
Engineering Fluid Mechanics
T. AlShemmeri
Engineering Fluid Mechanics
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2
Engineering Fluid Mechanics
© 2012 T. AlShemmeri & Ventus Publishing ApS
ISBN 9788740301144
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3 Engineering Fluid Mechanics Contents
Contents
Notation 7
1 Fluid Statics 14
1.1 Fluid Properties 14
1.2 Pascal’s Law 21
1.3 FluidStatic Law 21
1.4 Pressure Measurement 24
1.5 Centre of pressure & the Metacentre 29 360°
1.6 Resultant Force and Centre of Pressure on a Curved Surface in a Static Fluid 34
1.7 Buoyancy 37
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1.8 Stability of floating bodies 40
thinking
1.9 Tutorial problems 45
360°
2 Internal Fluid Flow 47
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2.1 Definitions 47
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2.2 Conservation of Mass 50
2.3 Conservation of Energy 52
2.4 Flow Measurement 54
2.5 Flow Regimes 58
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© Deloitte & Touche LLP and affiliated entities. Engineering Fluid Mechanics Contents
2.6 Darcy Formula 59
2.7 The Friction factor and Moody diagram 60
2.8 Flow Obstruction Losses 64
2.9 Fluid Power 65
2.10 Fluid Momentum 67
2.11 Tutorial Problems 75
3 External Fluid Flow 77
3.1 Regimes of External Flow 77
3.2 Drag Coefficient 78
3.3 The Boundary Layer 79
3.4 Worked Examples 81
3.5 Tutorial Problems 91
4 Compressible Fluid Dynamics 93
4.1 Compressible flow definitions 93
4.2 Derivation of the Speed of sound in fluids 94
4.3 The Mach number 96
4.4 Compressibility Factor 99
4.5 Energy equation for frictionless adiabatic gas processes 102
4.6 Stagnation properties of compressible flow 106
4.7 Worked Examples 109
4.8 Tutorial Problems  Compressible Flow 114
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5 Engineering Fluid Mechanics Contents
5 Hydroelectric Power 116
5.1 Introduction 117
5.2 Types of hydraulic turbines 117
5.3 Performance evaluation of Hydraulic Turbines 121
5.4 Pumped storage hydroelectricity 123
5.5 Worked Examples 127
5.7 Tutorial Problems 130
Sample Examination paper 131
Formulae Sheet 140
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6 Engineering Fluid Mechanics Notation
Notation
Symbol definition units
A area m2
D diameter m
F force N
g gravitational acceleration m/s2
h head or height m
L length m
m mass kg
P pressure Pa or N/m2
∆P pressure difference Pa or N/m2
Q volume flow rate m3/s
r radius m
t time s
V velocity m/s
z height above arbitrary datum m
Subscripts
a atmospheric
c crosssectional
f pipe friction
o obstruction
p pump
r relative
s surface
t turbine
x xdirection
y ydirection
z elevation
Dimensionless numbers
C discharge coefficient
d
f friction factor (pipes)
K obstruction loss factor
k friction coefficient (blades)
Re Reynolds number
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7 Engineering Fluid Mechanics Notation
Greek symbols
θ, α, φ angle degrees
µ dynamic viscosity kg/ms
ν kinematics viscosity m2/s
ρ density kg/m3
τ shear stress N/m2
η efficiency %
Dimensions and Units
Any physical situation, whether it involves a single object or a complete system, can be described in terms of a number
of recognisable properties which the object or system possesses. For example, a moving object could be described in
terms of its mass, length, area or volume, velocity and acceleration. Its temperature or electrical properties might also be
of interest, while other properties  such as density and viscosity of the medium through which it moves  would also be
of importance, since they would affect its motion. These measurable properties used to describe the physical state of the
body or system are known as its variables, some of which are basic such as length and time, others are derived such as
velocity. Each variable has units to describe the magnitude of that quantity. Lengths in SI units are described in units of
meters. The “Meter” is the unit of the dimension of length (L); hence the area will have dimension of L2, and volume L3.
Time will have units of seconds (T), hence velocity is a derived quantity with dimensions of (LT1) and units of meter per
second. A list of some variables is given in Table 1 with their units and dimensions.
Definitions of Some Basic SI Units
Mass: The kilogram is the mass of a platinumiridium cylinder kept at Sevres in France.
Length: The metre is now defined as being equal to 1 650 763.73 wavelengths in vacuum of the orange line
emitted by the Krypton86 atom.
Time: The second is defined as the fraction 1/31 556 925.975 of the tropical year for 1900. The second is
also declared to be the interval occupied by 9 192 631 770 cycles of the radiation of the caesium atom
corresponding to the transition between two closely spaced ground state energy levels.
Temperature: The Kelvin is the degree interval on the thermodynamic scale on which the temperature of the triple
point of water is 273.16 K exactly. (The temperature of the ice point is 273.15 K).
Definitions of Some Derived SI Units
Force:
The Newton is that force which, when acting on a mass of one kilogram gives it an acceleration of one metre per second
per second.
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8 Engineering Fluid Mechanics Notation
Work Energy, and Heat:
The joule is the work done by a force of one Newton when its point of application is moved through a distance of one metre
in the direction of the force. The same unit is used for the measurement of every kind of energy including quantity of heat.
The Newton metre, the joule and the watt second are identical in value. It is recommended that the Newton is kept for
the measurement of torque or moment and the joule or watt second is used for quantities of work or energy.
Quantity Unit Symbol
Length [L] Metre m
Mass [m] Kilogram kg
Time [ t ] Second s
Electric current [ I ] Ampere A
Temperature [ T ] degree Kelvin K
Luminous intensity [ Iv ] Candela cd
Table 1: Basic SI Units
Quantity Unit Symbol Derivation
Force [ F ] Newton N kgm/s2
Work, energy [ E ] joule J Nm
Power [ P ] watt W J/s
Pressure [ p ] Pascal Pa N/m2
Table 2: Derived Units with Special Names
Quantity Symbol
Area m2
Volume m3
Density kg/m3
Angular acceleration rad/s2
Velocity m/s
Pressure, stress N/m2
Kinematic viscosity m2/s
Dynamic viscosity Ns/m2
Momentum kgm/s
Kinetic energy kgm2/s2
Specific enthalpy J/kg
Specific entropy J/kg K
Table 3: Some Examples of Other Derived SI Units
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9 Engineering Fluid Mechanics Notation
Quantity Unit Symbol Derivation
Time minute min 60 s
Time hour h 3.6 ks
Temperature degree Celsius oC K  273.15
Angle degree o π/180 rad
Volume litre l 103 m3 or dm3
Speed kilometre per hour km/h 
Angular speed revolution per minute rev/min 
Frequency hertz Hz cycle/s
Pressure bar b 102 kN/m2
Kinematic viscosity stoke St 100 mm2/s
Dynamic viscosity poise P 100 mNs/m2
Table 4: NonSI Units
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