内容讲义教程lecture notes-module02a fluidstatics-hydrostatic forces and buoyan

1、1Fluid Mechanics and Hydraulics(Acknowledgement: Slides contain material from J. Ness and G. Jenkins and some copyright material from Wiley and Pearson Education) Associate Professor Hong ZhangEmail: .au2Module 2 Fluid StaticsHydrostatic forces (continued)BuoyancyReading: 1. Cr

2、owe et al. 9th Ed., Chapter 3, pages 48 - 55. 2. Crowe et al. 9thEd., Chapter 3, pages 55 - 563ObjectivesAt the end of this module you should:understand pressure in hydrostatic fluidsbe able to determine the hydrostatic pressure force acting on various surfacesbe able to determine the buoyancy of ob

3、jects immersed in fluids4Forces in static fluids (Hydrostatic Forces)Forces on a plane surfacePressure distributionTotal forceCentre of pressureForces on a curved surfaceHorizontalVerticalResultant5Forces in static fluidsPressure force normal to the boundary Flat surfaceCurved surfaceForce from flui

4、dReaction Force 6Forces in static fluidsPressure is force divided by area (by definition).We are now interested in calculating forces on surfaces produced by a fluid at rest due to the fluid pressure.If the pressure is uniform all over the surface of interest we simply have force F = p.A.When the pr

5、essure varies over the surface of interest, other methods must be used to account for this variation before we can determine the magnitude of the resultant force.We also need to determine the line of action of the resultant force if we wish to account for the effects the force can produce.7figure_03

6、_15figure_03_15Forces in static fluids: Centre of pressureCentre of pressureHydrostatic Pressure DistributionThe pressure distribution is linearArrows representing pressure are normal to the surfaceResultant force acts through the CP which is below the Centroid.8Hydrostatic pressure force acting on

7、a vertical plane surfaceSketch the pressure distribution for the following hydrostatic situation. yz9Hydrostatic pressure force acting on a vertical plane surfaceyLet w = width of wall, h = depth of fluid, dA = differential area of wall = wdyhdyh = h/210Hydrostatic force on a plane surface - summary

8、Forces on Planar SurfacesPc = Pressure at Centroid of SurfaceF = Pc APc = g hchc= Second Moment of Area of Surface (About the Centroidal Axis)Valid For Any Planar Surface, Regardless of Shape12Volume and area formulae:Figure A.1 (p. A-5)Centroids and moments of inertia (2nd moments of area) of plane

9、 areas13ExampleAn elliptical gate covers the end of a pipe 4 m in diameter. If the gate is hinged at the top, what normal force F is required to open the gate when water is 8 m deep above the top of the pipe and the pipe is open to the atmosphere on the other side? Neglect the weight of the gate.(An

10、s. 808 kN)Hydrostatic Forces on Curved SurfacesForces on Non-Planar SurfacesA Non-Planar SurfaceForces on Non-Planar SurfacesDefine a Control Volume(Liquid Above the Surface)Vertical PlaneVertical Force Component - FVFVFV Weight of Liquid in Control VolumeForce Acts Through Centre of Gravity of Cont

11、rol VolumeHorizontal Force Component - FHFHFH Hydrostatic Force on Vertical PlaneForce Acts Through Centre of Pressure on Vertical PlaneResultant Hydrostatic ForceFVFHFRFR Resultant Hydrostatic Force on the Non-Planar Surface20Hydrostatic forces on curved surfacesFigure 3.17 (a) Pressure distributio

12、n and equivalent force.(b) Free-body diagram and action-reaction force pair.Goal to model the force due to pressure with an equivalent force vector acting through the centre of pressureTwo approachesIntegrate the pressure along the curved surfaceSum forces for a free body FyFx21Example Surface AB is

13、 a circular arc with a radius of 2 m and a depth of 1 m into the page. The distance EB is 4 m. The fluid above surface AB is water and atmospheric pressure prevails on the free surface of the water and on the bottom side of surface AB. Find the magnitude and line of action of the hydrostatic force a

14、cting on surface AB.22Example answer23Hydrostatic forces on curved surfacesHorizontalVerticalResultantForces on curved surfaces may be determined from equilibrium concepts applied to systems comprised of the fluid in contact with the curved surface.24Hydrostatic forces on arbitrary surfacesFigure 3.

15、14 (Crowe)Thin-curved surfaceBuoyancyBuoyancy26mfluidgThe buoyancy force is the resultant of the hydrostatic pressure distribution on the outside of the submerged objectFBBuoyant ForceBuoyant Force = Weight of Fluid DisplacedGriffith University28Archimedes principle of buoyancyThe buoyancy (net upwa

16、rdly directed buoyant force) of an object either partially or completely submerged in a fluid is equal to the weight of the displaced fluid equilibrium concept.Figure 3.21 (Crowe)Centre of buoyancy is the centroid of the displaced volumeFigure 3.20 (Crowe)29Example The figure shows a metal part (obj

17、ect 2) hanging by a thin cord from a floating wood block (object 1). The wood block has a specific gravity S1 = 0.3 and dimensions of 50 x 50 x 10 mm. The metal part has a volume of 6600 mm3. Find the mass m2 of the metal part and the tension T in the cord.Solution:m2 = 17.8 g T = 0.11 NT m2g = 0.18 N An object will “weigh less in water than in air” !30S