USGS Bulletin 1141-A

8/2/2019 USGS Bulletin 1141-A

1/54


2/54

Ultrasonic M easurementof Suspended SedimentBy GORDON H. LAMMERC O N T R I B U T I O N S T O G E N E R A L G E O L O G Y

G E O L O G I C A L S U R V E Y B U L L E T I N 1 1 4 1 - A

Prefiared in cooperation w it h the FederalInter-Agency Sedimentation Projecti!i

-U N I T E D S T A T E S G O V E R N M E N T P R I N T I N G O F F I C E , W A S H IN G TO N 1 9 6 2


3/54

UNITED STATES DEPARTMENT OF THE INTERIORSTEWART L. UDALL. Secretary

GEOLOGICAL SURVEYT h o m a e B. Nolan. Director

Por asle by the Superlatendentof Document.. U.S.Government Rlntlng OmceWeehlngtm 15. D.C.


4/54

CONTENTSSymbols..........................................................Abstract..........................................................Introduction.....................................................Purpose and scope.................................... .......-.

Pcrsonqel and acknowledgments....... -.. -.-. . . . . .. .Review of theoretieai concepts.. ... . .. . . . . . ..Uniform particle sizes.. . . . .... .. . . ...... . . .Distributions of particle sizes.. . . . . .... .... ..... .....r .I heoretical development.. . .. . . . . . . .Experimental appa ratus and procedures............................Discussion of results. ............ ..................... -.........-Conclusions and mcommendatibns.................................Literature cited...........................................

-

ILLUSTRATIONS

FIGURE . Ultrasonic attenuation by suspensions of rigid particles ofuniform sizc.........................................2. Ultrasonic attenuation for lnixtures of riaid ~articlea avinga log-normal size distribution and falling within the scat-tering- and diffraction-loss ranyes.............. ........-3. Experimental results for ultrasqnic attenuation by size frac-

tions made up from Missouri River sand and blasting sand.4. Ultrnaonic attenuation a t 2.6 and 25 mc for lnixtures havinga log-normal size distribution.. . . . . .... . ....5. Ultrasonic attenuation a t 7.5 and 15 mc far mixtures havinga log-normal size distribution. .....----.. ..--.6. Ultrnaonic attenuation at 5.0 and 12.5 mc for mixtureshaving a log-normal size distribution.... .... ..7. Curves for th e determina tion of the size-distribution parame-ters d , and o., for r , equal to 1.4......................8. Curves for th e determination of the size-distribution parame-ters d, and o., for o, equal to 1.6.......................9. Curves for th e determination of the sire-distribution parame-ters d, and v , , for o. equal to 1.8.....................10. Curves for the determination of th e size-distribution parame-ters d . and o., for r, equal t o 2.0.....................

I11


5/54

F~OURE1. Curves for the determinat ion of t he size-distribution parame-ters d , and c for cr. equal t o 2.5.......................12. Curves for th e determination of the si~e-distributionparam-eters d, and r , , for cr, equal to 3 .0......................13. Curves showing th e sensitivity of measurement of the geomet-ric standard deviation, for d, equal to 150 microns14. Curves showing th e sensitivity of measurement of the geomet-ric staridard deviation, for d, equal t o 200 microns........15 . Block diagram of ultrasonic apparatus.. -.................10. Plug-in tranamitter units, crystal and reflector holders, andattenustor...........................................17. Transmi tter pulse edge and echo on oscilloscope.......-..18. General layout: recirculating sediment chamber, transmitter,receiver, at tenuator , and oscilloscope....... .-..- -.-.19 . Theoretical curves showing increased sensitivity of measura-

ment of the geometric standard deviation by using ahigher reference transducer frequeney, for d . equal to 150mlcrons.............................................20 . Theoretical ourves showing increased sensitivity of messurl-ment of the ueometrio standard deviation by usina a-higher reference transducer frequency, for d, equal to 200m~crons----........---.-.....-....-...-.-.--.....21 . Sensitivity of measurement of concentration for the mixtured, equal t o 200 and r , equal to 1.0... ................22 . Attenuation-coefficient relation for different sands a t 26 mc..23 . Attenuation-coefficient relation for different sands andmaterials at 25 mc....................................24 . Attenuation-coeffioient relation for different materials a t 6 rnc.

TABLE , Experimental and integrated values of t he att enuationcoefficient for a concentration of 1,000 pprn.............-

Pam

A30


6/54

CONTENTS

SYMBOLS

KIn

M.S. mixt"I

ppm7

[ P a sm those where thes ym bolsm Brst m d l

Constants..............................................Concentration as ratio of volume of sediment to volume ofwater................................................Particle diameter. in centimeters unless svecified otherwise....Arithmetio mean partiole diameter. in centimeters.......:...Geometric mean varticle diameter. in centimeters unless

specified othe-se .....................................Base of the Na~erianoaarithm.............................Sound-energy flux at a given point if sediment is suspended in

the transmitting fluid..................................Sound-energy flux a t thesame point if no sediment were present..Transducer frequenoy, in ~neaacyclea~ e recond.............-~A funetion of the optioal or sonio properties of the sediment..Equal t o 2r/A...........................................Naperianlogarithm ......................................

ure Mixture of Missouri River sand and blasting sand.......Number of particles of a disorete size......................Parts per million by volume (unless specified by weight) .....Particle radius, in centimeters............................Equal to [9/(4@7)][1+1/(@r)].............................Specifio gravity.........................................Equal to ln d................. ........................Equal to %-(In d,- lna o, ...............................Equal to u- (ln d8+3 lna 0 , ) .............................Distanoe from point of measurement t o sound source along

