1. Fluid Mechanics Fluid Statics

2. Pressure field Pressure is a scalar field: p = p(x; y; z; t) The value of p varies in space, but p is not associated with a direction. The pressure at any point in a stationary fluid is independent of direction. A pressure sensor will not detect different values of pressure when the orientation of the sensor is changed at a fixed measurement point.

3. Pascal’s law

6. Variation of pressure with elevation

7. Equality of pressure at the same level in a static fluid

8. Equality of pressure at the same level in a continuous body of fluid

9. General variation of pressure in a static fluid due to gravity

10. for vertical direction:  = 0

11. Variation of pressure in an incompressible fluid (liquid) for liquids:  = const.

12. Variation of pressure in an incompressible fluid (liquid) at z 1 =0 p 1 =p atm h is called pressure head

13. Variation of pressure in an compressible fluid (gas) for liquids:  is variable, e.g. for an ideal gas:

14. Variation of pressure in an compressible fluid (gas) need to know T=T(z)

15. Variation of pressure in an compressible fluid (gas) case of uniform temperature: T=T o

16. Variation of pressure in an compressible fluid (gas) case of linear temperature variation: T=T o +  z at z 1 =0 (sea level) T=T o p 1 =p o

17. Pressure scales Absolute pressure: p abs is measured relative to an absolute vacuum; it is always positive. Gage pressure: p gage is measured relative to the current pressure of the atmosphere; it can be negative or positive.

18. Barometers A barometer is a device for measuring atmospheric pressure. h=760 mm of mercury why not water or ethanol? is the vacuum on top really empty space?

19. Manometers A manometer is a device for measuring fluid pressure consisting of a bent tube containing one or more liquids of different densities. A known pressure (which may be atmospheric) is applied to one end of the manometer tube and the unknown pressure (to be determined) is applied to the other end. Differential pressure manometer measures only the difference between the two pressures.

20. Manometer types Simple U - tube manometer Inverted U - tube manometer U - tube with one leg enlarged Two fluid U - tube manometer Inclined U - tube manometer

21. Simple U - tube manometer

22. Inverted U - tube manometer

23. U - tube with one leg enlarged used for more accurate readings

24. Two fluid U-tube manometer used for more accurate readings of small pressure differences

25. Inclined U-tube manometer used for more accurate readings of small pressure differences