`
`Marks’
`
`Standard Handbook for
`
`Mechanical Engineers _
`
`Revised by a staff of specialists
`
`EUGENE A. AVALLONE Editor
`Consulting Engineer; Professor Emeritus of Mechanical Engineering,
`The City College of the City University of New York
`
`Editor
`THEODORE BAUMEISTER |||
`Retired Consultant, Information Systems Department,
`E. I. du Pont de Nemours & Co.
`
`Ninth Edition
`
`McGRAW-HILL BOOK COMPANY
`NewYork St. Louis San Francisco Auckland
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`
`
`
`

`

`
`
`2"va wrwmmev ;.r’
`
`~ *~ '1:-
`
`Library of Congress Cataloged The First Issue
`of this title as follows:
`
`Standard handbook for mechanical engineers. 1st—ed.;
`1916—
`'
`’
`"
`New York, McGraw-Hill.
`v. Illus. 18—24 cm.
`
`Title varies: 1916—58: Mechanical engineers‘-- handbook.
`Editors: 1916—51, L. S. Marks.——1958— T. Baumeister.
`Includes bibliographies.
`I. Marks,
`1. Mechanical engineering—Handbooks, manuals, etc.
`Lionel Simeon, 1871— ed.
`11. Baumeister, Theodore, 1897-—
`ed.
`III. Title: Mechanical engineers’ handbook.
`TJl5l.S82
`502’.4’621
`16—12915
`
`ISBN 0-07-004127-X
`Library of Congress Catalog Card Number: 87-641-192
`
`MARKS’ STANDARD HANDBOOK FOR MECHANICAL ENGINEERS"
`
`Copyright © 1987, 1978, 1967, 1958 by McGraw-Hill, Inc.
`Copyright renewed 1986 by Theodore Baumeistcr, III. All rights reserved.
`Copyright renewed 1979 by Lionel P. Marks and Alison P. Marks.
`Copyright renewed 1952 by Lionel S. Marks. Copyright renewed 1969, 1958 by Lionel
`Peabody Marks.
`'
`Copyright 1951, 1941, 1930, 1924, 1916 by McGraw-Hill, Inc. All Rights Reserved.
`Printed in the United States of America. No part of this publication may be repro-
`duced, stored in a retrieval system, or transmitted, in any form or by any means,
`electronic, mechanical, photocopying, recording, or otherwise, without the prior
`written permission of the publisher.
`
`,
`
`4567890 DOC/DOC
`
`932
`
`ISBN D—D?-DDHLE?—X
`
`Third Edition
`First Edition
`Eleven Printings Seven Printings
`
`Seventh Edition
`Fifth Edition
`Seven Printings Fifteen Printings
`
`Eighth Edition
`Sixth Edition
`Second Edition Fourth Edition
`Seven Printings Thirteen Printings Eight Printings Eleven Printings
`
`The editors for this book were Betty Sun and David E. Fogarty
`and the production supervisor was Teresa F. Leaden.
`It was set in Times Roman by University Graphics, Inc.
`
`Printed and bound by R. R. Donnelley & Sons Company.
`
`The editors and the publishers will be grateful to readers who notify them
`of any inaccuracy or important omission in this book
`
`For the data.
`The alphabe
`
`List of Cont:
`Preface to :1
`Preface to tl
`Symbols an:
`
`1. Matl
`1.1 Matl
`1.2 Mea
`
`2. Matl
`2.1 Matl
`2.2 Con
`
`3. Mec
`3.1 Me(
`3.2 Fric
`3.3 Me(
`
`4. Hea
`4.1 The
`4.2 The
`4.3 Rat
`4.4 Tra
`
`5. Strt
`5.1 Me
`5.2 Me
`5.3 Pip
`5.4 Vila
`5.5 No
`
`6. Ma
`6.1 Ge
`6.2
`Iro
`6.3
`lro
`6.4 No
`6.5 Co
`6.6 Pa
`6.7 WI
`6.8 Nc
`6.9 Ce
`
`
`
`

`

`
`
`Table 15.1.1 Electrical Units
`
`ELECTRICAL AND MAGNETIC UNITS
`
`15-3
`
`\
`Ratio of
`SI unit
`magnitude of
`Quantity
`Symbol
`Equation
`SI unit
`symbol
`CGS unit
`SI to cgs unit
`
`Current
`Li
`I = E/R; I = E/Z; I = Q/t
`Ampere
`A
`Abampere
`10‘1
`Quantity
`Q, q
`Q = it: Q = CE
`Coulomb
`C
`Abcoulomb
`10‘I
`Electromotive force
`E, e
`E = IR; E = W/Q
`Volt
`V
`Abvolt
`108
`Resistance
`R, r
`R = E/!; R = pl/A
`Ohm
`t2
`Abohm
`109
`Resistivity
`p
`p = RA/l
`‘
`Ohm-metre
`Qrm
`Abohm-cm
`10”
`Conductance
`G, g
`G = 7A/I;G = A/pl
`Siemens
`S
`Abmho
`10"9
`Conductivity
`7
`'y = l/p; 'y = l/RA
`Siemens/meter
`S/m
`Abmho/cm
`10‘“
`Capacitance
`C
`C = Q/E
`Farad
`F
`Abfarad‘
`10"
`Permittivity
`e
`Farads/meter
`F/m
`Stat farad*/cm
`8.85 X 10‘'2
`e, = 5/50
`Relative permittivity
`e,
`Numerical
`Numerical
`l
`L = —N(d¢/dt)
`Self-inductance
`, L
`Henry
`H
`Abhenry
`lO9
`M = 1((LIL2)I/2
`Mutual inductance
`M
`Henry
`H
`Abhenry
`109
`.l = all
`Energy
`J
`Joule
`J
`Erg
`107
`kwh = kW/3600; 3.6 M]
`kwh
`Kilowatthour
`kWh
`36 X 1012
`W = J/r; W = E! cos 0
`W
`Watt
`*
`W
`107
`Active power
`Q = E] sin 0
`jQ
`Var
`var
`107
`Reactive power
`VA = E!
`VA
`Volt-ampere
`VA
`Apparent power
`pf = W/ VA; pf = W/(W+ jQ)
`pf
`Power factor
`XL = 27rfL
`XL
`Reactance, inductive
`X5 = l/(21rfC)
`X5
`Reactance, capacitive
`Z = E/I; Z = R + j(XL — XC)
`Z
`Impedance
`G = R/Z2
`G
`Conductance
`B = X/Z2
`B
`Susceptance
`Y = I/E; Y = G +jB
`Y
`Admittance
`f = l/T
`f
`Frequency
`T = l/f
`_ T
`Period
`L/R; RC
`T
`Time constant
`w = 27rf
`, a)
`Angular velocity
`'1 Abl'amd (EMU Units) = 9 x |0_2°stat farads (ESU units).
`
`Abwatt
`Abvar
`
`-
`
`Abohm
`Abohm
`Abohm
`Abmho
`Abmho
`Abmho
`Cps, Hz
`Second
`Second
`Radians/second
`
`i
`109
`109
`109
`10‘9
`10“9
`10“9
`1
`1
`1
`l
`
`Ohm
`Ohm
`Ohm
`Siemens
`Siemens
`Siemens
`Hertz
`Second,
`Second
`Radians/second
`
`Q
`$2
`Q
`S
`S
`S
`Hz
`5
`5
`rad/s
`
`lI
`l1
`
`l li
`
`rtion of the
`
`cal conduc-
`tpere is pro-
`)lt, One sie-
`
`is the dc
`al
`’a portion of
`tion.
`f conductors
`,tricity when
`.. Its value is
`3 a' potential
`The farad is
`tes of which
`nit when it is
`coulomb.
`:static energy
`tial gradient.
`..85 x 10‘12
`
`, the ratio of
`ielectric for a
`of a vacuum.
`
`circuit which
`in the circuit,
`= — Ldi, / (It,
`the coefficient
`
`t in which an
`n the electric
`per second.
`y of two asso-
`g'iven rate of
`induced in the
`,/dz, where er
`, and M is the
`
`parate circuits
`~oduced in one
`:uit varies unt-
`
`ts and k is the
`.x produced by
`L|L2)l/2~ where
`ie two circuits.
`mount of work
`the work done
`, newton is dis-
`of the force.
`if transforming
`. the production
`
`Active Power (P) at the points of entry of a single-phase, two-
`wire circuit or of a polyphase circuit is the time average of the
`values of the instantaneous power at the points of entry, the
`average being taken over a complete cycle of the alternating
`current. The value of active power is given in watts when the
`rms currents are in amperes and the rms potential differences
`are in volts. For sinusoidal emf and current, P = E! cos 0,
`where E and I are the rms values of volts and currents, and 0
`is the phase difference of E and 1.