...........................................ound pathAttenuation coefficient due to presence of suspended sediment.Attenuation coefficient for siae d per unit concentration by

..............................................olumeAttenuation coefficient due to siae fraction 1................Attenuation coefficient due to size fraction 2................Attenuation coefficient for a mixture of discrete partiole siaes..Attenuation coefficient for a given transducer frequency f ....Attenuation oooffioient for a transducer frequency of 25 mc. .Attenuation coeffioient for a transducer frequency of 100 mc... ~Attenuatipn coeffioient for Light waves .....................Equal to [w/(~v) ]+......................................Equal top, p, ..........................................Ultrasonic wavelength, in centimeters......................Siae-frequenoy distribution ...............................Densities of the particle and fluid, respectively (cgs system)..Standarddeviation ......................................Geometric standard deviation.............................Equal to %+9/(467).....................................Micron or 10-4 centimeter................................Kinematic visoosity, in stokes.............................Equal to 2rf............................................


7/54

CONTRIBUTIONS TO GENERAL GEOLOGY

ULTRASONIC MEASUREM ENT OF SUSPENDED SEDIMENT

One of th e most serious obstacles to rapid progress in studying the mechanics ofsediment movement in streams is the inadequacy of instruments for'measuringsediment loads in streams. A new method based on ultrasonic attenuation(docrease in amplitude of the wave from point of origin) by sediment in suspen-sion is Dresented for determining sus~ended-sediment i ~ eistribution and concen-. .tration.

The theoretical studv covered three ~ r i n c i ~ a ltems:1. Existing attenuation relations for an ultrasonic beam passing through a suspen-

sion of particles of uniform s i ~ e ere extended to include parameters describ-ing size distribution. The resulting equations gave the attenuation relationsfor water-sediment mixtures having log-normal size distributions. The-log-normal distribution has wide application because i t is typical of naturalsediments.

2. A method based on the variation of frequency of the sound wave was developedfor the unique determination of the log-normal particle-size di~t ribu tionparameters of an unknown sample.

3. After the particle-size distribution parameters were determined, the sedimentconcentration was obtained from the attenuation relation for mixtures ofsediment sizes.

The experimental study included the following three phases: (a) The attenuationrelation for sediment of uniform sieve size was determined for the diffraction-lossand scattering-loss ranges and for the intermediate transition region, for which nosatisfactory theoretical equation^ were available; (b) the theoretical concepts wereverified by using the experimental attenuation relations; and (c) some preliminarytests were made of the effects of different types of sediment materials on therelation of attenuation to particle diameter.

Experimental attenuation varied as the 0.33 power of the frequency aridinversely as sediment s i ~ en the diffraction-loss range and aa the 2.4 power of thefrequency and the 1.3power of the size in the transition range.

The sensitivity of measuring the geometric mean size was high, and the sensi-tivity of measuring standard deviation and concentration would be improved byincreasing the range of frequencies t o 60 mc (megacycles) or higher.

The ultrasonic method was experimentally verified; however, an extensiveequipment-development program is needed to make the instrument operationalfor laboratory or field use. Also, the effects of sediment properties on ultrnnonicattenuation require further studv.

A1


8/54

A2 CONTRIBUTIONS T,O GENERAL QEQLOGYINTRODUCTION

A basis phase of the modern scientific revolution has been theadvance in measurement techniques, particulilrly during the pastdecade or two. The adaptation of electronics to instrumentation hasrevolutionized many types of measurements, and continued develop-ment holds great promise for tlie future. Such factors as sensitivityof measurement, accuracy, and relative ease of recording are allsignificant advantages of electronic methods.

One of tlie most serious limitations in studying the mechanics ofsediment movement in a flowing stream has been the lack of adequatelne~lsuring nstruments. Present methods take only intermittentsamples, and the analysis of these samples is lnborious and timeconsu~ning. As rneasurenielit technique improves, the rate of progressin tlie cliscovery of tlie bnsic principles of sediment-motion mechanicswill increase accordingly.

In nil attempt t,o improve the quality and to rcduce tlie cost ofrecords of serlinient discharge in streams, the Federal Inter-AgencyScdimenlation Project at Minneapolis, Minn. was assigned tlie tasksof improving sm~plingmethods and equipinelit and of dcvelopingautoinatic devices for determining sediment concentration and dis-rliarge. The iiii~nediate objective was to develop an ~lutomaticiiis trun~ent or obtaining, either periodically or continuously, thesnspri~rled-srdimentr,oncentration a t one point in the cross scctioiiof :I streaiii. Meusuring tlir attenuations of all ultrt~sonicbeamseemed to be n possible way to deterrnine the concentration of sedimentin suspension.

PURPOSE AND SCOPE

The present investigation was made to deterrnine theoreticallyand experimentally if the att.enuations at a few frequencies woulddefine the size distribution uniquely, and if field and laboratoryinstruments having sufficient accurncy to determine the size dis-tribution could be made. Size distributions are infinitely vuriable,but a log-normal distribution is typical of natural sediments. Onlylog-normal distributions are treated in this study so that the sizedistribut.ion can be defined by two parameters, a geometeric meanparticle diameter and the geometric standard deviat.io11. The samemethods of investigation could be adapted to other than log-normaldistributions whenever some other systernaticully definable dis-tribution bet,ter applies.

