1. Fluid Statics

2. Definition of Pressure
Pressure is defined as the amount of force exerted on a unit area of a substance:

3. Direction of fluid pressure on boundaries
Furnace duct
Pipe or tube
Heat exchanger
Pressure is a Normal Force
(acts perpendicular to surfaces)
It is also called a Surface Force
Dam

4. Absolute and Gauge Pressure
Absolute pressure: The pressure of a fluid is expressed relative to that of vacuum (=0)
Gauge pressure: Pressure expressed as the difference between the pressure of the fluid and that of the surrounding atmosphere.
Usual pressure guages record guage pressure. To calculate absolute pressure:

5. Definition or Relationship
Units for Pressure
Unit
Definition or Relationship
1 pascal (Pa)
1 kg m-1 s-2
1 bar
1 x 105 Pa
1 atmosphere (atm)
101,325 Pa
1 torr
1 / 760 atm
760 mm Hg
1 atm
pounds per sq. in. (psi)

6. Pressure distribution for a fluid at rest
Let’s determine the pressure distribution in a fluid at rest in which the only body force acting is due to gravity
The sum of the forces acting on the fluid must equal zero

7. What are the z-direction forces?
Let Pz and Pz+Dz denote the pressures at the base and top of the cube, where the elevations are z and z+Dz respectively. z y x

8. Pressure distribution for a fluid at rest
A force balance in the z direction gives:
For an infinitesimal element (Dz0)

9. Incompressible fluid
Liquids are incompressible i.e. their density is assumed to be constant:
When we have a liquid with a free surface the pressure P at any depth below the free surface is:
Po is the pressure at the free surface (Po=Patm)
By using gauge pressures we can simply write:

10. Example
In deep water oil fields offshore Louisiana one occasionally encounters a reservoir pressure of 10,000 psig at a depth of 15,000 ft. If this pressure is greater than the hydrostatic pressure of the drilling fluid in the well bore the result may be a well “blowout” which is dangerous to life and property. Assuming that you are responsible for selecting the drilling fluid for an area where such pressures are expected, what is the minimum density drilling fluid you can use ? Assume a surface pressure of 0 psig.

11. Static pressure - 10 minute problem:
Rainwater collects behind the concrete retaining wall shown below.
If the water-saturated soil (specific gravity = 2.2) acts as a fluid,
determine the force on a one-meter width of wall.
Water 1m
Soil 3m

12. Buoyancy
A body immersed in a fluid experiences a vertical buoyant force equal to the weight of the fluid it displaces
A floating body displaces its own weight in the fluid in which it floats
Free liquid surface F1
The upper surface of the body is subjected to a smaller force than the lower surface
 A net force is acting upwards h1 H h2 F2

13. Buoyancy The net force due to pressure in the vertical direction is:
FB = F2- F1 = (Pbottom - Ptop) (DxDy)
The pressure difference is:
Pbottom – Ptop = r g (h2-h1) = r g H
Combining:
FB = r g H (DxDy)
Thus the buoyant force is:
FB = r g V

14. Practical Application of Buoyancy
Nimitz Class Aircraft Carrier (100,000 tons)

15. Measurement of Pressure
Manometers are devices in which one or more columns of a liquid are used to determine the pressure difference between two points.
U-tube manometer
Inclined-tube manometer

16. Measurement of Pressure Differences
Apply the basic equation of static fluids to both legs of manometer, realizing that P2=P3.

17. Manometer - 10 minute problem
A simple U-tube manometer is installed across an orifice plate. The manometer is filled with mercury (specific gravity = 13.6) and the liquid above the mercury is water. If the pressure difference across the orifice is 24 psi, what is the height difference (reading) on the manometer in inches of mercury ?

18. Compressible Flow
Tall Mountains
Natural gas well

19. Compressible fluid
Gases are compressible i.e. their density varies with temperature and pressure r =P M /RT
For small elevation changes (as in engineering applications, tanks, pipes etc) we can neglect the effect of elevation on pressure
In the general case start from:

20. Compressible Linear Temperature Gradient

21. Atmospheric Equations
Assume constant
Assume linear
Temperature variation with altitude for the U.S. standard atmosphere

22. Compressible Isentropic

23. Compressible Fluid – 10 minute problem
The temperature of the earth’s surface drops about 5 C for every 1000 m of elevation above the earth’s surface. If the air temperature at ground level is 15 C and the pressure is 760 mm Hg, what is the air pressure on top of Mt. Everest at 8847 m ? Assume air behaves as an ideal gas.