流體力學第二章

1、1White:Chapter 2潘錦珊：第一章Chapter 2 Pressure Distributionin a fluid (Fluid Statics Basic)2AFpAlim0Definition:Unit:2mNPa(SI)2cmkgatmPSImmHgOmmH2(Pound per Squire Inch)q Vertical to the surface and point into it.q At any point, pressure is independent of orientation.Properties of PressurePressure3At any

2、point in a static fluid, pressure is independent of orientation.Verification:zgppppnznx210zWhenppppnzxnpyxzxzpxp)21(zxbgG(up)sinsinybpybpnxsinybpPnnybpPxxForces on left and up surface:x4Fluid MechanicsAerodynamicsFluid at restFluid StaticsFluid DynamicsFluid in motion5q Pressure is the only surface

3、force.q Pressure distribution relates to body force only.q Dams（水壩）q Buoyancy related instrument（利用浮力的裝置）q Fluid power system（液壓驅(qū)動系統(tǒng)）q Connected vessel （連通器）q Applications: 2.1 Fluid rest6Consider a cube in a static fluidPressure at the center is p;Body forces are kZjYiXRdxdydzrightpleftpp22dxxpppdx

4、xpppleftleft 2.2 Equilibrium of a Fluid Element7dxdydzXdxdydzZdxdydzYdxdydzdxdydz2dxxpp2dxxpppPressure:Body force:8022XdxdydzdydzdxxppdydzdxxppIn x direction:Force on left surfaceForce on right surfaceBody force in x directionXxpZzpYypEuler Equilibrium Equations(Euler 1775)(ZdzYdyXdxdp9ZzpYypXxpPres

5、sure increase in the direction of body force. Surfaces in fluid with same pressure, vertical to body force everywhere, in gravity field it is a horizontal plane.Equipressure surface（等壓面）Rp)(kZjYiXkzpjypixp10)(ZdzYdyXdxdpxzzhz0p0Zdzdp)(gZgdz1Basic rule:CgzpGeneral solution2Boundary condition:00,ppzz0

6、0gzpC)(00zzgpphpghpp00 2.3 Pressure Distribution under Gravity11ghphpp00Pressure at free surfacePressure due to weight on topAny point with the same depth h under free surface has the same pressure.equipressure surface（等壓面）Free surface is an equipressure surface12p0Water manometer（水柱壓力計）phPressure s

7、ourceConnected water tubeApplication ?Absolute pressure （絕對壓力）Relative pressure（相對壓力）Gauge pressure（表壓力）Vacuum degree（真空度）Pressure measurementh (mmH2O)h+p0 (mmH2O)pA 絕壓pG 表壓13P2.7Homework:14AAAhAppPdd0sinyh dAhppdAdP)(0AAAyApAyApPdsindsin00AydAyAxdAxAcAc,Centroid（形心，重心）AhApAyApPcc00sinhcycChyxAyxp0F

8、ind total force P 2.4 Hydrostatic Force on Plane Surface15AhpPc)(0hc: depth of centroidThe force on a submerged plane equals the pressure at the plate center times the plate area, independent of the shape of the plate or the angle .Center of pressureIs the center of pressure at centroid ?hcycChdydDh

9、yxAyxp016AyIyyCCCDAydAayp)sin(0AcdAyAyp20sinAyIA2AyIICC2hcycChdydDhyxAyxp0AAydAhpydp)(0Moment to x axis17ExampleThe gate is 5m wide,is hinged at point B,and rest against a smooth wall at point A.Find (a) The force on the gate exerted by seawater pressure, (b) The horizontal force Px exerted by the w

10、all at point Am8m6ABmN210050m15cxP18AhFc1051210050N1003. 66(a) Centroid: 3m above BSolution:3121bLIcALILLcccd6xdPFL(b)BPxAccpFLcLNPx106059. 46m8m6ABmN210050m15cxP19Hoover DamChannel 1. Select a dA and find the three forces on it2. Integration 2.5 Hydrostatic Forces on Curved Surfaces20Conclusion:x1.

11、 Horizontal forces: xcxAhpp)(0 xOzAAx2. Vertical forces: VAppzz0OzV21Example:Find the forces acting on the hemi-spherical covers.RFOxyH45oSolution:222gHRAHFxxsygVFFFFyX22FFxytan1222245sinRRAx45cos3223HRRVs22 2.6.1 Uniform Linear Acceleration （恒加速度直線運動）aX= -agxGravityBody forceInertia Force 2.6 Fluid

12、 in rigid body motion23azgxaxxagdzdxaxBoundary condition:0, 0ppzx)(0gzxappx0pp At free surface（自由液面）xgazxEquipressure surface（等壓面）CxgazxEuler Equilibrium Equations)(ZdzXdxdp24A cup of coffee is 7cm deep at rest.1. Whether it will spill out while ax=7m/s2?2. Gage pressure of point A? Example:cmDz14. 2tan2gaxtanSolution:AAghP31010mkgPa906)0214. 007. 0(8 . 91010Azcm6cm7cm3g27smaxxaIt will not spill out !25 2.6.2 Rigid body rotation （整體旋轉(zhuǎn)）g2rzfO2yxyROf2xryxgZyYxX,22Body force:)(ZdzYdyXdxdp)(22gdzydyxdxEquipressure sur