces  Pressure varies with height ordepth.PRESSURE – force applied uniformly over a surfaceCommon units: psi(lb/in^2), psf(lb/^2), Pa(N/m^2)  Atmospheric pressure, Patm – pressure exerted bythe weight of air above us.Patm at sea level = 1 atm = 101.325kPa (14.7psi) = 760mmHg (29.9in Hg) = 10.34m H 2 O (33.91 H 2 O)  Absolute zero – the lower limit of atmosphericpressure or the perfect vacuum  Gauge pressure, Pg = the pressure measuredrelave to atmosphere as datum -Taken posive (+) if measured aboveatmosphere-Taken negave (-) if measured belowatmosphere.  Absolute pressure, Pabs – pressure measuredabove absolute zero, always posive (+)HYDROSTATIC PRESSURE –pressure acted by liquid (gaugepressure) plus any pressure acng on the surface of theliquid  General Idea – weights acts stac liquid thuscreang pressure, assuming weight of air on liquidsurface is zero.  Derivaon   Variaon of Pressure in Stac LiquidsPressure increases with depth, hLATERAL PRESSURE DISTRIBUTIONVERTICAL PRESSURE DISTRIBUTIONPRESSURE ON OTHER SURFACESPRESSURE VARIATION OF DIFFERENT LIQUIDSPressure Head – the vercal height h of any liquid of specic weight,  L , which can be converted to a gaugepressure PEQUIVALENT HEIGHT – height of another liquid which givesthe same amount of pressure as a certain liquidPrinciple: two liquids with dierent heights exert the sameamount of pressure.MANOMETERS – devices used to measure pressureA. PIEZOMETER COLUMN – vercal, open glass tubeB. U TUBE OPEN TYPE – U shaped glass tube, with one legopen to atmosphere, parally lled with liquid of knownproperty called manometer liquidC. U TUBE DIFFERENTIAL TYPE - both legs are exposed todierent pressures thus measuring pressure dierence. HYDROSTATIC FORCE ON PLANE SURFACESHydrostac force is located at center of pressure which isalways at distance “e” below the center of gravity of submerged area, A.HYDROSTATIC FORCE ON CURVED SURFACESThe total hydrostac force, F is the resultant of thehydrostac force from lateral pressure (acng on vercalsurface) and direct weight of the uid above the curve.LIQUID ABOVE  THE CURVELIQUID BELOW THE CURVEARCHIMEDES’ PRINCIPLE OF BOUYANCYThe net hydrostac force on any submerged body in astac uid is the vercal upli force called buoyant forcewhich equals the weight of the displaced liquid.P= ±  Pg +  L h   0 =F 1  - F 2  – Wsinθ0 = -PxA + (P+ Δ P)xA –  L (AS)x( Δ h/S)P 2  – P 1  =  L (h 2  – h 1 )  Floang BodiesW = BFSINKING BODIESW > BFWapp = W- BFLIQUIDS IN RIGID BODY MOTION – the uid will move as arigid mass with each parcle having the same acceleraon.A. VERTICAL ACCELERATION – liquid gets heaviear (up) orlighter (down)B. HORIZONTAL ACCELERATION – liquid surface becomeinclined. C. ROTATIONAL ACCELERATION – liquid surface becomesparabolic.FLUID DYNAMICS – the natural science of uids in moonHYDRODYNAMICS – study of liquids in moonHYDRAULICS – concerned with the praccal applicaons of uids, primarily liquids in moon. It deals with suchmaers as the ows in pipes, rivers, and channels.FLUID FLOW – connuous deformaon of uid upon theapplicaon of shear. CLASSIFICATION OF FLOWA.Real Flow - considers energy losses in the owB.Ideal Flow – neglects the eects of viscosity andfricon in uid ow, thus no energy losses are considered.C.Uniform Flow – ow velocity and cross seconalarea of ow at a given instant do not change with distance.D.Non – Uniform Flow – ow velocity and crossseconal area of ow varies with distance E.Steady Flow – ow velocity and area of ow do notchange with me, a = 0F.Unsteady ow – ow velocity and area of owwith me, FLOW RATE – amount of ow with meA.Mass ow rate B.Volume ow rate Problem:1.The density of oil is 850kg/m^3 and its dynamicviscosity is 5x10^-3 kg/m-s. Determine its relave density,  specic weight in kN/m^3 and its kinemac viscosity. (0.85,8.3385, 5x10^-6m^2/s)2.The velocity distribuon of a viscous liquid withdynamic viscosity owing over a xed plateis given by u = 0.68y-y 2 , where u is velocity in m/s and y isthe distance from the plate in m. What is the velocitygradient at plate surface, shear stress and the shear stressat a point 0.17m from the xed plate. ( 0.68, 0.612, 0.306)3.A 1 inch wide space between two horizontal planesurfaces is lled with lubricang oil with viscosity . A very thin plate of 4 2  area is to bedragged through the oil at velocity of 20/min. If the plate0.33” from one surface, calculate the shear stress on top pf the thin plate, the shear stress on the boom of the thinplate and the required drag force. (F=0.463lb)
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