1. 1 White:Chapter 2 潘锦珊：第一章 Chapter 2 Pressure Distribution in a fluid (Fluid Statics Basic )

2. 2 Definition: Unit:(SI) (Pound per Squire Inch)  Vertical to the surface and point into it.  At any point, pressure is independent of orientation. Properties of Pressure Pressure

3. 3 At any point in a static fluid, pressure is independent of orientation. Verification: When (up) Forces on left and up surface:

4. 4 Fluid Mechanics Aerodynamics Fluid at rest Fluid Statics Fluid Dynamics Fluid in motion

5. 5  Pressure is the only surface force.  Pressure distribution relates to body force only.  Dams （水坝）  Buoyancy related instrument （利用浮力的装置）  Fluid power system （液压驱动系统）  Connected vessel （连通器）  …… Applications: § 2.1 Fluid @ rest

6. 6 Consider a cube in a static fluid Pressure at the center is p; Body forces are dx dy dz § 2.2 Equilibrium of a Fluid Element

7. 7 dx dy dz dx dy dz Pressure: Body force:

8. 8 In x direction: Force on left surface Force on right surface Body force in x direction Euler Equilibrium Equations (Euler 1775)

9. 9 Pressure 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 （等压面）

10. 10 x z z h z0z0 p0p0 1 Basic rule: General solution 2 Boundary condition: § 2.3 Pressure Distribution under Gravity

11. 11 Pressure at free surface Pressure due to weight on top Any point with the same depth h under free surface has the same pressure. equipressure surface （等压面） Free surface is an equipressure surface

12. 12 p0p0 Water manometer （水柱压力计） p h Pressure source Connected water tube Application ? Absolute pressure （绝对压力） Relative pressure （相对压力） Gauge pressure （表压力） Vacuum degree （真空度） Pressure measurement h (mmH 2 O) h+p 0 (mmH 2 O) p A 绝压 p G 表压

13. 13 P2.7 Homework:

14. 14 Centroid （形心，重心） hchc ycyc C h y x A α y x p0p0 Find total force P § 2.4 Hydrostatic Force on Plane Surface

15. 15 h c : depth of centroid The 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 pressure Is the center of pressure at centroid ? hchc ycyc C hdhd ydyd D h y x A α y x p0p0

16. 16 hchc ycyc C hdhd ydyd D h y x A α y x p0p0 Moment to x axis

17. 17 Example The 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 P x exerted by the wall at point A

18. 18 (a) Centroid: 3m above B Solution: (b) LcLc L

19. 19 Hoover DamChannel 1.Select a dA and find the three forces on it 2.Integration § 2.5 Hydrostatic Forces on Curved Surfaces

20. 20 Conclusion: x 1. Horizontal forces: x O z A AxAx 2. Vertical forces: O z V

21. 21 Example: Find the forces acting on the hemi- spherical covers. R F Ox y H 45 o  Solution:

22. 22 § 2.6.1 Uniform Linear Acceleration （恒加速度直线运动） a X= -a g x Gravity Body force Inertia Force § 2.6 Fluid in rigid body motion

23. 23 Boundary condition: At free surface （自由液面） Equipressure surface （等压面） Euler Equilibrium Equations

24. 24 A cup of coffee is 7cm deep at rest. 1. Whether it will spill out while a x =7m/s 2 ? 2. Gage pressure of point A? Example: Solution: It will not spill out !

25. 25 § 2.6.2 Rigid body rotation （整体旋转） g ω2rω2r z f O ω2yω2y ω x y R O f ω2xω2x r y x θ Body force: Equipressure surface: dp=0

26. 26 Parabola dish （抛物面） Free surface: g ω2rω2r z f O z0z0 How to find z 0 ? 旋转抛物面体的体积是同底面 积和高的圆柱体积的一半。

27. 27 P2.64 P2.97 (selective) P2.147 P2.152 Homework: