H
`
`A (cid:9)
`
`A
`
`A
`
`A
`
`4
`
`.
`
`. (cid:9)
`
`. (cid:9)
`
`4
`
`p
`
`.
`
`..
`
`. (cid:9)
`
`(cid:149)t (cid:9)
`
`. (cid:9)
`
`.
`
`:p
`
`-
`
`(cid:149)(cid:149)--
`
`? (cid:9)
`
`I (cid:149) (cid:9)
`I
`
`4
`
`ENGEL
`AJNUS A
`SJOHNM CIMBALA
`
`1
`
`

`
`
`
`FLUID MECHANICS
`FLUID MECHA
`
`t:::i§:
`U......
`
`F U N pm EN TA,L$ A“.\}I:¢;D' A P P'u_—1‘-_<5-.'2"x_‘.‘r‘1_"e)_"l‘o¢§g'
`FUNDAMENTALS AND APPLICATIONS
`|-
`'..|¢-'.‘_.
`
`n._..,
`
`2
`
`

`
`Higher Education
`
`FLUID MECHANICS: FUNDAMENTALS AND APPLICATIONS
`
`Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc.,
`1221 Avenue of the Americas, New York, NY 10020. Copyright ' 2006 by
`The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication
`may be reproduced or distributed in any form or by any means, or stored in a database
`or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc.,
`including, but not limited to, in any network or other electronic storage or transmission,
`or broadcast for distance learning.
`
`Some ancillaries, including electronic and print components, may not be available
`to Customers outside the United States.
`
`This book is printed on acid-free paper.
`
`345 67 8 9 0 DOW/DOW 098 76
`
`ISBN-13: 978-0--07-247236-3
`ISBN-10: 0-07--247236-7
`
`Senior Sponsoring Editor: Sszanne Jeans
`Managing Developmental Editor: Debra D. Matteson
`Developmental Editor: Kate Schein,nan
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`Compositor: Lachina Publishing Services
`Typeface: 10.5112 Times Roman
`Printer: R. R. Donnelley Willard, OH
`
`Library of Congress Cataloging-in-Publication Data
`
`cengel, Yunus A.
`Fluid mechanics : fundamentals and applications / Yunus A. cengeL John M. Cimbala.(cid:151)1 St ed.
`cm.(cid:151)(McGraw-Hill series in mechanical engineering)
`p. (cid:9)
`ISBN 0-07-247236-7
`1. Fluid dynamics. I. Cimbala, John M. II. Title. III. Series.
`
`TA357.C43 2006
`620.1 ’06(cid:151)dc22
`
`www.mhhc.com
`
`2004058767
`CIP
`
`3
`
`(cid:9)
`

`
`FLOW IN PIPES
`
`F luid flow in circular and noncircular pipes is commonly encountered in
`
`practice. The hot and cold water that we use in our homes is pumped
`through pipes. Water in a city is distributed by extensive piping net-
`works. Oil and natural gas are transported hundreds of miles by large
`pipelines. Blood is carried throughout our bodies by arteries and veins. The
`cooling water in an engine is transported by hoses to the pipes in the radia-
`tor where it is cooled as it flows. Thermal energy in a hydronic space heat-
`ing system is transferred to the circulating water in the boiler, and then it is
`transported to the desired locations through pipes.
`Fluid flow is classified as external and internal, depending on whether the
`fluid is forced to flow over a surface or in a conduit. Internal and external
`flows exhibit very different characteristics. In this chapter we consider inter-
`nal flow where the conduit is completely filled with the fluid, and flow is
`driven primarily by a pressure difference. This should not be confused with
`Open-channel flow where the conduit is partially filled by the fluid and thus
`the flow is partially bounded by solid surfaces, as in an irrigation ditch, and
`flow is driven by gravity alone.
`We start this chapter with a general physical description of internal flow
`and the velocity boundary layer. We continue with a discussion of the
`dimensionless Reynolds number and its physical significance. We then dis-
`cuss the characteristics of flow inside pipes and introduce the pressure drop
`")II-lations associated with it for both laminar and turbulent flows. Then
`ve Present the minor losses and determine the pressure drop and pumping
`requirements for real-world piping systems. Finally, we present an
`ervlesv of flow measurement devices.