`Reactive Power (Q) at the points of entry of a single-phase,
`two-wire circuit, or for the special case of a sinusoidal current
`and sinusoidal potential difference of the same frequency, is
`equal to the product obtained by multiplying the rms value of
`the current by the rms value of the potential difference and by
`the sine of the angular phase difference by which the current
`leads or lags the potential difference. Q = E] sin 0. The unit
`of Q is the var (volt-ampere-reactive). One kilovar = l03 var.
`Apparent Power (E1) at the points of entry of a single~phase,
`two—wire circuit is equal to the product of the rms current in
`One conductor multiplied by the rms potential difference
`between the two points of entry. Apparent power = E].
`Power Factor (pf) is the ratio of power to apparent power. pf
`= P/EI = cos 0, where 0 is the phase difference between E
`and I, both assumed to be sinusoidal.
`The reactance (X) of a portion of a circuit for a sinusoidal
`Current and potential difference of the same frequency is the
`product of the sine of the angular phase difference between the
`Current and potential difference times the ratio of the rms
`
`potential difference to the rms current, there being no source
`of power in the portion of the circuit under consideration. X =
`(E/I) sin 0 = 21rfL ohms, wherefis the frequency, and L the
`inductance in hcnries; or X = l/27rfC ohms, where C is the
`capacitance in farads.
`'
`I
`The impedance (Z) of a portion of an electric circuit to a
`completely specified periodic current and potential difference
`is the ratio of the rms value of the potential difference between
`the terminals to the rms‘ value of the current, there being no
`source of power in the portion under consideration. Z = E/[
`ohms.
`
`Admittance (Y) is the reciprocal of impedance. Y = I/E
`siemcns.
`'
`The susceptance (B) of a portion of a circuit for a sinusoidal
`current and potential difference of the same frequency is the
`product of the sine of the angular phase difference between the
`current and the potential difference times the ratio of the rms
`current to the rms potential difference, there being no source
`of power in the portion of the circuit under consideration. B =
`(I/ E) sin 0.
`Magnetic Units
`(See Table |5.lr2.)
`
`(12)
`
`is the magnetic flow that exists in any
`
`Magnetic Flux ("1),
`magnetic circuit.
`The weber is the magnetic flux which, linking a circuit of one
`turn, produces in it an electromotive force of one volt as it is
`reduced to zero at a uniform rate in one second.
`
`
`
`

`

`
`
`loat level) must
`ay be calibrated
`ate scale on the
`:nds on the 11031
`'hc equation for
`1/2
`
`t)
`
`)at position), Ar
`= float density,
`.fl‘icient (usually
`ith the fluid vis-
`ilable which are
`:0, fluid density
`
`:ording and con.
`hich connects to
`iture forms part
`ed electronically
`tic transmission,
`ieumatic motion
`his generates an
`ioat.
`operation. Flow
`ght cylinder with
`in is transmitted
`ge circuit.
`usually employ
`' designs include
`linear—flow char-
`) weir). The flow
`isurface relative
`[red by a liquid-
`ll (float chamber
`-f the weir or the
`
`placement due to
`up of solids. (569
`
`nents which serve
`)lication. The pro-
`he average veloc-
`
`ii)! in the path of the propeller, assuming negligible friction.
`The propeller may be mechanically geared to a tachometer to
`indicate flow rate and to a counter to show total quantity flow.
`The magnetic pickup (Fig. 16.1.31) generates a pulse each
`time a propeller tip passes. The frequency of pulses (measured
`
`
`
`
`
`Magnetic
`sensing element
`
`
`
`Propeller-type flowmcter.
`
`Fig. 16.1.31
`
`by means of appropriate electronic circuitry) is then propor-
`tional
`to the local stream velocity. If the propeller occupies
`only part of the flow stream, an individuaLcalibration is nec-
`essary and the velocity distribution must remain constant. The
`turbine type is similar, but is fabricated as a unit in a short
`length of pipe with vanes to guide the flow approaching the
`rotor. Its magnetic pickup permits hermetic sealing. A mini-
`mum flow is needed to overcome magnetic cogging and start
`the rotor turning.
`The metering pump is an accurately calibrated positive-dis-
`placement pump which provides both measurement and con—
`trol of fluid-flow rate. The pump may be either fixed volumetric
`displacement—variable speed or constant speed-variable dis-
`placement.
`For air flow, a vane-type meter (anemometer) is often used. A
`mechanical counter counts the number of revolutions of the
`vane shaft over a timed interval. Instantaneous airflow read-
`ings are more readily obtained with the hot-wire anemometer.
`Here, a resistance wire heated by an electric current is placed
`in the flow stream. The temperature of the wire depends on the
`current and the rate at which heat is conducted away from it.
