1. Pharos University ME 259 Fluid Mechanics II Review of Previous Fluid Mechanics Dr. Shibl

2. Fluid Properties: Liquid or Gas
Liquids are:
Incompressible, DV ≠ f(DP)
Viscous (high viscosity)
Viscosity decreases with temperature
Gases are:
Compressible, DV = f(DP)
Low viscosity
Viscosity increases with temperature

3. Equations for Fluid Property
Circular Area:
Weight: w = m*g Newton
Density: r = m/V Kg/m3
Specific Weight: g = w/V N/m3
Specific gravity: SG=r/rwater
Area = p/4*D2

4. Viscosity = Shear Stress/Slope of velocity profile
Dynamic Viscosity
= Shear Stress/Slope of velocity profile
Kinematic Viscosity cS (centistokes) or m2/Sec.
cP (centipoise) or Pa-sec n v F
Slope = v/y y

5. Pressure and Elevation
Change in pressure in homogeneous liquid at rest due to a change in elevation
DP = gh
Where,
DP = change in pressure, kPa
= specific weight, N/m3
h = change in elevation, m

6. Pressure-Elevation Relationship
Valid for homogeneous fluids at rest (static)
P2 = Patm + rgh
Free Surface
Free Surface P2 P1
P1 > P2

7. Example: Manometer
Calculate pressure (psig) or kPa (gage) at Point A. Open end is at atmospheric pressure. A
0.15 m
Water
0.4 m
Hg: SG = 13.54

8. Forces due to Static Fluids
Pressure =Force/Area (definition)
Force = Pressure*Area
Example:
If a cylinder has an internal diameter of 50 mm and operates at a pressure of 20 bar, calculate the force on the ends of the cylinder.

9. Force-Pressure: Rectangular Walls
Patm
Vertical wall
DP = g*h d

10. Flow Classification Classification of Fluid Dynamics Laminar Inviscid
µ = 0
Viscous
Turbulent
Compressible
Incompressible
ϱ = constant
Internal
External
22-Apr-17

11. Q = Area*Distance/Unit Time
Definitions
Volume (Volumetric) Flow Rate
Q = Cross Sectional Area*Average Velocity of the fluid
Q = A*v
Weight Flow Rate
W = g*Q
Mass Flow Rate
M = r*Q v
Volume
Q = Volume/Unit time
Q = Area*Distance/Unit Time

12. Key Principles in Fluid Flow
Continuity for any fluid (gas or liquid)
Mass flow rate In = Mass Flow Rate out
M1 = M2
r1*A1*v1 = r2*A2*v2
Continuity for liquids
Q1 = Q2
A1*v1 = A2*v2 M1 M2

13. Newton’s Laws
Newton’s laws are relations between motions of bodies and the forces acting on them.
First law: a body at rest remains at rest, and a body in motion remains in motion at the same velocity in a straight path when the net force acting on it is zero.
Second law: the acceleration of a body is proportional to the net force acting on it and is inversely proportional to its mass.
Third law: when a body exerts a force on a second body, the second body exerts an equal and opposite force on the first.

14. Momentum Equation Steady Flow Average velocities
Approximate momentum flow rate

15. Total Energy and Conservation of Energy Principle
E = FE + PE + KE
Two points along the same pipe:
E1 = E2
Bernoulli’s Equation:

16. Conservation of Energy

17. Bernoulli’s Equation

18. piezometric head
kinetic head

19. Flow through a contraction1 2
head
Total Energy
Kinetic Head
Piezometric Head
position

20. head
Energy Grade Line
Kinetic Head
Hydraulic Grade Line
Piezometric Head
position

21. Bernoulli’s Equation No heat transfer No shear work (frictionless)
Single uniform inlet and single uniform outlet
No shaft work
Steady state
Constant temperature
Incompressible

22. Frictional Effects Pipes are NOT frictionless
Add a loss due to friction to Bernoulli’s eq.
Head loss due to friction

23. head
EGL (ideal) hL
EGL (actual)
HGL (actual)
position

24. Friction Losses hL = head losses due to friction Fittings (valves,
elbows, etc)
Pipe friction

25. Minor Losses
Km - minor loss coefficient

26. Pipe Friction Losses Darcy-Weisbach equation Kinetic pressure
Length/diameter ratio
Darcy friction factor
- pipe roughness (Table 6.1)
- Reynolds number

27. Reynolds Number Dimensionless
Ratio of inertial forces to viscous forces
Used to characterize the flow regime 27

28. Reynolds Number Describes if the flow is: Laminar - smooth and steady
Turbulent - agitated, irregular
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29. Osborne Reynolds Tests
Laminar
Turbulent
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 29

30. Friction Factor For circular pipe Re ≈ 2300 for transition
L = Diameter of pipe
Laminar flow
Turbulent flow
Colebrook
Equation 30

32. Piping Systems
Three examples of piping systems
Pipes in series 32

33. Home work
Two reservoirs are connected by a pipe as shown. The volume flow rate in pipe A is L/s. Find the difference in elevation between the two surfaces.
r = 1000 kg/m3
m = kg/(m·s)
e = 0.05 mm Dz B A
D = 2 cm
L = 5 m
D = 4 cm
L = 5 m 33 33

34. Centrifugal Pumps
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

35. Head increase over pump

36. Fixed system
pressure
Variable system
pressure

37. Nature of Dimensional Analysis
Example: Drag on a Sphere
Drag depends on FOUR parameters: sphere size (D); speed (V); fluid density (r); fluid viscosity (m)
Difficult to know how to set up experiments to determine dependencies
Difficult to know how to present results (four graphs?)

38. Nature of Dimensional Analysis
Example: Drag on a Sphere
Only one dependent and one independent variable
Easy to set up experiments to determine dependency
Easy to present results (one graph)

39. Buckingham Pi Theorem Step 1:
List all the dimensional parameters involved
Let n be the number of parameters
Example: For drag on a sphere, F, V, D, r, m, and n = 5

40. Buckingham Pi Theorem Step 5
Set up dimensional equations, combining the parameters selected in Step 4 with each of the other parameters in turn, to form dimensionless groups
There will be n – m equations
Example: For drag on a sphere

41. Dimensional Analysis and Similarity
Geometric Similarity - the model must be the same shape as the prototype. Each dimension must be scaled by the same factor.
Kinematic Similarity - velocity as any point in the model must be proportional
Dynamic Similarity - all forces in the model flow scale by a constant factor to corresponding forces in the prototype flow.
Complete Similarity is achieved only if all 3 conditions are met.

42. Flow Similarity and Model Studies
Example: Drag on a Sphere
For dynamic similarity …
… then …

43. Flow Similarity and Model Studies
Scaling with Multiple Dependent Parameters
Example: Centrifugal Pump (Negligible Viscous Effects)
If …
… then …

44. System Curve
Static head

45. Pump Curve

47. System pressure
Pump pressure

48. Operating point

50. changing

51. changing

52. Pump Power
Recall that
Power provided to fluid
Power required by pump

54. Home Work
Water is pumped between two reservoirs at 0.2 ft3/s (5.6 L/s) through
400 ft (124m) of 2-in (50mm) -diameter pipe and several minor losses,
as shown. The roughness ratio is e/d =
Compute the pump horsepower required