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REVIEW IN FLUID MECHANICS
FLUID MECHANICS – the branch of applied mechanicsconcerned with the stacs and dynamics – both liquid andgases. The analysis of the behavior of uids is based on thefundamental laws of mechanics which relate connuity of mass and energy with force and momentum together withthe familiar solid mechanics properes. FLUID – any substance that
fows
or deforms connuouslywhen subjected to shearing forces.LIQUID – incompressible uid, constant volume, variabledensityGAS – compressible uid, variable volume, variable densityDENSITY – quanty of maer contained in a unit volume of substance.TYPES OF DENSITY:
Mass Density
Specic Weight (Unit Weight)
Relave Density (Specic 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 andinteracon between molecules, which oers resistance toshear deformaon.
Dynamic viscosity
Kinemac 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 astac uid
Pressure at a point is same in alldirecons (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 measuredrelave to atmosphere as datum -Taken posive (+) if measured aboveatmosphere-Taken negave (-) if measured belowatmosphere.
Absolute pressure, Pabs – pressure measuredabove absolute zero, always posive (+)HYDROSTATIC PRESSURE –pressure acted by liquid (gaugepressure) plus any pressure acng on the surface of theliquid
General Idea – weights acts stac liquid thuscreang pressure, assuming weight of air on liquidsurface is zero.
Derivaon
Variaon of Pressure in Stac LiquidsPressure increases with depth, hLATERAL PRESSURE DISTRIBUTIONVERTICAL PRESSURE DISTRIBUTIONPRESSURE ON OTHER SURFACESPRESSURE VARIATION OF DIFFERENT LIQUIDSPressure Head – the vercal height h of any liquid of specic 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 dierent heights exert the sameamount of pressure.MANOMETERS – devices used to measure pressureA. PIEZOMETER COLUMN – vercal, open glass tubeB. U TUBE OPEN TYPE – U shaped glass tube, with one legopen to atmosphere, parally lled with liquid of knownproperty called manometer liquidC. U TUBE DIFFERENTIAL TYPE - both legs are exposed todierent pressures thus measuring pressure dierence. HYDROSTATIC FORCE ON PLANE SURFACESHydrostac 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 hydrostac force, F is the resultant of thehydrostac force from lateral pressure (acng on vercalsurface) and direct weight of the uid above the curve.LIQUID
ABOVE
THE CURVELIQUID BELOW THE CURVEARCHIMEDES’ PRINCIPLE OF BOUYANCYThe net hydrostac force on any submerged body in astac uid is the vercal 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
)
Floang BodiesW = BFSINKING BODIESW > BFWapp = W- BFLIQUIDS IN RIGID BODY MOTION – the uid will move as arigid mass with each parcle having the same acceleraon.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 moonHYDRODYNAMICS – study of liquids in moonHYDRAULICS – concerned with the praccal applicaons of uids, primarily liquids in moon. It deals with suchmaers as the ows in pipes, rivers, and channels.FLUID FLOW – connuous deformaon of uid upon theapplicaon of shear. CLASSIFICATION OF FLOWA.Real Flow - considers energy losses in the owB.Ideal Flow – neglects the eects of viscosity andfricon in uid ow, thus no energy losses are considered.C.Uniform Flow – ow velocity and cross seconalarea of ow at a given instant do not change with distance.D.Non – Uniform Flow – ow velocity and crossseconal 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 relave density,
specic weight in kN/m^3 and its kinemac viscosity. (0.85,8.3385, 5x10^-6m^2/s)2.The velocity distribuon 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 lubricang 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 boom of the thinplate and the required drag force. (F=0.463lb)

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