`
`6
`
`

`
`330
`FLUID MECHANICS
`
`mp=16hP (cid:9)
`
`D (cid:9)
`
`v (cid:9)
`
`= I hp (cid:9)
`
`- (cid:9)
`
`2D (cid:9)
`
`- (cid:9)
`
`FUR1 4- (cid:9)
`The pumping power requirement for (cid:9)
`a laminar flow piping system can be (cid:9)
`reduced by a factor of 16 by doubling (cid:9)
`the pipe diameter, (cid:9)
`
`[also called the Fanning friction factor, named after the American ergj1
`John Fanning (1837-1911)], which is defined as Cf = 2T ,, /(pV 2
`f/4
`(cid:176)eC
`av-, ) (cid:9)
`Setting Eqs. 8-20 and 8-21 equal to each other and solving forf gi ve
`friction factor for fully developed laminar flow in a circular pipe,
`64i (cid:9)
`64
`------ =
`
`Circi.thu pipe. lcituivii
`
`/ = (cid:9)
`
`This equation shows that in laminar flow, the friction factor is a functj 00
`the Reynolds number only and is independent of the roughness of the
`Pe
`surface. (cid:9)
`In the analysis of piping systems, pressure losses are commonly expressed
`in terms of the equivalent fluid column height, called the head loss hL , N
`ing from fluid statics that AP = pgh and thus a pressure difference of
`corresponds to a fluid height of h = iXP/pg, the pipe head loss is obtained
`by dividing APL by pg to give
`
`110(1(1 los: (cid:9)
`
`li (cid:9)
`
`P1 (cid:9)
`
`L
`= .1. - --- (cid:9)
`
`(8-24
`
`(8-25)
`
`The head loss hL represents the additional height that the fluid needs to b e
`raised by a pump in order to overcome the frictional losses in the pipe. The
`head loss is caused by viscosity, and it is directly related to the wall shear
`stress. Equations 8-21 and 8-24 are valid for both laminar and turbulent
`flows in both circular and noncircular pipes, but Eq. 8-23 is valid only r
`fully developed laminar flow in circular pipes.
`Once the pressure loss (or head loss) is known, the required pumpin g
`power to overcome the pressure loss is determined from
`L =APL = lip gh = thgh (cid:9)
`where li is the volume flow rate and this the mass flow rate.
`The average velocity for laminar flow in a horizontal pipe is, from Eq. 8-20.
` D2
`F - P(L) (cid:9)
`_\P
`(cid:9) = ---- (cid:9)
`32pL
`
`Hori:oii to! pipo: (cid:9)
`
`V (cid:9)
`
`P - P)R (cid:9)
`8pL (cid:9)
`Then the volume flow rate for laminar flow through a horizontal pipe of
`diameter D and length L becomes
`
`=
`
`32jrL (cid:9)
`
`(8--26)
`
`(= V A = (cid:9)
`
`= (cid:9)
`
`- (cid:9)
`128pL (cid:9)
`
`(8-27)
`
`= AP’’ (cid:9)
`28ts1.
`p.L (cid:9)
`This equation is known as Poiseuille’s law, and this flow is called Hagen
`Poiseuille flow in honor of the works of U. Hagen (1797-1884) and J.
`Poiseuille (1799-1869) on the subject. Note from Eq. 8-27 that
`for a spec"
`fled flow rate, the pressure drop and thus the required pumping power is p10
`portional to the length of the pipe and the viscosity of the fluid, but it /1
`inversely proportional to the fourth power of the radius (or diameter) of tin
`bL
`pipe. Therefore, the pumping power requirement for a piping system can
`reduced by a factor of 16 by doubling the pipe diameter (Fig. 8-14
`eicTbe ti
`course the benefits of the reduction in the energy costs must be
`against the increased cost of construction due to using a larger-diameter PiPt
`The pressure drop A P equals the pressure loss LPL in the case of a hO
`izontal pipe, but this is not the case for inclined pipes or pipes with
`able cross-sectional area. This can be demonstrated by writing the eflet.
`
`7
`
`

`
`(8-28)
`
`equation for steady, incompressible one-dimensional flow in terms of heads
`as (see Chap. 5)
`V
`F) (cid:9)
`V (cid:9)
`F i (cid:9)
`- + n i- + Z1 + hpmp.0 =
`+ a2 - + Z2 + hturhjnee + hL (cid:9)
`2g
`P9 (cid:9)
`P9 (cid:9)
`is the useful pump head delivered to the fluid, hturbifle e is the
`where hpump ,
`turbine head extracted from the fluid,
`h1 is the irreversible head loss
`between sections 1 and 2, V 1 and V2 are the average velocities at sections
`1 and 2, respectively, and cr and a2 are the kinetic energy correction factors
`at sections 1 and 2 (it can be shown that a = 2 for fully developed laminar
`flow and about 1.05 for fully developed turbulent flow). Equation 8-28 can
`be rearranged as
`- P2 = p(aV - 1 V)I2 + pg[(z 2 - z 1 ) + h5ar5jnee - hpumpu + hL]
`(829)
`Therefore, the pressure drop A P = P1 - P2 and pressure loss APL = pghL
`for a given flow section are equivalent if (1) the flow section is horizontal
`so that there are no hydrostatic or gravity effects (z 1 = z2) (2) the flow sec-
`tion does not involve any work devices such as a pump or a turbine since
`(hpump, u = hturbine e = 0), (3) the cross-sectional
`they change the fluid pressure
`area of the flow section is constant and thus the average flow velocity is
`constant (V1 = V2), and (4) the velocity profiles at sections 1 and 2 are the
`same shape (a 1 = a7).
`
`Inched Pipes
`Relations for inclined pipes can be obtained in a similar manner from a force
`balance in the direction of flow. The only additional force in this case is the
`Component of the fluid weight in the flow direction, whose magnitude is
`= W sin 0 = (cid:9)
`sin 0 = pg(27rr dr dx) sin 6
`(8-30)
`Where 0 is the angle between the horizontal and the flow direction (Fig. (cid:9)
`8-15). The force balance in Eq. 8-9 now becomes (cid:9)
`(2r dr P) - (2r dr (cid:9)
`+ (2r dx r) (cid:9)
`- (2rdxT),. +ar - pgrrdrdx)sin 0 = 0 (cid:9)
`Which results in the differential equation
`i d ( du) - dP
`m
`r dx U - U - pgs
`P011o:jg the same solution procedure, the velocity profile can be shown to be
`R2 (dP (cid:9)
`r’\
`"ii (cid:9)
`u(r) = -- (cid:9)
`- -) (cid:9)
`4A dx
`It can also be shown that the alerage velocity and the volume flow rate rela-
`for laminar flow through inclined pipes are, respectively,
`’L sin H: (cid:9)
`ID (cid:9)
`1L i H )D n
`
`-- (cid:9)
`= ----(cid:149) p- (cid:9)
` --
`128 10 1,
`.
`Which
`are identical to the corresponding relations for horizontal pipes, except
`at AP is replaced by LIP - pgL sin 9. Therefore, the results already
`that ’fled for horizontal pipes can also be used for inclined pipes provided
` AP is replaced by LIP - pgL sin 0 (Fig. 8-16). Note that 0> 0 and thus
`0 for uphill flow, and 0 < 0 and thus sin 0 <0 for downhill flow.
`
`(8-31)
`
`(8-32)
`
`(8-33)
`
`+ pg sin (cid:9)
`
`and (cid:9)
`
`/ = - (cid:9)
`
`
`
`(8-34)
`
`CHAPTER (cid:9)
`
`-
`
`sinO
`
`X (cid:9)
`
`71
`
`FIGURE 8-15
`Free-body diagram of a ring-shaped
`differential fluid element of radius r,
`thickness dr, and length dx oriented
`coaxially with an inclined pipe in fully
`developed laminar flow.
`
`Ho,’ontal (cid:9)
`
`AP 7TD 4
`1285tL
`
`Inclined pipe: (cid:9)
`
`- pgL sin 0)77D4
`128sL
`
`- (cid:9)
`
`Uphill flow: 0 >0 and sin 0>0
`
`Downhill flow: 0 <Band sin 0 <0
`
`FIGURE 8-16
`The relations developed for fully
`developed laminar flow through
`horizontal pipes can also be used
`for inclined pipes by replacing
`LIP with 4T- pgL sin 8.
`.7
`
`8
`
`(cid:9)
`(cid:9)
`(cid:9)
`(cid:9)
`

`
`a
`
`a, a
`A, A c
`Ar
`AR
`b
`
`bhp
`B
`
`Bi
`Bo
`
`C
`
`C’
`
`C
`
`P
`
`C V
`C
`C
`
`Ca
`
`CD, C0
`
`Cd
`C1, C1
`
`CH
`
`CL, C1_1
`
`31s: height from
`Manning constant, m(cid:176)
`channel bottom to bottom of sluice gate, m
`Acceleration and its magnitude, m/s 2
`Area, m 2 ; cross-sectional area, m2
`Archimedes number
`Aspect ratio
`Width or other distance, m; intensive
`property in RTT analysis; turbomachinery
`blade width, m
`Brake horsepower, hp or kW
`Center of buoyancy; extensive property in
`RTT analysis
`Biot number
`Bond number
`Specific heat for incompressible
`substance, kJ/kg (cid:9) K; speed of sound, m/s;
`speed of light in a vacuum, m/s;
`chord length of an airfoil, m
`Wave speed, mis
`Constant-pressure specific heat, kJ/kg (cid:9) K.
`Constant-volume specific heat, id/kg (cid:9) K
`Dimension of the amount of light
`Bernoulli constant, M2/S2 or m/t 2 (cid:9) L,
`depending on the form of Bernoulli
`equation; Chezy coefficient, in 1/2/s;
`circumference, in
`Cavitation number
`Drag coefficient; local drag coefficient
`Discharge coefficient
`Fanning friction factor or skin friction
`coefficient; local skin friction coefficient
`Head coefficient
`Lift coefficient; local lift coefficient
`
`CNPSH
`CP
`C0
`C0
`CQ
`cs
`cv
`cd
`D or d
`
`DAB
`D1
`D1,
`e
`-,
`e, (cid:9) e 0
`
`E
`E, E
`Ec
`EGL
`E
`Eu
`f
`
`F, F
`F5
`F0
`F1
`
`FL
`
`Suction head coefficient
`Center of pressure
`Pressure coefficient
`Power coefficient
`Capacity coefficient
`Control surface
`Control volume
`Weir discharge coefficient
`Diameter, m (d typically for a smaller
`diameter than D)
`Species diffusion coefficient, m2/s
`Hydraulic diameter, in
`Particle diameter, m
`Specific total energy, kJ/kg
`
`Unit vector in r- and 0-direction,
`respectively
`Voltage, V
`Total energy, kJ: and rate of energy, kJ/s
`Eckert number
`Energy grade line, m
`Specific energy in open-channel flows, m
`Euler number
`Frequency, cycles/s; Blasius boundary
`layer dependent similarity variable
`Darcy friction factor; and local Darcy
`friction factor
`Force and its magnitude, N
`Magnitude of buoyancy force, N
`Magnitude of drag force, N
`Magnitude of drag force due to friction, N
`Magnitude of lift force, N
`
`ho
`Fr
`FT
`,’, g
`
`g
`
`C
`GM
`Gr
`h
`
`hfg
`hL
`H
`
`H,H
`
`HGL
`
`I
`/
`
`Fourier number
`Froude number
`Magnitude of tension force, N
`Gravitational acceleration and its
`magnitude, m/s 2
`Heat generation rate per unit volume,
`W/m3
`Center of gravity
`Metacentric height, m
`Grashof number
`Specific enthalpy, Id/kg; height, m: head,
`rn; convective heat transfer coefficient,
`W/m2 K
`Latent heat of vaporization. kJ/kg
`Head loss, m
`Boundary layer shape factor; height, in:
`net head of a pump or turbine, m; total
`energy of a liquid in open-channel flow,
`expressed as a head, in; weir head, rn
`Moment of momentum and its magnitude,
`Nm’s
`Hydraulic grade line, in
`Gross head acting on a turbine, in
`Index of intervals in a CFD grid (typically
`in x-direction)
`Unit vector in x-direction
`Dimension of electric current
`2. current, A;
`Moment of inertia, N m
`turbulence intensity
`Second moment of inertia, m 4
`Reduction in Buckingham Pi theorem;
`index of intervals in a CFD grid (typically
`in y-direction)
`
`9
`
`

`
`j
`Ja
`k
`
`k
`ke
`K
`KE
`KL
`Kn
`
`L
`L
`Le
`L.
`
`m
`M, th
`M
`M, M
`
`Ma
`n
`
`ri, it
`
`n
`N
`N
`
`N
`NPSH
`N
`
`Unit vector in y-direction
`Jakob number
`Specific heat ratio; expected number of
`ils in Buckingham Pi theorem; thermal
`conductivity, W/m (cid:9) K; turbulent kinetic
`energy per unit mass, m 2/s2; index of
`intervals in a CFD grid (typically in
`z-direction)
`Unit vector in z-direction
`Specific kinetic energy. kJ/kg
`Doublet strength, rn 3/s
`Kinetic energy, kJ
`Minor loss coefficient
`Knudsen number
`Length or distance, in; turbulent length
`scale, m
`Dimension of length
`Length or distance, rn
`Lewis number
`Chord length of an airfoil, rn;
`characteristic length, m
`Hydrodynamic entry length, in
`Weir length, m
`Dimension of mass
`Mass, kg; and mass flow rate, kg/s
`Molar mass, kg/kmol
`Moment of force and its magnitude,
`N m
`Mach number
`Number of parameters in Buckingham Pi
`theorem; Manning coefficient
`Number of rotations; and rate of rotation,
`rpm
`Unit normal vector
`Dimension of the amount of matter
`Number of moles, mol or kmol; number
`of blades in a turbomachine
`Power number
`Net positive suction head, in
`Pump specific speed
`
`NS ,
`Nu
`p
`pe
`p, P’
`
`PE
`Pe
`Pgage
`
`Pr
`
`or P
`Pva~
`P1v
`q
`q
`
`Q, Q
`
`QEAS
`r
`
`R
`
`Ra
`Re
`Rh
`Ri
`R
`
`s
`
`S0
`
`Sc
`Sc
`
`Sf
`SG
`
`Turbine specific speed
`Nusselt number
`Wetted perimeter, rn
`Specific potential energy, kJ/kg
`Pressure and modified pressure, N/rn 2
`or Pa
`Potential energy, kJ
`Peclet number
`Gage pressure, N/rn2 or Pa
`Mechanical pressure, N/rn 2 or Pa
`Prandtl number
`Saturation pressure or vapor pressure, kPa
`Vacuum pressure, N/rn 2 or Pa
`Weir height, in
`Heat transfer per unit mass, kJ/kg
`Heat flux (rate of heat transfer per unit
`area), W/rn 2
`Total heat transfer, kJ; and rate of heat
`
`trans transfer, (cid:9)
`W
`kW
`or
`Equiangle skewness in a CFD grid
`Moment arm and its magnitude, m; radial
`coordinate, m; radius, m
`Gas constant, kJ/kg ’K; radius, in;
`electrical resistance,
`Rayleigh number
`Reynolds number
`Hydraulic radius, rn
`Richardson number
`Universal gas constant, kJ/kmol ’ K
`Submerged distance along the plane of
`a plate, ml; distance along a surface or
`streamline, m; specific entropy, kJ/kg ’ K;
`fringe spacing in LDV, m; turbomachinery
`blade spacing, m
`Slope of the bottom of a channel in open-
`channel flow
`Schmidt number
`Critical slope in open-channel flow
`Friction slope in open-channel flow
`Specific gravity
`
`Sh
`SP
`St
`Stk
`t
`
`t
`T
`T
`T, T
`a
`
`U1.
`
`U r
`
`U0
`
`U
`
`v
`
`v
`v, i1
` V, V
`
`V0
`
`w
`
`W
`W, W
`
`We
`X
`
`2
`
`Sherwood number
`Property at a stagnation point
`Stanton number; Strouhal number
`Stokes number
`Dimension of time
`Time, s
`Dimension of temperature
`Temperature, C or K
`Torque and its magnitude, N (cid:9)
`in
`Specific internal energy, kJ/kg; Cartesian
`velocity component in x-direction, rn/s
`Friction velocity in turbulent boundary
`layer, rn/s
`Cylindrical velocity component in
`r-dircction, mis
`Cylindrical velocity component in
`0 - direction, mis
`Cylindrical velocity component in
`z-direction, rn/s
`Internal energy, kJ; x-component of
`velocity outside a boundary layer (parallel
`to the wall), mis
`Cartesian velocity component in
`y-direction, rn/s
`Specific volume, m3/kg
`Volume, in 3 ; and volume flow rate, m3/s
`Velocity and its magnitude (speed), mis;
`average velocity, rn/s
`Uniform-flow velocity in open-channel
`flow, mis
`Work per unit mass, kJ/kg; Cartesian
`velocity component in z-direction, mis;
`width, m
`Weight, N; width, in
`Work transfer, kJ; and rate of work
`(power), W or kW
`Weber number
`Cartesian coordinate (usually to the right),
`in
`Position vector, in
`
`10
`
`

`
`Cartesian coordinate (usually up or into
`the page), m; depth of liquid in open-
`channel flow, in
`Normal depth in open-channel flow, in
`Cartesian coordinate (usually up), in
`
`Greek Letters
`Angle; angle of attack; kinetic energy
`a
`correction factor; thermal diffusivity,
`III 2/S; isothermal compressibility, kPa
`or atm
`Angular acceleration and its magnitude,
`
`a
`
`Y
`
`/3
`
`6
`
`6*
`c
`
`E Y
`
`F
`
`K
`
`A
`
`V
`P(Ma)
`
`IT
`
`Coefficient of volume expansion, K_ 1;
`momentum-flux correction factor; angle;
`diameter ratio in obstruction flowmeters;
`oblique shock angle; turbomachinery
`blade angle
`Boundary layer thickness, m; distance
`between streamlines, m; angle; small
`change in a quantity
`Boundary layer displacement thickness, m
`Mean surface roughness, m; turbulent
`dissipation rate, m2/s3
`Strain rate tensor,
`3
`Dissipation function, kg/rn (cid:9)
`Angle; velocity potential function, m2/8
`Specific weight, N/rn3
`Circulation or vortex strength, m 2/s
`Efficiency; Blasius boundary layer
`
`independent similarity variable
`Bulk modulus of compressibility, kPa or
`atm; log law constant in turbulent
`boundary layer
`Mean free path length, m; wavelength, m;
`second coefficient of viscosity, kg/rn
`Viscosity, kg/m- s; Mach angle
`Kinematic viscosity ni/S
`Prandtl(cid:151)Meyer function for expansion
`waves, degrees or rad
`Nondiniensional parameter in dimensional
`analysis
`
`Imna
`
`0
`
`p
`
`CT
`
`T
`
`T 11
`
`Ttj Wrb,,lent
`w, w
`
`1,fi
`,
`
`Subscripts
`
`0
`
`abs
`atm
`avg
`b
`
`C
`C
`cr
`CL
`CS
`CV
`e
`eff
`
`H
`lam
`L
`in
`
`Angle or angular coordinate; boundary
`layer momentum thickness, m; pitch angle
`of a turhomachiriery blade; turning or
`deflection angle of oblique shock
`Density, kg/m3
`Normal stress, N/rn2
`Stress tensor, N/rn 2
`Surface tension, N/rn
`Shear stress, N/m2
`Viscous stress tensor (also called shear
`stress tensor), N/rn 2
`Specific Reynolds stress tensor, m2/s2
`Angular velocity vector and its
`magnitude, rad/s; angular frequency, rad/s
`Stream function, m2/s
`Vorticity vector and its magnitued,
`
`Property of the far field
`Stagnation property; property at the origin
`or at a reference point
`Absolute
`Atmospheric
`Average quantity
`Property of the back or exit of a nozzle,
`e.g., back pressure Pb
`Acting at the centroid
`Pertaining to a cross section
`Critical property
`Pertaining to the centerline
`Pertaining to a control surface
`Pertaining to a control volume
`Property at an exit; extracted portion
`Effective property
`Property of a fluid, usually of a liquid
`Acting horizontally
`Property of a laminar flow
`Portion lost by irreversibilities
`Property of a model
`
`max
`mech
`min
`n
`P
`P
`
`R
`r
`rec
`ri
`rt
`S
`S
`sat
`sI
`st
`sub
`Sys
`t
`tri
`turb
`u
`V
`v
`vac
`w
`
`Maximum value
`Mechanical property
`Minimum value
`Normal component
`Acting at the center of pressure
`Property of a prototype; property of a
`particle; property of a piston
`Resultant
`Relative (moving frame of reference)
`Rectangular property
`Property of the rotor leading edge
`Property of the rotor trailing edge
`Acting on a surface
`Property of a solid
`Saturation property; property of a satellite
`Property of the stator leading edge
`Property of the stator trailing edge
`Submerged portion
`Pertaining to a system
`Tangential component
`Trianglular property
`Property of a turbulent flow
`Useful portion
`Acting vertically
`Property of a vapor
`Vacuum
`Property at a wall
`
`Superscripts
`- (overbar)
`Averaged quantity
`(overdot)
`Quantity per unit time; time derivative
`’(prime)
`Fluctuating quantity; derivative of a
`variable; modified variable
`Nondirnensional property; sonic property
`Law of the wall variable in turbulent
`boundary layer
`(over arrow) Vector quantity
`
`–
`
`11
`
`

`
`(cid:149) VISUAL NATURE OF FLUID MECHANICS by featuring
`more illustrations and photographs than other fluid
`mechanics texts.
`
`(cid:149) CURRENT RESEARCH with our Application Spotlight
`feature, written by guest authors and designed to show how
`fluid mechanics has diverse applications in a wide variety of
`fields.
`
`(cid:149) COMPUTATIONAL FLUID DYNAMICS (CFD) with
`examples throughout the text generated by CFD software.
`An introductory chapter also introduces students to the capa-
`bilities and limitations of CFD as an engineering tool.
`
`(cid:149) PRECISE DEFINITIONS OF KEY TERMS with a compre-
`hensive end-of-book glossary providing detailed definitions
`of fundamental fluid mechanics terms and concepts.
`
`(cid:149) PHYSICAL INTUITION to help students develop a sense
`of the underlying physical mechanisms and a mastery of
`solving practical problems that an engineer is likely to face
`in the real world.
`
`TOPIC FLEXIBILITY to facilitate different approaches to
`the course. After covering the basics for all majors, the text
`offers robust coverage to allow for mechanical, civil, or
`aeronautics and aerospace engineering approaches.
`
`:; (cid:9)
`
`:d
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`(cid:149) STUDENT DVD: Packaged free with the text, the Student
`Resources DVD features: 1) Limited Academic Version of
`EBS (Engineering Equation Solver) software-2) narrated, state
`of the art Videos including both experimental footage and CFD
`(computational fluid dynamics) animations. closely tied to the
`text content, and 3) Animations Library (Courtesy of Fluent,
`Inc.) offering dozens of animations created with CFD.
`
`(cid:149) ONLINE LEARNING CENTER
`Offers resources for instructors and students including chap-
`ter-by-chapter Internet content and learning tools, scripted
`EES solutions to select text problems, self-quizzing and
`instructor classroom presentation resources.
`
`Also available from McGraw-Hill in the CENGEL SERIES
`IN ENGINEERING THERMAL-FLUID SCIENCES:
`
`Second Edition
`
`(cid:149) Heat Transfer: A Practical Approach,
`Yunus A. cengel, 2003
`(cid:149) Thermodynamics: An Engineering Approach, Fourth
`Edition Yunus A. (cid:231)engel and Michael A. Boles, 2002
`(cid:149) FundamentaLs of Thermal-Fluid Sciences, Second
`Edition Yunus A. cengel and Robert H. Turner, 2005.
`Visit the book websites for all texts in the series at
`
`ISBN-1 3: 978-0-07-247236-3
`ISBN-10: 0-07-247236-7
`Part of
`ISBN-1 3: 978-0-07-304465-1
`ISBN-10: 0-07-304465-2
`
`90000
`
`IflI IMI II
`
`llI (cid:9)
`
`I ll IIII (cid:9)
`
`Ill (cid:9)
`
`LA
`
`9
`
`7 80073044651
`
`-- (cid:9)
`
`, ,.. (cid:9)
`
`--.--,------
`
`12