After an intensive study of available literature, a method wasdeveloped theoretically for defining the two size-distribution param-eters by varying the frequency. The sediment concentrationcould be determined after the size distribution was obtained. The


9/54

requirements of an instrument for determining size distribution andconcentration of a sediment in suspension were predicted.Equipment was designed and built for measuring attenuations atfrequencies of 2.5, 5.0, 7.5, 12.5, 15, and 25 mc (megacycles). Samplesof sediments of known size distribution and concentration wereanalyzed to find basic attenuation relations for narrow ranges of sedi-ment sizes and for mixtures of sizes, to check theoretical concepts,and to evaluate instrument accuracy. Samples containing sizessmaller than 44 microns could not be tested because of equipment lim-itations, and sizes larger than 1,000 microns could irot be testedwithout damage to the circulation equipment.PERBONNEL AND AOKNOWLEDOMENTB

The investigation of the application of ultrasonics to the analysisof sediments in suspension was made in collaboration with the FederalInter-Agency Sedimentation Project a t Minneapolis, Minn. TheInter-Agency Project is guided by a Field Technical Committee underthe general supervision of the Subcommittee on Sedimentation.of theFederal Inter-Agency Committee on Water Resources. B. C. Colby,project supervisor, and F. S. Witzigman, assistant supervisor, pro-vided nupervision and counsel. The report was prepared under thedirection of Mr. Colby.The research work was done at the St. Anthony Falls hydrauliclaboratory of the University of Minnesota. The assistance of L. G.Straub, Director of the laboratory and head of civil engineering;

J. M. Killen, research engineer; Prof. Edward Silherman; and A. G.Anderson is gratefully acknowledged.REVIEW OF THEORETICAL CONCEPT8

UNIFORM PABTIDLE 81ZE8The attenuation of an ultrasonic wave passing through a fluid is

greater when suspended particles are present than when they areabsent. The basic relation for the increased energy loss that is dueto the presence of suspended sediment in a sound field isE=E -2-z~e (1)where

E is sound-energy flux a t a given point if sediment is suspendedin the transmitting fluidE, is sound-energy flux at the same point if no sediment werepresente is base of the Naperian logarithma is attenuation coefficient that is due to the sediineiit alonex is distance from the point of measurement to the sound source.044442 0--02--2


10/54

The attenuation coefficient a is the logarithm of a power ratio andis measured in nepers per centimeter in the metric system. In theEnglish system E = E ~ ~ O - " ~ ~ Z (la)and or is in decibels per inch. A decibel of attenuation is equivalentto a 20.6-percent decrease in power intensity. A neper equals '8.68db (dccibel), and a neper per centimeter equals 22.05 db per in. Inthis report all numerical values of a will be in decibels per inch.

The attenuation eoefficient or is made up of three loss mechanisms.The first is associated with shear waves (a viscosity phenomenon)set up at the liquid-solid interface because the particle vibrates inresponse to bu t lags bchind the sound wave. The magnitude of thisloss depends on the amount of. lag and on the surface area. Ex-tremely small particles tend to move at the same rate as the fluid,and the lag is very small. As size increases, the particles tend tolag more and more behind the movement of the fluid, bu t a t thesame time the total surface area of the particles decreases for a con-stan t concentration. These opposing factors result in an attenua-tion maximum for the "viscous-loss range" (Urick, 1948, p. 284,fig. 1, p. 287). Fluid viscosity and the ratio of particle density tofluid density are liltewise important in determining the amount of lag.

The second loss mechanism is the scattering of energy due to areradiation by the particle of the incident plane wave. The patternand intensity of the reradiated waves are functions of the ratio ofwavelength A to particle circumference 2sr. For A>>2ar, thescattering-intensity pattern of a particle is concentrated in the back-ward directious. As A approaches 2w, the scattering distributionbecomes more complicated, and 'the pattern changes rapidly as thefrequency changes. For A


11/54

ULTRASONIC MEASUREMENT OF SUBPENDED BEDIMENT A5Rayleigh ( 1937 ) . Sewell ( 1910 ) , Epstein ( 1941 ) , Urick ( 1948 ) , andC arh ar t derived ma them atical expressions for the energy loss causedby a single spherical particle in a plane sound field. Sewell assumedth e sphere to be rigid an d fixed. Bot h Epstein and U rick considereda rigid sphe re t h a t is free to move; and Ca rha rt included also therma leffects, which are important when either the suspended sphere or thesuspending medium is highly compressible. I n all these studies th ewavelength was much greater than the particle circumference( h>>21 r ) . Weinel showed th a t for solid spheres in wa ter thevarious expressions for the viscous atten uat ion are identical. I n 1936Morse (1948 , p. 346-357) derived an equation for the scattering ofenergy by rigid immovable circular cylinders and spheres that werenot necessarily small compared with th e wavelength. La ter, Morseand others (1946) extended the equation to include the effects ofcompression wavea inside th e scattere rs; th e suspended particles wereconsidered to be elastic for both applications. Fo r an elastic sphere,in the region where X f ; 2 a r , Faran (1951) showed that the efl'ect ofshear waves in a dense particle must be considered in addition to theeffects of com pression waves. Anderson (1950) studied the sc atteringof soun d from spherical particles having diam eters close to or a fewtimes larger tha n th e wavelength. I n hie st ud y th e specific gra vityof th e spheres ranged from 0.5 to 2.0 , and t h e sound velocities of th espheres ranged from 0.5 to 2.0 times th a t of the suspending medium.Simplifying assumptions are made in order to determine the com-plex attenuation relations. Th e first assumption is th a t the suspended-sed iment particles in flowing wa ter are rigid spheres. Anderson (1950 ,p. 431 , fig. 6) compared the scattering cross section for a rigid sphereto t h a t for a sphere of density an d sound velocity ratio twice those ofth e supp orting medium. Hi s work indicated tha t a dense particlewhose circumference is less than half the sound wavelength may beconsidered rigid. Fu rth er, he showed th at a particl


