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Fluid mechanics
Lecture 2
Dr. Ahmed Adel Saleh
Course Contents
Introduction, Dimensions and units,
Fluid physical properties
Fluid Statics
Fluid Kinematics
Fluid Dynamics
Momentum analysis of flow Systems
Flow through pipe lines
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
Introduction
https://youtu.be/VF_fl8nNIBU
Dimensions and units
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
Dimensions and units
Deriving dimensions
Length {L},
time {t},
temperature {T}
velocity, {Lt−1}
acceleration, {Lt−2}
Base dimensions Supplementary dimensions
System of measurement
Source: https://slideplayer.com/slide/6936847/
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.
Unit Conversions
• the concept of multiplication by unity.
Dimensions, Dimensional Homogeneity
Dimensions, Dimensional Homogeneity
Q=A*V
Fluids physical properties
density, specific weight, specific gravity, viscosity,
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
Measures of Fluid Mass and Weight
• The specific weight
PropertiesofFluids
γgamma
A measure of the “heaviness” of the fluid
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
Measures of Fluid Mass and Weight
PropertiesofFluids
A measure of the “heaviness” of the fluid
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
Measures of Fluid Mass and Weight
PropertiesofFluids
• The Specific Gravity
a dimensionless ratio to express density
A measure of the “heaviness” of the fluid
Measures of Fluid Mass and Weight
PropertiesofFluids
• Viscosity μ
A measure of the “heaviness” of the fluid
mu
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
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
Capillarity
Upward
force
Downward
force
Types of flow
• 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
https://en.wikipedia.org/wiki/Reynolds_number
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.
Munson, Bruce Roy, et al. Fundamentals of Fluid Mechanics. John Wiley & Sons, Inc., 2013.
Dimensions of flows
One, two and three dimensional flows

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Fluid Mechanics Course - Civil Engineering -Lec 02

  • 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
  • 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
  • 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.
  • 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
  • 24.
  • 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
  • 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.
  • 32. One, two and three dimensional flows