`This latter factor is related to the thermal properties of the air
`and its velocity past the wire. Airflow can be measured in terms
`of (1) the current through the wire to maintain a fixed tem—
`perature, (2) temperature of the wire for a fixed current, or (3)
`temperature rise of the air passing the wire for fixed current.
`The wire temperature is readily measured in terms of its resis-
`tance. The anemometer must be specially calibrated for the
`application. Lasers have also been applied to anemometer use.
`The electromagnetic flowmeter has no moving parts and does
`not require any insertions in the flow stream. It is based on the
`Voltage induced by the flow of charged particles of the fluid
`past a strong magnetic field. It is suitable for liquids having
`resistivities of 50 ku-cm or less. The vortex-shedding meter has
`a flow obstruction in the pipe; vortices form behind it at a rate
`nearly proportional to the volume flow rate. Vortex-formation-
`rate data give flow rate; a counter gives the integrated flow.
`Doppler-eflect flowmeters depend on reflection from parti-
`cles moving with the fluid being metered; the shift in frequency
`01 the reflected wave is proportional to velocity. Two trans-
`
`nmwks.,.
`
`K...»4.1.x“..”2--
`
`ii
`i'.t4
`
`POWER MEASUREMENT
`
`16<17
`
`ducers are used side by side, directed so that there is a large
`component of flow velocity along the sound path. One trans—
`mits and one receives.
`Transit-time ultrasonic flowmeters use one or more pairs of
`transducers on opposite sides of the pipe, displaced along the
`length of the pipe. The apparent velocity of sound is c i v,
`where c is the speed of sound with no flow, and v is the com-
`ponent of flow velocity in the direction of the sound propaga-
`tion path. The diflerence in sound velocity in the two directions
`is proportional to the flow’s velocity component along the sound
`propagation path. The transit time difference is 2111/(02 + Dz),
`where I is the path length. For 1) << c, the factor (C2 + 1):) is
`nearly constant. These meters cause no pressure drop and can
`be applied to pipes up to very large diameters. Multipath
`meters improve accuracy. See Erickson and Graber, Ultra-
`sonic Flowmeters for Hydroelectric Plants, Mechanical Engi—
`neering, Nov. 1983, pp. 84—88, and Graber, Ultrasonic Flow-
`metering, Measurements and Control, Feb. 1984, pp. 176—
`182.
`Mass flowmeters measure changes in momentum related to the
`mass flow rate.
`.
`Flowmeters measure rate of flow. To measure the total
`quantity of fluid flowing during a specified interval of time, the
`flow rate must be integrated over that interval. The integration
`may be done manually by estimating from the chart record the
`hourly flow averages or by measuring the area under the flow
`curve with a special square-root planimeter. Mechanical integra-
`tors use a constant-speed motor to rotate a counter. A cam con-
`verts the square-root meter reading into a linear displacement
`such that the fraction of time that the motor is engaged to the
`counter is proportional to the flow rate, resulting in a counter
`reading proportional to the integrated flow.‘Electrical integrators
`are similar in principle to the watthour meter in that the speed
`of the integrating motor is made proportional to the magnitude
`of the flow signal (see Sec. 15).
`
`POWER MEASUREMENT
`
`Power is defined as the rate of doing work. Common units are
`the horsepower and the kilowatt: 1 hp = 33,000 ft-lb/min =
`0.746 kW. The power input to a rotating machine in hp (W)
`= 21rnT/k, where n = r/min of the shaft where the torque T
`is measured in lbf-ft (N'm), and k = 33,000 ft'lbf/hp-min
`[60 N - m/(W)(min)] . The same equation applies to the power
`output of an engine or motor, where n and Trefer to the output
`shaft. Mechanical power-measuring devices (dynamometers) are
`of two types: (1) those absorbing the power and dissipating it
`as heat and (2)
`those transmitting the measured power. As
`indicated by the above equation,
`two measurements are
`involved: shaft speed and torque. The speed is measured
`directly by means of a tachometer. Torque is usually measured
`by balancing against weights applied to a fixed lever arm; how-
`ever, other force measuring methods are also used. In the trans-
`mission dynamometer‘, the torque is measured by means of strain-
`gage elements bonded to the transmission shaft.
`There are several kinds of absorption dynamometers. The Prony
`brake'applies a friction load to the output shaft by means of
`wood blocks, flexible band, or other friction surface. The fan
`brake absorbs power by “fan” action of rotating plates on sur-
`rounding air. The water brake acts as an inefficient centrifugal
`pump to convert mechanical energy into heat. The pump cas-
`
`
`
`