12/54

apart so that one does not affeat the attenuation of another. Thecomputed scattering for a single particle may be multiplied by thenumber of particles in th3 sound path to obtain the total scattering.This assumption haa been proved valid for X>>2sr by the linearattenuation-concentration relation for concentrations as high as265,000 ppm by weight (Urick, 1948, p. 286, fig. 5; Busby and Rich-ardson, 1955, p. 193, fig. 2, p. 197). For X nearly equal to 2sr theattenuation-concentration relation was still linear for concentrationsof 200,000 ppm by weight (Smoltczyk, 1955, p. 37-38, figs. 26-27).For X


13/54

Equation 2, which is valid for X>>2w, was used to compute at-tenuation coefficients for a range of sound frequencies and particlediameters. The results for rigid particles were plotted on figure 1;


14/54

A8 CONTRIBUTI~SEO GENERAL G E ~ G Ytherefore, the transition region, which exists for elastic particles, doesnot appear on this plot. Mathematical expressions for the attenua-tion coefficient in the transition region involve infinite series and aretoo complicated to be of practical use in this study.

For X


15/54

the value of h. Light has no expression corresponding to the ultra-sonic viscous loss because light waves do not cause particle vibrationas do sound waves. The factor h is a function of the optical or sonicproperties of the sediment. Important optical properties, such ascolor, index of refraction, absorption coefficient, and transparencyenter into h, and these p1,operties may vary considerably amongnatural sediments. Corresponding sonic properties are index ofrefraction, absorption, and transparency; however, these propertiesare relatively more uniform among natural sediments.For the diffraction-loss range of a dielectric, the reflected light isalmost independent of wavelength; i t is affected only slightly bychange in index of refraction with change in wavelength. Theoreticalexpressions for sonic scattering in the diffraction-loss range alsoare independent of wavelength.Of special note is the expression for rr in the transition region whereA =.2rr for light. A correspondiog expression for the attenuation ofsound in the transition region, r r = h a P 4 8C , is experimentally de-rived in this report. (See equation 19, p. A35.)

DIBTRIBUTIONB OF PARTICLE BIZEB

Generally, sediment suspensions contain particles of many sizes;therefore, development of relations for the sonic attenuation causedby mixtures of sizes is necessary for measuring concentration by thosonic method. An obvious problem is the variety of size-distributionfunctions necessary to describe all mixtures.Very little work has been done with mixtures. The use of thesonic-attenuation relations for discrete particle sizes in conjunctionwith a sedimentation chamber to determine size distribution ofmixtures has been suggested by Busby and Richardson (1955, p.202) and Killen; the use of attenuation relations for light has givenvarying degrees of success (Traxler and Bnum, 1935, p. 466). Grassy(1941) studied the use of the turbidity meter in estimating the sus-pended load of natural streams.Gamble and Barnett (1937, p. 311-313, figs. 1-8) varied the wave-length of light through mixtures and found that by plotting percent.-age of transmission against wavelength, qualitative information onsize distribution could be obtained. The shape of the curves indi-cated very roughly the mean size and the spread of particle Gizes.Their results were not quantitative.

Smoltczyk (1955) studied simple mixtures. He first found thesonic attenuations caused by several uniform sizes-actually heused fractions of narrow size ranges obtained by sieving-then took1Killen, J . M.. 1968. OD, o l t


16/54

A10 CONTRIBUTIONS TO GENERAL O-GIYtwo of these fractions, mixed them in a variety of proportions, andfound the attenuation caused by the mixtures. The relation obtainedWas E=E - Z G Z , + ~ ~ S~e (7)where

a, s attenuation coefficient due to the presence of size fraction1 in the suspension

rr, is attenuation coefficient due to the presence of size fraction 2.This relation further verifies the basic assumption that the particlesare far enough apart so there is no interaction or interferencebetween them. Smoltczyk also studied the relationship of theattenuation coefficient to frequency for a given size fraction (250 to300 p ) . The transducer frequencies he used were 1, 2, 3, and 4 mc.

THEORETICAL DEVELOPMENTIn order to use the ultrasonic method for measuring concentration

and size distribution, parametem that define size distrihhtion must beincluded in the equations. The size parameten will be based on anassumed distribution, such as the normal distribution. The usualnormal-probability equation applies only to distributions that aresymmetricel about a vertical axis; therefore, it does not apply to mostnatural sedimente, the distributions of which are asymmetrical orskewed. However, for the majority of natural sediments the fre-quency curves are normal if the logarithm of the size is substitutedfor the size. The truth of this statement is verified by the fact thattheir distributions when plotted on log-probability paper yield straightlines, except at the extremes. The deviation at the extremes is unim-portant because the areas under the curvea extending from the pointsof deviation to infinity are negligible compared to the total area underthe curves between the largest and amallest particlea measured(DallaValle, 1948, p. 53-54). Not only moat natural aediments(Hatch and Choate, 1929, p. 379; Einatein, 1944,figs. 9 and 29; Blench,1952, p. 147; Chow, 1954, p. 2; Colby and Hembree, 1955, figs. 13and 32) hut alao the products of many manufacturing and chemicalprocesses, such as those from crushing and grinding and chemical pre-cipitation (Austin, 1939, figa. 3-7; Hatch and Choate, 1929, p. 380-383), are log normal. Thua, this distribution has wide application.The important parameters describing the straight-line plot on log-probability paper are do, the geometric mean, which is the 50-percentaize, and a,, he geometric standard deviation, which is the ratio of the84.13-percent size to the 50-percent size or of the 50-percent aize tothe 15.87-percent aize.


