Fenômentos de Transporte
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Fenômentos de Transporte


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-1 Momentum flux offluid in laminar flow in 
circular pipe 
4.1.1 Types of forces 
4.1.2 Influence of uniform pressure over entire surface of irregular 
objects 
Figure 4.1.2- 1 Approximation of solid by prisms 
Figure 4.1.2-2 Detail of prism 
4.1.3 Averages and the momentum equation 
Momentum balance approximation - turbulent flow 
Momentum balance approximation - laminar flow 
Example 4.1.3-1 Force on a nozzle 
Example 4.1.3-2 Thrust of aircru? engine 
Example 4.1.3-3 Piping support 
Example 4.1.3-4 Jet bout 
Exclmple 4.1.3-5 Horizontal force on tunk 
4.2 The Microscopic Momentum Balance 
4.3 Summary of Balance Equations and Constitutive Relationships 
4.4 The Momentum Equation in Non-Inertial Reference Frames 
Chapter 4 Problems 
Table 4.3-1 Tabulation of balance equations 
Table 4.3-2 Tabulation of common constitutive relationships 
5 APPLICATION OF DIMENSIONAL 
ANALYSIS 
5.1 Systems of Measurement 
Example 5. I -I Weight vs. mass; g vs. g, 
Table 5.1 - la Systems of Units 
Table 5.1 - 1 b Systems of Units 
Table 5.1-2 SI Prefixes 
5.2 Buckingham's Theorem 
Example 5.2-1 Dimensionless variables for pipe flow 
5.2.1 Friction factors and drag coefficients 
5.2.2 Shape factors 
Example 5.2.2-1 Drag force on ship hull 
Exumple 5.2.2-2 Deceleration of compressible fluid 
5.3 Systematic Analysis of Variables 
Example 5.3-1 Drag force on a sphere 
Example 5.3-2 Dimensionless groups foraflow over u flut 
plate 
Example 5.3-3 Consistency of dimensionless groups across 
system of dimensions 
Example 5.3-4 Capillary interface height via dimensional 
analysis 
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5.4 Dimensionless groups and differential models 
Example 5.4-1 Pipe jlow of incompressible fluid with 
constant viscosity 
Example 5.4-2 One-dimensional energy transport 
Example 5.4-3 Mass transport in a binary mixture 
Example 5.4-4 Extrapolating m d e l results j?om one 
category of momentum, heat, or m s s transport to another 
Table 5.4- 1 Dimensionless variables 
Table 5.4-2 Dedimensionalized balance equations 
Table 5.4-3 Dimensionless numbers 
5.5 Similarity, Models and Scaling 
Example 5.5-1 Drag on immersed body 
Example 5.5-2 Scale effects 
Chapter 5 Problems 
6 MOMENTUM TRANSFER IN FLUIDS 
6.1 Fluid Statics 
6.1.1 Manometers 
Example 6.1.1 -1 Pressure difference using a manometer 
Figure 6.1.1 - 1 Measurement of pressure difference with 
manometer 
Example 6.1.1-2 Pressure dinerence between tanks 
Figure 6.1.1-2 Pressure difference between tanks 
Example 6.1.1-3 Differential manometer 
Figure 6.1.1-3 Differential manometer 
Figure 6.2-1 Paths between streamlines 
6.2 Description of Flow Fields 
6.2.1 Irrotational flow 
6.3 Potential Flow 
Table 6.3-1 Elementary plane flows 
Table 6.3-2 Superposition of elementary plane flows 
Example 6.3-1 Flow around a circular cylinder 
Example 6.3-2 Flow of an ideal jluid through a corner 
Example 6.3-3 Flow around a rotating cylinder 
Figure 6.3- 1 Flow around circular cylinder 
Figure 6.3-2 Flow through a corner 
6.4 Laminar Flow 
6.4.1 Laminar flow between infinite parallel plates 
Figure 6.4.1-1 Steady flow between infinite stationary parallel 
plates 
Example 6.4. I - I Steady flow between infinite parallel 
plates 
Figure 6.4.1-2 Flow between infinite parallel plates, top plate 
moving at vo 
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Figure 6.4.1-3 Velocity profiles for laminar flow of 
Newtonian fluid between parallel plates with imposed pressure 
drop, top plate moving at steady velocity 
Example 6.4.1-2 Flow between infinite rotating concentric 
cylinders 
6.4.2 Laminar flow in a circular pipe 
Figure 6.4.2-1 Control volume for force balance on fluid in 
Figwe 6.4.2-2 Velocity profile for laminar flow of a 
Newtonian fluid in a pipe or duct of circular cross-section 
Figure 6.4.2-3 Shear stress profile for laminar flow of a 
Newtonian fluid in a pipe or duct of circular cross-section 
Pipe 
Example 6.4.2-1 Flow in a capillary viscometer 
Example 6.4.2-2 Flow between two concentric cylinders 
Example 6.4.2-3 Film jlow down U wall 
Example 6.4.2-4 Flow adjacent to ujlat plate 
instantuneously set in motion 
Figure 6.4.2-4 Viscometric flow between cylinders 
Figure 6.4.2-5 Film flow down wall 
Figure 6.4.2-6 Flow adjacent to flat plate instantaneously set 
in motion 
6.5 Turbulent Flow 
Figure 6.5-1 Local velocity in turbulent flow as a function of 
time 
Figure 6.5-2 Laminar and time-smoothed turbulent (1/7 power 
model) velocity profiles in steady pipe flow 
6.5.1 Time averaging the equations of change 
Exumple 6.5-2 Time averaging of velocity product 
6.5.2 The mixing length model 
Figure 6.5.2-1 Mixing length model 
Figure 6.5.2-2 Universal velocity distribution 
Example 6.5.2-1 Size of sublayer and bu$er tone in 
turbulent jlow 
6.6 The Boundary Layer Model 
Figure 6.6-1 Boundaq layer development on flat plate 
6.6.1 Momentum balance - integral equations 
Figure 6.6.1-1 Element in boundary layer 
Figure 6.6.1-2 Velocity profile development in the entrance 
region to a pipe 
6.6.2 De-dimensionalhation of tbe boundary layer equations 
6.6.3 Exact solution of the momentum boundary layer equations via 
similarity variables 
Example 6.6-1 Displacement thickness 
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xviii Tuble of Contents 
Example 6.6.3-1 Similarity vuriuble developed from 
dimensional analysis 
Example 6.6.3-2 Runge-Kuttu solution of Blusius problem 
Figure 6.6.3-1 Solution to Blasius boundary layer equation 
6.7 Drag Coefficients 
Figure 6.7-1 Flow around an airfoil (a) without and (b) with 
separation 
6.7.1 Drag on immersed bodies (external flow) 
Figure 6.7.1-1 Drag coefficient for smooth flat plate oriented 
parallel to flow stream 
Example 6.7.1-1 Drag on u flat plute 
Figure 6.7.1-2 Flow past circular cylinder 
Figure 6.7.1-3 Drag coefficient for circular cylinder 
Figure 6.7.1-4 Drag coefficient for sphere 
Exumple 6.7.1-2 Wind force on U distillation column 
Exumpk 6.7.1-3 Ternziniil velocity of a polymer sphere in 
water 
6.7.2 Drag in conduits - pipes (internal flow) 
Table 6.7.2- 1 Properties of pipe 
Figure 6.7.2-1 Momentum balance on cylindrical fluid element 
in horizontal pipe 
Figure 6.7.2-2 Momentum balance on cylindrical fluid element 
in non-horizontal pipe 
Figure 6.7.2-3 Moody friction factor chart 
Figure 6.7.2-4 Relative roughness for clean new pipes 
Example 6.7.2-1 Expunsion losses 
Figure 6.7.2-5 Equivalent lengths for losses in pipes 
Example 6.7.2-2 Direction o f f o w between tunks at 
differing pressures und heights 
Exmzple 6.7.2-3 Friction loss in (I piping system 
Case 1: Pressure drop unknown 
Exumple 6.7.2-4 Pressure loss for flow between tunks 
Case 2: Diameter unknown 
Example 6.7.2-5 Transfer line from tank to column 
Example 6.7.2-6 Minimum pipe diameter 
Exumple 6.7.2-7 Air supply through hose 
Emrnple 6.7.2-8 Flow rute unknown 
Example 6.7.2-9 Culculution o f f o w rute via Kurmun 
number when pressure drop is known 
Friction factor calculations - serial paths 
Case 3: Length unknown 
Case 4: Flow rate unknown 
Figure 6.7.2-6 Friction factor vs. Karman number 
Non-circular