IntoductionChee 2231.1 Introduction to Fluid Mechanics Fluid Mechanics is concerned with the...
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Intoduction Chee 223 1.1
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.
Intoduction Chee 223 1.2
Course Organization
Textbook: deNevers “Fluid Mechanics for Chemical Engineers”
Introduction (Chapter 1) / Dimensions, Units
Fluid statics: Fluid is at restFluid 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)
Intoduction Chee 223 1.3
Introduction
Intoduction Chee 223 1.4
Dimensions and UnitsIn 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, MTemperature,
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
Intoduction Chee 223 1.5
Dimensions and Units
Primary Dimension
SI UnitBritish
Gravitational (BG) Unit
English Engineering (EE) Unit
Mass [M] Kilogram (kg) SlugPound-mass (lbm)
Length [L] Meter (m) Foot (ft) Foot (ft)
Time [T] Second (s) Second (s) Second (s)
Temperature [] Kelvin (K) Rankine (°R) Rankine (°R)
Force [F]Newton
(1N=1 kg.m/s2)Pound (lb) Pound-force (lbf)
Conversion factors are available in the textbook inside of front cover.
Intoduction Chee 223 1.6
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), 32.174 ft/s2.
Intoduction Chee 223 1.7
Units of Force – EE system
To make Newton’s law dimensionally consistent we must include a dimensional proportionality constant:
cg
gmF
where
2f
mc )s)(lb(
)ft)(lb(1740.32g
Intoduction Chee 223 1.8
Example: Newton’s Law
• An astronaut weighs 730N in Houston, TX, where the local acceleration of gravity is g=9.792 m/s2. What is the mass of the astronaut? What is his weight on the moon, where g=1.67 m/s2?
• Redo the same problem in EE units. In EE units the astronaut weighs
164.1lbf, gHouston=32.13 ft/s2 and gmoon=5.48 ft/s2.
Intoduction Chee 223 1.9
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
Intoduction Chee 223 1.10
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
Intoduction Chee 223 1.11
Measures of Fluid Mass and Weight• Density of a fluid, (rho), is the amount of mass per unit volume of a
substance: = m / V
– For liquids, weak function of temperature and pressure
– For gases: strong function of T and P
from ideal gas law: = P MR T
where R = universal gas constant, M=mol. 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)
)T,P(
(1.1)
Intoduction Chee 223 1.12
Measures of Fluid Mass and Weight
• Specific volume: = 1 /
• Specific weight is the amount of weight per unit volume of a substance:
= w / V = g
• Specific Gravity (independent of system of units)
C4@OH2
SG