17/54

ULTRASONIC MEABUREMENT O F SUSPENDED SEDIMENT A l lT he equation of the normal-frequency size distribution is

whered is particle diameterd is arithmetic mean particle diameterr is stan dard deviation and is equal to \ /Ec (~ ;~ ' I

Fo r an asym metric distribution, the logarithms of the sizes are sub-stituted for the sizes:

Because +On d) fits most natural sediments, it was chosen as the dis-tribution function for this study.T he basic relation necessary to include the size-distribution param -eters in the attenuation equation is

(10)where

a, is att en ua tion coefficient for a mixture of discrete particle sizesa f( d ) s attenua tion coefficient for size d per un it concentration byvolume+(d) is size-frequency distribution;

or for a log-normal distribution

Equations 10 and 11 follow directly from the assumption that theparticlee are sufficiently far ap ar t so th at one does not affect the a tte n-uatio n of an othe r.


18/54

A12 CONTRIBUTION~STO GENERAL ~EQI~OGYThe attenuation coefficient has three loss ranges; therefore, threedifferent integrals have to be evaluated. (Uriclr's relation will beused.)1. Viscous-loss range:

Kal(d)=- (y-1)2 db2 22.057S2+(r+r)' in. (2)which is the first part of equation 2. By substituting,

K (ln d-l n d,)9a 2- (7-1)'- 1+- C e 2mlr.aT.=s-s $ d [ ;dl d(ln d)& 1+3+[7+:+&]

which beconies after soine n~a~iipulation:

wilere thc a's ore constants for a given sediment in wator understandard conditions and for a given frequency.Equation 13 seems to requiro numerical integration by ~iieallfiof 8coniputer. As this study will not extend into the viscous-loss range,no attempt was made to evaluate the equation.2. Scattering-loss range:

K4@ 358.5d8 dbaf(d)=-=- -.30 A' in.- In d-ln d.)l

" 358.5@(7e a'"r. d(ln d)making the substitution u=ln d

making another substitution, w=u-(ln d0+3 ln2o,)


19/54

U L T ~ O N I C EABUREMENT OF BUBPENDED SEDIMENT A13with the final result:

a*= 358.54"" e4.6 I,,, r,A' (15)3 . Diffraction-loss range:

a*=+(do, UO ,Q)33 dba' (d)=- -inch

which becomes by substituting u=ln d

By substituting u=u- (ln do-lnz u,)

which integrates to

Equations 15 and 17 for tlie scattering- and diffraction-loss ranges,respectively, include size;distribution parameters so they apply tomixtures of particles that have log-normal distributions. Either ofthese equations will give the attenuation for rigid particles if thesizes for any given distribution are entirely within either the scattering-loss or the diffraction-loaa range. For suspensions having sizes inboth ranges, equation 1 1 must be numerically integrated. Theprocedure used for integration is as follows:1. Log-normal size distributions for a wide range of d , and a , are

plotted on log-probability paper. From tlie plots the con-centrations and mean sizes of the arbitrarily chosen size incre-ments are read. The concentration increments are based on atotal concentration of 1,000 ppm.

2. The attenuation coefficient for the mean size of eacli incrementis read from figure 1 for eacli frequency.3. Then aT was con~putedas Za'(d)C(d) for each size distribution

and frequency. C(d) is the concentration of size d material.The resulting curves'are shown on figure 2. The solid lines show


20/54

I-ZW-U-I,. 0.I,.W0U

C ON TR IB UT IO ~~ S O GENERAL GEXUlOGY

2 10 I00 1000G E O M E T R I C M E A N P A R T I C L E D I A M E T E R . I N M I C R O N S

FIGURE.-Ultr88onlc attenuationfor mixturap of rigid particles having a log-normal slze dlstdbu -tion and falling w ithin the scatterlng- and dlffractlon-lossranges.


21/54

tlre results of the numerical integration, and these lines approachasymptotically the dashed l i e s , which are plots of e qu atio ns 15 and 17.For th e initial phases of this stu dy no relations were available forthe transition region (for elastic particles) from the scattering-loss todiffraction-loss ranges (0.5


22/54

CONT RIBUTION ,S TO GENER AL GEOLOGY

40 100 1000P A R T I C L E D I A M E T E R , I N M I C R O N S

FIGURE.-Experimental results for ultrasonic attenuation bj slze fractions made up fromMissouri Rive r sand and blastlng sand.


23/54

40 100 1000G E O M E T R IC M E A N P A R T I C L E D I A M E - T E R

I N M I C R O N SF I G U R E 4.-Ultrasonic attenuation at 2.5 an d 25 mc for nllxtures having a log-normal size

distribution.


24/54

A18 C O N T R I B W ~ O N I S O G E NE R AL G E0,LO GY

FIGURE .-Ultrasonic attenuation at 7.6 and 16 mc for mixtures havlng a log-normal sinedlstrlbutlon.


25/54

FIGURE .-Ultrasonic attenu ation at 5.0 and 12.6 mc for mixtures having a log-normal sizedistribution.


26/54

A20 CONTRIBUTION,^ TO GENERAL OEOUIQYBecause of its linear relation to attenuation, concentration may be

eliminated as a variable by using a ratio of the attenuation for a givenfrequency (a,) o the attonuation for a frequency of 25 mc (a2s).The reference chosen for the ratios is the attenuation for the highestfrequency used (25 mc) because the sensitivity of attenuation measure-ment increases as the frequency increases. Figures 7 through 14were obtained by plotting a,/a2sgainst transducer frequency and b yusing d, and v , as parameters. These figures show that the curvefor any given combination of d , and a , is unique.

