the second lecture of fluid mechanics course - in civil engineering

1. Fluid mechanics
Lecture 2
Dr. Ahmed Adel Saleh

2. Course Contents
Introduction, Dimensions and units,
Fluid physical properties
Fluid Statics
Fluid Kinematics
Fluid Dynamics
Momentum analysis of flow Systems
Flow through pipe lines

3. Course Contents - detailed
Introduction,
Dimensions and units,
Fluid properties
•density,
•specific weight,
•specific gravity,
•specific heat,
•vapor pressure
•compressibility,
•viscosity,
•surface tension
Fluid Statics
•absolute and gage
pressure,
•pressure at a point,
•pressure transmition
•pressure
measurements,
•pressure prism,
•hydrostatic force on a
plane surface,
•hydrostatic force on a
curved surface,
•buoyancy,
•flotation, and stability
•Rigid body motion of
a fluid,
Fluid Kinematics
•continuity equation,
•steady and unsteady
flow,
•laminar and turbulent
flows,
•path line and stream
line,
•ideal and real,
•rotational and ir-
rotational flow,
Fluid Dynamics
•Bernoulli’s Equation,
•total and hydraulic
gradient lines,
•application of
Bernoulli Equation,
•Pitot Tube,
•stagnation point,
•Venturi Meter ,
•orifice ,
•nozzles ,
•flow over notches and
weirs
Momentum analysis of
flow Systems
•conservation of
momentum,
•control volume,
•forces on control
volume,
•forces acting on
plates
•turbines concept,
•forces acting on
bends & reducers ,
•calculations of minor
losses
Flow through pipe
lines
•Reynold's Number,
•Darcy-Weisbach
Equation,
•friction head losses,
•Moody Charts,
•design of pipe flow
system,
•branching pipe,
•pipes in series and in
parallel,
•head loss problems,
•discharge problems,
•sizing problem,
•reservoir system

4. Introduction
https://youtu.be/VF_fl8nNIBU

5. Dimensions and units

6. SI base unit
Symbol Name Quantity
s second time
m metre length
kg kilogram mass
A ampere electric current
K kelvin temperature
mol mole amount of substance
cd candela luminous intensity

7. Dimensions and units

8. Deriving dimensions
Length {L},
time {t},
temperature {T}
velocity, {Lt−1}
acceleration, {Lt−2}
Base dimensions Supplementary dimensions

9. System of measurement
Source: https://slideplayer.com/slide/6936847/

10. Psychological
• old habits and customs are hard to change.
Economics
• existing unit systems entail massive capital investments
Relevance
• certain classes of problems are easier to solve in
• specific unit systems.

11. Unit Conversions
• the concept of multiplication by unity.

12. Dimensions, Dimensional Homogeneity

13. Dimensions, Dimensional Homogeneity
Q=A*V

14. Fluids physical properties
density, specific weight, specific gravity, viscosity,

15. Measures of Fluid Mass and Weight
• Density
PropertiesofFluids
ρ
https://www.nuclear-power.net
https://www.instructables.com/
rho
A measure of the “heaviness” of the fluid

16. Measures of Fluid Mass and Weight
• The specific weight
PropertiesofFluids
γgamma
A measure of the “heaviness” of the fluid

17. Measures of Fluid Mass and Weight
• Vertical cylindered tank (d=7m,H=12m)
• Completely filled with water
• @ 20°c
• Heated to 50°c
• How much water will be spilled over?
PropertiesofFluids
A measure of the “heaviness” of the fluid

18. Measures of Fluid Mass and Weight
PropertiesofFluids
A measure of the “heaviness” of the fluid

19. Measures of Fluid Mass and Weight
• Volume Tank= 𝜋(
7
2
)2
∗ 12 = 461.82 m3
• Weight of the water in the tank = γ*V
= 9.789*461.82 = 4520.76 kN
• Volume of the same weight @ 50°c
• 4520.76/9.69 = 466.54 m3
• Volume of water spilled
• 466.54 - 461.82 = 4.72 m3
PropertiesofFluids
A measure of the “heaviness” of the fluid

20. Measures of Fluid Mass and Weight
PropertiesofFluids
• The Specific Gravity
a dimensionless ratio to express density
A measure of the “heaviness” of the fluid

21. Measures of Fluid Mass and Weight
PropertiesofFluids
• Viscosity μ
A measure of the “heaviness” of the fluid
mu

22. Measures of Fluid Mass and Weight
PropertiesofFluids
• Viscosity μ
A measure of the “heaviness” of the fluid
Fluids for which the shearing stress is linearly related to the
rate of shearing strain ( Newtonian fluids )
most common fluids, both liquids and gases, are Newtonian.
mu

23. Measures of Fluid Mass and Weight
PropertiesofFluids
• Viscosity μ
A measure of the “heaviness” of the fluid
mu
rate of shearing strain
(velocity gradient)
the absolute viscosity
the dynamic viscosity
the viscosity
the shearing stress
μ of a fluid is a measure of the internal resistance (“fluidity” or “internal
stickiness”) to shear or angular deformation

25. Capillarity
Upward
force
Downward
force

26. Types of flow

27. • used to display laminar and
turbulent flows.
• the Reynolds number
where:
•ρ is the density of the fluid (SI units: kg/m3)
•V is the velocity of the fluid with respect to the object (m/s)
•L is a characteristic linear dimension (m)
•μ is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/m·s)
https://en.wikipedia.org/wiki/Reynolds_number

28. https://en.wikipedia.org/wiki/Reynolds_number

29. Munson, Bruce Roy, et al. Fundamentals of Fluid Mechanics. John Wiley & Sons, Inc., 2013.
ρ the fluid density,
V the mean fluid velocity,
D the pipe diameter, and
μ the fluid viscosity.

30. Munson, Bruce Roy, et al. Fundamentals of Fluid Mechanics. John Wiley & Sons, Inc., 2013.

31. Dimensions of flows

32. One, two and three dimensional flows