REVIEW IN FLUID MECHANICS

REVIEW IN FLUID MECHANICS FLUID MECHANICS – the branch of applied mechanics concerned with the statics and dynamics – both liquid and gases. The analysis of the behavior of fluids is based on the fundamental laws of mechanics which relate continuity of mass and energy with force and momentum together with the familiar solid mechanics properties. NEWTON’“ LAW OF VI“CO“ITY – in a fluid, shear strain φ increases for as long as shear stress () is applied. Therefore, the fluid flows. FLUID – any substance that flows or deforms continuously when subjected to shearing forces. LIQUID – incompressible fluid, constant volume, variable density GAS – compressible fluid, variable volume, variable density DENSITY – quantity of matter contained in a unit volume of substance. TYPES OF DENSITY:  Mass Density  Specific Weight (Unit Weight)  Relative Density (Specific Gravity) ACCELERATION DUE TO GRAVITY  g = 32.2ft/s^2 = 9.81m/s^2 DENSITY OF WATER AT STANDARD TEMPERATURE  = 1000kg/m^3  VISCOSITY – is the property of a fluid, due to cohesion and interaction between molecules, which offers resistance to shear deformation.  Dynamic viscosity  Kinematic Viscosity FLUID STATICS – study of fluids at rest in stable equilibrium HYDROSTATICS – the study of liquids at rest and the forces exerted on them or by them. PRINCIPLES:  There are no shear stresses  Pressure exists at every point in a static fluid  Pressure at a point is same in all dire tions Pas al’s La .  Pressure acts normal to all boundary surfaces  Pressure varies with height or depth. PRESSURE – force applied uniformly over a surface Common units: psi(lb/in^2), psf(lb/ft^2), Pa(N/m^2)  Atmospheric pressure, Patm – pressure exerted by the weight of air above us. Patm at sea level = 1 atm = 101.325kPa (14.7psi) = 760mmHg (29.9in Hg) = 10.34m H2O (33.91ft H2O)  Absolute zero – the lower limit of atmospheric pressure or the perfect vacuum  Gauge pressure, Pg = the pressure measured relative to atmosphere as datum - Taken positive (+) if measured above atmosphere - Taken negative (-) if measured below atmosphere.  Absolute pressure, Pabs – pressure measured above absolute zero, always positive (+) HYDROSTATIC PRESSURE –pressure acted by liquid (gauge pressure) plus any pressure acting on the surface of the liquid  General Idea – weights acts static liquid thus creating pressure, assuming weight of air on liquid surface is zero.  Derivation PRESSURE ON OTHER SURFACES Pressure liquid alone P=W/A=LIQV/A = LIQh P=± Pg + Lh PRESSURE VARIATION OF DIFFERENT LIQUIDS Pressure Head – the vertical height h of any liquid of specific weight, L, which can be converted to a gauge pressure P  Variation of Pressure in Static Liquids 0 =F1 - F2 – Wsinθ 0 = -PxA + (P+ΔP)xA – L(AS)x(Δh/S) P2 – P1 = L(h2 – h1) Pressure increases with depth, h LATERAL PRESSURE DISTRIBUTION EQUIVALENT HEIGHT – height of another liquid which gives the same amount of pressure as a certain liquid Principle: two liquids with different heights exert the same amount of pressure. MANOMETERS – devices used to measure pressure A. PIEZOMETER COLUMN – vertical, open glass tube B. U TUBE OPEN TYPE – U shaped glass tube, with one leg open to atmosphere, partially filled with liquid of known property called manometer liquid C. U TUBE DIFFERENTIAL TYPE - both legs are exposed to different pressures thus measuring pressure difference. HYDROSTATIC FORCE ON PLANE SURFACES Hydrostatic force is located at center of pressure which is al ays at distan e e elo the enter of gra ity of submerged area, A. HYDROSTATIC FORCE ON CURVED SURFACES The total hydrostatic force, F is the resultant of the hydrostatic force from lateral pressure (acting on vertical surface) and direct weight of the fluid above the curve. LIQUID ABOVE THE CURVE VERTICAL PRESSURE DISTRIBUTION LIQUID BELOW THE CURVE LIQUIDS IN RIGID BODY MOTION – the fluid will move as a rigid mass with each particle having the same acceleration. A. VERTICAL ACCELERATION – liquid gets heaviear (up) or lighter (down) ARCHIMEDE“’ PRINCIPLE OF BOUYANCY The net hydrostatic force on any submerged body in a static fluid is the vertical uplift force called buoyant force which equals the weight of the displaced liquid. B. HORIZONTAL ACCELERATION – liquid surface become inclined. Floating Bodies HYDRODYNAMICS – study of liquids in motion HYDRAULICS – concerned with the practical applications of fluids, primarily liquids in motion. It deals with such matters as the flows in pipes, rivers, and channels. FLUID FLOW – continuous deformation of fluid upon the application of shear. CLASSIFICATION OF FLOW A. Real Flow - considers energy losses in the flow B. Ideal Flow – neglects the effects of viscosity and friction in fluid flow, thus no energy losses are considered. C. Uniform Flow – flow velocity and cross sectional area of flow at a given instant do not change with distance. D. Non – Uniform Flow – flow velocity and cross sectional area of flow varies with distance E. Steady Flow – flow velocity and area of flow do not change with time, a = 0 F. Unsteady flow – flow velocity and area of flow with time, FLOW RATE – amount of flow with time W = BF C. ROTATIONAL ACCELERATION – liquid surface becomes parabolic. SINKING BODIES W > BF Wapp = W- BF FLUID DYNAMICS – the natural science of fluids in motion A. Mass flow rate B. Volume flow rate