When the size distribution of a given sediment suspension has beendetermined, the concentration may be obtained from figures 4, 5, or 6.

The laboratory measurement of an unknown sediment samplewould proceed as follows:1. The attenuation of the dtrasonic beam passing through a suspen-

sion containing sediment of unknown size distribution andconcentration is read and recorded for each of several specifiedfrequencies.

2. The recorded attenuations are then divided by the attenuationfor 25 mc and plotted against frequency on log paper of thesame wale as figures 7 to 12. The plotted curve is placed, inturn, over figures 7 to 12 to find a matching curve, from whichd, and a, are read.

3. The values of d, and a, are then used to enter figures 4 to 6 , fromwhich the attenuation per 1,000-ppm concentration a t anydesired frequency is read; the highest frequency will give thegreatest measurement sensitivity. The unknown concentra-tion of the sample is obtained by dividing this attenuation intothe attenuation recorded a t the desired frequency and multiply-ing by 1,000.

Thus, the size distribution and concentration for any log-normalsediment sample falling in the scattering-loss and diffraction-lossranges may be determined. The exthnsion of the relations into theviscous-loss range would follow the same procedure aa outlined forthe other two ranges.


27/54

2 10 30T R A N S D U C E R F R E Q U E N C Y , I N M E G A C Y C L E SFIGURE .-Curves for the determination of the size-dlatrihution parameters d , an d r , , for r ,equal to 1.4.


28/54

I

M . S . m i x t u r e

2 10 30T R A N S D U C E R , F R E Q U E N C Y , I N M E G A C Y C L E SFIGURE.-Curves for the determination of the size-distribution parameters d , and r. , for a,

equal to 1.6.


29/54

2 10 30T R A N S D U C E R F R E Q U E N C Y , I N M E G A C Y C L E SFIGURE.-Curve8 for the determination of the size-distribution parameters d , and a,, for a,equal to 1.8.


30/54

A24 CONTRIBUTIONS TO GENERAL GE,OIA~'GY

2 10 30T R A N S D U C E R F R E Q U E N C Y , I N M E G A C Y C L E SFIGURE 10.-Curves for the determlnatlon of the size-distrlbotlon parameters d, and a,, lor a,equal to 2.0.


31/54

2 10 30T R A N S D U C E R F R E Q U E N C Y , I N M E G A C Y C L E SFIGURE1.-Curvea lor the deternlination of the dze-dlstrlbution parameters d, and r,, for a ,

equal to 2.5.


32/54

A26 CONTRIBUTION~STO GENERAL GE,OQOGY

2 10 30T R A N S D U C E R F R E Q L I E N C Y , I N M E G A C Y C L E S

FIGURE2.-Curves for the determination of the slzedstribution parameters d, and r,, for r,equal to 3.0.


33/54

2 10 30T R A N S D U C E R F R E Q U E N C Y , I N M E G A C Y C L E SFIGURE3.-Curv89 show ing the sen sitiv ity of mea surem ent of the geometric stand ard deviation ,for d , equal to 150 micron s.


34/54

A28 CONTRIBU~,ON~SO GENERAL GXOLOGY

M . S . m i x t u r e

2 10 30T R A N S D U C E R F R E Q U E N C Y , I N M E G A C Y C L E SFIGURE14.-Curves showing the sensitivity of measurement of the geometric standard deviatlon,

d, equal to 200microns.


35/54

ULTRASONIC MEASUREMENT OF BUBPENDED SEDIMENT A29EXPERIMENTAL APPARATUB AND PROCEDURE8

A block diagram of the experimental apparatus is shown on figure15. The equipment is based on the sameprinciples as depth soundersor underwater suhmarinedetection devices; however, the attenuationis measured instead of range, and considerably higher frequencies areused.The pulse generator actuates the transmitter for 6 microsecondsat a repetition rate of 200 times per second, and it simultaneouslytriggers the oncilloscope sweep. The transmitter drives an x-cut

i quartz crystal, which transforms the electric wave into a pressurei wave. This ultrasonic pressure wave travels as a plane wave acrossthe sediment chamber to the reflector and back to the crystal. Thei: returning echo is transformed by the crystal into an electric wave,which then passes through an attenuator into the receiver and appearson the oscilloscope. (See figs. 16-18.)Plug-in transmitter units generate the frequencies, and eachplug-in uiiit is designed to operate at a specific frequency. Becauseonly odd harmonics of the quartz crystals are usable, the first, third,and fifth harmonics of the 2.5- and 5.0-mc crystals were used. Higherharmonics were very much desired, but funds and power output werelimited. Not only does the power output from the crystal decreasewith the higher order harmonics, but the attenuation due to thewater in the sediment chamber increases as the square of the fre-quency; therefore, as the frequency increases, the power output mustbe increesed. The upper limit for power output is determined bythe occurrence of cavitation in the water. The highest of the oixfrequencies used in this study was 25 mc.The crystal and reflector faces must be parallel to each other.Both lateral and longitudinal adjustmente of these components weremade by means of thumbscrews on spring-loaded bolts through

backing plates (figs. 15, 16). The longitudinal adjustment is princi-pally to place the components flush with the chamber walls forminimum flow disturbance.The sediment chamber is rectangular (3 by 3 in.) and has fillets ineach corner to reduce corner effecte on flow. The shape was mostconvenient to construct, especially for the refleetor and crystal ports.Clear-plastic walls allow observation of the flow.The concentration in the vicinity of the ultrasonicbeam pathshould be as uniform and steady as possible; therefore, a recirculatingsystem is used. The mixture is pumped from the bottom of thechamber through a plastic hose nnd discharges into the top of thechamber through 10 holes in the hose wall; the end of the hose isplugged (fig. 15). The jets fmm these holes cause extreme turbulence,


36/54

FIGURE6.-Blook diagram of ultrasonio appara tus.


