1. Static flow and Its Application
Text book, Chapter 2

2. Fluids: Statics vs Dynamics

3. Fluid Statics Basic Principles: Fluid is at rest : no shear forces
Pressure is the only force acting
What are the forces acting on the block?
Air pressure on the surface - neglect
Weight of the water above the block
Pressure only a function of depth

4. Section 1: Pressure

14. Example 2.4
Consider a tank containing mercury, water, benzene, and air as shown. Find the pressure
(gauge) over the benzene. If an opening is made in the top of tank. Given SG of mercury, benzene
and water are 13.55, and 1.00 respectively. Use the density of water equal to 999
Kg/m3

15. Solution

16. First what is the direction of the fluid?
Example 2.5
First what is the direction of the fluid?

17. Solution

19. Example: Find PA- PB

20. What is h?

21. A B

23. x

24. Hydrostatic Equation : Compressible Fluids
By the Ideal gas law:
Hydrostatic Equation : Compressible Fluids
R is the Gas Constant
T is the temperature
ρ is the density
Then,
Note: γ = ρg and not a constant, then
Using special R
Gases such as air, oxygen and nitrogen are thought of as compressible, so we must consider the variation of density in the hydrostatic equation: 24

25. Case of uniform temperature: T=To
Text Book Example 2.2
At an altitude z, of 11,000 m, the atmospheric temperature T is C and
The pressure p is 22.4 KN/m2 .Assuming that the temperature remains the
Same at higher altitudes, calculate the density of the air at an altitude of z2 of
15,000 m. Assume R = 287 J/Kg.K. 25

26. 26 26

27. Case of Non-uniform temperature
Now, for the Troposphere, Temperature is not constant:
Substitute for temperature (T) and Integrate:
β is known as the lapse rate, K/m (z=0~11 km), and Ta is the temperature at sea level, K.
pa is the pressure at sea level, kPa, R is the gas constant, J/kg.K
Starting from, 27

28. Pressure Distribution in the Atmosphere28

29. For Adiabatic atmosphere
let = = 29

30. Also from Thermodynamic (for adiabatic)30 30

31. 31

32. For Isentropic Process
An isentropic flow is a flow that is both adiabatic and reversible
We can extended from the adiabatic equation 32 32

33. Text Book Example 2.3
Calculate the Pressure, Temperature and density of atmosphere at an
altitude z, of 1200 m, if zero altitude temperature is 15 0C and Pressure
101 KN/m2 . Assume that conditions are adiabatic (k = 1.4) and R = 287 J/Kg.K. 33

34. P1 = kN/m-2
T1 = 3.3 oC 34