Introduction to Fluid Mechanics

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.

2
Course Organization

• Textbook deNevers Fluid Mechanics for Chemical
  Engineers
• Introduction (Chapter 1) / Dimensions, Units
• Fluid statics Fluid is at rest
• Fluid mechanics
• Fluid dynamics Fluid is moving
• Fluid statics (Chapter 2) Pressure, measurement
  of pressure, hydrostatic forces, buoyancy
• Fluid dynamics (Chapters 3-5, 7) Mass, energy
  and momentum balances
• Applications in Engineering (Chapters 6, 9, 11,
  12) Flow in pipes, turbomachines, flow over
  immersed bodies, flow through porous media
• Dimensional analysis and modeling (Chapter 13)

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

4
Dimensions and Units

• Conversion factors are available in the textbook
  inside of front cover.

5
Units of Force Newtons Law Fm.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), 32.174
  ft/s2.

6
Units of Force EE system

• To make Newtons law dimensionally consistent we
  must include a dimensional proportionality
  constant

where
7
Example Newtons Law

• An astronaut weighs 730N in Houston, TX, where
  the local acceleration of gravity is g9.792
  m/s2. What is the mass of the astronaut? What is
  his weight on the moon, where g1.67 m/s2?
• Redo the same problem in EE units. In EE units
  the astronaut weighs 164.1lbf, gHouston32.13
  ft/s2 and gmoon5.48 ft/s2.

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

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

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, Mmol. weight
• R 8.314 J/(g-mole K)0.08314 (liter
  bar)/(g-mole K)
• 0.08206 (liter atm)/(g-mole K)1.987
  (cal)/(g-mole K)
• 10.73 (psia ft3)/(lb-mole R)0.7302 (atm
  ft3)/(lb-mole R)

(1.1)
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)