37/54


38/54

I A32 CONTRIBTPPIONS TO GENERAL (f.EOU)OYwhich thoroughly mixes the sediment with the water. A doublescreen just below the inlet section reduces the turbulence. SteadyRow is attained rapidly (within about 10 seconds). A clear-plastictransition a t the bottom converges to fit the suction hose of the pump.The attenuator is a commercially available unit and measures upto 32 db, in 1-db steps. I t has a flat-frequency response up to 500mc. The reeeiver is of standard superheterodyne design. Theoscilloscope is a commercial unit and has good stability characteriatica.The operating procedure for a typical test proceeds as follows:

1. The sediment chamber is flled with distilled water by means of asiphon.., Care must be taken duringfilling to entrain as little airas possible because entrained air attenuates the ultrasonic wavemore strongly than does the sediment. After the chamber isfilled to a prescribed level, the pump is freed of air by operatingit in short. bursts and allowing sufficient time intervals betweenfor all air bubbles to rise to the surface. The pump dischargehove is placed deep onough below the surface so no air is en-trained by vortexes and yet shallow enough so the concentrationis uniform up to the surface. Actually, because of the caretaken, little trouble was encountered with entrained air.

2 . Two transmitter units are plugged in: one of them is transmittingwhile the other is warming up. The frequency that is beingtransmitted is tuned in on the receiver dial: the transmittersmay require retuning. After the apparatus is tuned, the echotrace on the oscilloscope is set to an arbitrary height by ad-justing the attenuator and the volume control on the oscillo-scope. The amount of attenuation in the circuit is read; asmuch attenuation is placed in the circuit as is allowed by the

I

#,

transmitter power output and the chosen trace height.3. After the trace is set the pump is shut off, and the sediment sample

. is introduced a t the top of the chamber. Again care must be; taken not to entrain air; the sample is poured in slowly, and1 , < ...,,I.? time is allowed for trapped air bubbles to come to the surface.iI , ; The finer samples are'more inclined to trap air bubbles, how-i ever, no difficulty was encountered when the above procedurewas followed.4eb,,&ter all air bubbles drawn into the water by the sediment samplereturn to the surfam, the pump is turned on. When the con-centration becomes uniform, the echo becomes relatively steady;but the echo hae decreased because of the additional energy losscaused by the presence of the sediment. The trace is adjustedI back to its original height by changing the attenuator to de-crease the attenuation in the electric circuit. The amount ofthe decrease is the additional attenuation of the ultrasonic beam


39/54

caused by the suspended sediment. Any effect of nonlinearitiesin the receiver or oscilloscope or of dissolved solids in the fluidis eliminated by confining the measurement to the effect ofsediment only.5 . Because drift of some of the transmitter frequencies is sometimes aproblem, each run is checked by shutting off the pump after thetest and allowing the sediment to settle. If no drift has oc-curred, the t raw will return to its original height with the initialattenuation. If any drift is found, the sample is rerun. Ofcourse, short-time drift might not be detected.6. When a test is completed, the recirculating system is thoroughlywashed out, in preparation for the next run.

The first step in the experimental program was to obtain the relationof attenuation coefficient to particle size for the six frequencies. Sizefractions having as narrow a spread of sizes as poqsible were required.An investigation of methods for obtaining size fractions indicated thatsieving would probably be the most suitable. The range of particlesizes from 44 to 1,000 microns was broken into 17 fractions, whosea, was leas than 1.2 . Because figure 2 shows that the attenuationcoefficient for size distributions having a a, equal to 1.2 is very nearlythe same as for a, equal to 1.0, these fractions were considered to benarrow enough for testing.The samples were all sieved twice. For the firat sieving the sandwas placed on the top sieve of the nest and run in the sieve shaker for15 minutes. The fractions were collected in separate jars. Thenfor the second sieving about 5 grams from each jar was placed on thesieve above the one on which it was originally retained and again runin the shaker for 15 minutes. The inherent inaccuracies of sieving'undoubtedly account for least part of the experimental scatter.Size fractions were obtained in this way for Minnesota silica sand,blasting sand, and a mixture of Missouri River sand and blasting sand.The mixture was necessary to obtain sufficient amounts of each sizefraction.Some sand fractions that had been prepared by other experimenterswere available. Because tests on these fractions were run prior tothe design and construction of the present variable-frequency ap-paratus, they were run a t only one frequency, 25 mc. The sands areCheyenne River sand, Taylow Falls sand, Republican River sand,Powder River sand, and a specially mixed sand.

Other materials available in size fractions were glass beads andabrasive grits of aluminum oxide and of silicon carbide. The glassbeads were sieved according to the above method, but the size rangeof the abrasive grits was considered to be narrow enough in range toforego the ndded labor of sieving. The a, of the gri t was less than 1 .2


40/54

A34 CONTRIBUTIONS TO GENERAL bEOXlQYexcept for the very h e grits, which were far below the sieving range.

All these materials have been uaed in this study, although onlythe M.S. mixture was thoroughly tested. The others will aid inresearch extending beyond this study.

DIBCUBBION O F REBULTBFigure 3 shows the results of the M.S. mixture size-fraction tests

for the six frequencies. A comparison of this figure with figure 1,which shows the theoretical curves for the scattering- and diffraction-loss ranges, reveals some interesting differences.

