1. Introduction to Fluid Mechanics
Fluid Mechanics is concerned with the behavior of fluids at rest and in motion
Distinction between solids and fluids:
According to our experience: A solid is “hard” and not easily deformed. A fluid is “soft” and deforms easily.
Fluid is a substance that alters its shape in response to any force however small, that tends to flow or to conform to the outline of its container, and that includes gases and liquids and mixtures of solids and liquids capable of flow.
A fluid is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude.
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2. Introduction Fluid statics: Fluid is at rest Fluid mechanics
Fluid dynamics: Fluid is moving
Fluid statics: Pressure, measurement of pressure, hydrostatic forces, buoyancy
Fluid dynamics: Mass, energy and momentum balances
Applications in Engineering: Flow in pipes, turbo machines, flow over immersed bodies, flow through porous media
Dimensional analysis and modeling
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3. Dimensions and Units
In fluid mechanics we must describe various fluid characteristics in terms of certain basic quantities such as length, time and mass
A dimension is the measure by which a physical variable is expressed qualitatively, i.e. length is a dimension associated with distance, width, height, displacement.
Basic dimensions: Length, L
(or primary quantities) Time, T
Mass, M
Temperature, Q
We can derive any secondary quantity from the primary quantities i.e. Force = (mass) x (acceleration) : F = M L T-2
A unit is a particular way of attaching a number to the qualitative dimension: Systems of units can vary from country to country, but dimensions do not
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4. Operations with Units
Only add and subtract numbers with the same associated units
2 kg + 3 m Invalid
If the dimensions are the same but the units differ, first convert to a common set of units
1 lb g Invalid
1 lb g lb lb = 1.88 lb Valid
You can multiply and/or divide unlike units, but you cannot cancel units unless they are the same
Valid
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5. Dimensions and Units
Primary Dimension
SI Unit
British Gravitational (BG) Unit
English Engineering (EE) Unit
Mass [M]
Kilogram (kg)
Slug
Pound-mass (lbm)
Length [L]
Meter (m)
Foot (ft)
Time [T]
Second (s)
Temperature [Q]
Kelvin (K)
Rankine (°R)
Force [F]
Newton
(1N=1 kg.m/s2)
Pound (lb)
Pound-force (lbf)
Conversion factors are available in the front page of many text books.
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6. Units of Force: Newton’s Law F=m.g
SI system: Base dimensions are Length, Time, Mass, Temperature
A Newton is the force which when applied to a mass of 1 kg produces an acceleration of 1 m/s2.
Newton is a derived unit: 1N = (1Kg).(1m/s2)
BG system: Base dimensions are Length, Force, Time, Temperature
A slug is the mass which produces an acceleration of 1 ft/s2 when a force of 1lb is applied on it:
Slug is a derived unit: 1slug=(1lb) (s2)/(ft)
EE system: Base dimensions are Length, Time, Mass, Force and Temperature
The pound-force (lbf) is defined as the force which accelerates 1pound-mass (lbm), ft/s2.
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7. Units of Force – EE system
To make Newton’s law dimensionally consistent we must include a dimensional proportionality constant:
where
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8. Dimensional Homogeneity
All theoretically derived equations are dimensionally homogeneous: dimensions of the left side of the equation must be the same as those on the right side.
Some empirical formulas used in engineering practice are not dimensionally homogeneous
All equations must use consistent units: each term must have the same units. Answers will be incorrect if the units in the equation are not consistent. Always chose the system of units prior to solving the problem
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9. Properties of Fluids
Fundamental approach: Study the behavior of individual molecules when trying to describe the behavior of fluids
Engineering approach: Characterization of the behavior by considering the average, or macroscopic, value of the quantity of interest, where the average is evaluated over a small volume containing a large number of molecules
Treat the fluid as a CONTINUUM: Assume that all the fluid characteristics vary continuously throughout the fluid
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10. Measures of Fluid Mass and Weight
Density of a fluid, r (rho), is the amount of mass per unit volume of a substance: r = m / V
For liquids, weak function of temperature and pressure
For gases: strong function of T and P
from ideal gas law: r = P M/R T
where R = universal gas constant, M=mol. weight
R= J/(g-mole K)= (liter bar)/(g-mole K)=
(liter atm)/(g-mole K)=1.987 (cal)/(g-mole K)=
10.73 (psia ft3)/(lb-mole °R)= (atm ft3)/(lb-mole °R)
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11. Measures of Fluid Mass and Weight
Specific volume: u = 1 / r
Specific weight is the amount of weight per unit volume of a substance: g = w / V = r g
Specific Gravity (independent of system of units)
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12. Pressure Pascal’s Laws Pascals’ laws:
Pressure is defined as the amount of force exerted on a unit area of a substance:
P = F / A
Pascal’s Laws
Pascals’ laws:
Pressure acts uniformly in all directions on a small volume (point) of a fluid
In a fluid confined by solid boundaries, pressure acts perpendicular to the boundary – it is a normal force.
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13. Direction of fluid pressure on boundaries
Furnace duct
Pipe or tube
Heat exchanger
Pressure is due to a Normal Force
(acting perpendicular to
the surface)
It is also called a Surface Force
Dam
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14. Absolute and Gauge Pressure
Gauge pressure: Pressure expressed as the difference between the pressure of the fluid and that of the surrounding atmosphere.
Usual pressure gauges record gauge pressure. To calculate absolute pressure:
Pabs = Patm + Pgauge
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15. Units for Pressure Unit Definition or Relationship 1 pascal (Pa)
1 kg m-1 s-2
1 bar
1 x 105 Pa
1 atmosphere (atm)
101,325 Pa
1 torr
1 / 760 atm
760 mm Hg
1 atm
pounds per sq. in. (psi)
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16. Pressure distribution for a fluid at rest
We will determine the pressure distribution in a fluid at rest in which the only body force acting is due to gravity
The sum of the forces acting on the fluid must equal zero
Consider an infinitesimal rectangular fluid element of dimensions Dx, Dy, Dz z y x
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17. Pressure distribution for a fluid at rest
Let Pz and Pz+Dz denote the pressures at the base and top of the cube, where the elevations are z and z+Dz respectively.
Force at base of cube: Pz A=Pz (Dx Dy)
Force at top of cube: Pz+Dz A= Pz+Dz (Dx Dy)
Force due to gravity: m g=r V g = r (Dx Dy Dz) g
A force balance in the z direction gives:
For an infinitesimal element (Dz0) 
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18. Incompressible fluid
Liquids are incompressible i.e. their density is assumed to be constant
When we have a liquid with a free surface the pressure P at any depth below the free surface is:
where Po is the pressure at the free surface (Po=Patm) and h = zfree surface - z
By using gauge pressures we can simply write:
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19. Examples
SG= 13.6
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20. Solution:
1.1
1.2
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21. 1.3
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22. Dr Mustafa Nasser

23. Dr Mustafa Nasser

24. Example 1: 5. 6m3 of oil weighs 46 800 N
Example 1: 5.6m3 of oil weighs N. Find its mass density, and relative density, g.
Example 2: In a fluid the velocity measured at a distance of 75mm from the boundary is 1.125m/s. The fluid has absolute viscosity Pa s and relative density What is the velocity gradient and shear stress at the boundary assuming a linear velocity distribution.
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25. Solution 2 Solution 1: Weight 46 800 = mg
Mass m = / 9.81 = kg
Mass density r = Mass / volume = / 5.6 = 852 kg/m3
Relative density 
Solution 2
m = Pa s
g = 0.913
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