The theoretical relation for the diffraction-loss range is mdependentof frequency, whereas figure 3 indicates that attenuation is dependenton frequency. Similar plots, not included in this study, for Minnesotasilica sand, aluminum oxide abrasive grits, and glass beads alsoindicated frequency dependence. The theoretical relation for thediffraction-loss range is

The empirical relation for the M.S. mixture for this range is(IS)

or for C=1,000 ppm,(I=0.000122f'ad

wheref is the transducer frequency in cycles per second.The experimental diffraction-loas curvea of figure 3 begin to deviate

from a straight-line relation a t about 500 microns for 25 mc and a tincreasingly larger sizes for lower frequencies. The curves seem toapproach independence of frequency near the 1,000-micron size,though additional data for sizes greater than 1,000 microns areneeded to determine the relation conclusively. Accurate measure-ment is rather difficult to achieve for these large sizes owing to theunsteadiness of the echo.

Anderson's results (1950) indicate that the transition region betweenthe scattering- and diffraction-loss ranges extends from 0.5


41/54

3.0 for each frequency. F or each of th e six frequencies used, therange of sizes in th e tra nsition region is as follows:Porllclc-d b m a mP T C Y U ~ C Y r o n o a(mcoawclra) (mlcraa)

2.5................................................. 4-5605.0................................................. 46-2827.5................................................. 31-18812.5................................................. 19-11215.0................................................. 16- 9425.0................................................. 9- 56

For all the frequencies except 2.5 mc the smallest size tested wasstill in the transition region. The oretically, th e lower limit of t h etransition region would approach the scattering-loss curves; however,th e lower limit for 2.5 m c does no t appea r to do so. A possible expla-nation may be that the transition regions from diffraction loss toscattering loss and from scattering loss to viscous loss overlap for2.5 mc. U nfortu nate ly, no size fractions were available in the M. S.mixture smaller tha n 44 to 62 microns. Fu rtherm ore, the equ ipm entlimitatio ns were m os t evident a t the small sizes, th e testing of whichinvolved long periods with attendant drift.T h e empirical expression for the straight-line p a rt of th e transition-region curves of figure 3 for the M.S. m ixture is

a=0.361P4d"'C (19)orforC= 1,000 ppm , a=0.000361P4d1"I n th e expression for the a ttenua tion of light in th e transition region,where X=2m, a r is proportional to K2 equation 6, p. A8). T hi sequation further shows the similarity between light and soundattenuations.Artificial m ixtures were mqde u p from th e size fractions of th eM.S. mixture to tes t th e theore tical propositions. T h e following sizedistributions were mixed a nd tested:

aeomb i c meen aim(mlcr ona) Geom cI~Ic landard der,i&iolt100................................... .4150................................... 1.4, 1.6, 1.8, 2.0200................................... .4, 1.0, 1.8, 2.0, 2.5...................................00 1.4, 1.8500................................... 1.4

Ta ble 1 shows a, for the experimental an d integ rated values for thesedistribution s for a conc entration of 1,000 pp m . Only 5 of 95 experi-me ntal readings differed by more th an 10 percent from the integratedvalues; the 2.51mc readings are excepted here because they are sosmall in magnitude th a t their accuracy is poor.6


42/54

T A B L ~.-Ezperimental and integrated vallree of the ollenualion coeficienl for aconoenlralim of 1,000 ppn I


43/54

Table 1 also s h o w the a,/a2, for the experimental and integratedvalues, represen tative curves of which are show n on figures 7 to 14.Data for the series in which d, is equal to 150 microns were incon-sistent a t first. Comparison with th e integrated valuea showed th atthe experimental readings at 25 mc were in error. Investiga tionindicated th a t a t the higher concentrations th e frequency of thetransmitter shifted slightly so the receiver was no longer exactly intune and the attenuation reading was too large.Fo r the teats of mixtures, concentrations were varied w ith frequen cy.At the higher frequencies the maximum concenbation was limited bythe power o utp ut available, and a t the lower frequencies the m inimumconcentration w as limited by the increased accuracy desired. T h elimitations resulted in the use of a low concentration for the highestfrequency an d a high concentration for the lowest frequency. Tab le1 shows the results of the attenuation readings at various concentra-tions adjusted to 1,000 ppm for each frequency. T h e adjus tmen t isno t strictly valid because all the factors entering into t he m easurementerror, such as the drift, are not proportional to concentration. How-ever, in spite of ignoring these facto rs, most of the experimen talresults agree within 10 percent of th e integ rated values; therefo re,figures 4 to 6 may he considered sufficiently accu rate for c oncen trationdetermination.

Figures 7 to 12 indicate th a t for a given geometric stan da rd devia-tion, the sen sitivity of measuring th e different geom etric mean sizeswith th e method is high. Also, the agreement between th e experi-m ental and integrated d at a is reasonably good.Figures 13 and 14 indicate th at for 150 and 200 microns, the sensi-tivity of measuring the different geometric standard deviations withth e method is no t as high as th at for the geometric mean sizes. T h ecurves are so close together that the experimental equipment inac-curacies are m ore serious, especially if th e highest frequency used is a tall unstable, because d other attenuations are divided by thisfrequency.T h e sensitivity of measureinent m ay he increased b y using a fre-quency higher than 25 mc. Figures 19 and 20 are theoretical plotsfor the sam e geometric mean s i z e and geometric stand ard deviationsas those on figures 13 and 14, but the highest, or reference, frequencyis 100 mc.Present indications are that the highest frequency usable in anexperimental apparatus would he somewhat less than 100 mc-probably around 50 mc-because of prac tical lim itations such asth e structu ral limit on thinness of a crystal, wbich determ ines itshighest fundamental frequency, and such as the difficultiea causedb y s tra y capacitance and inductance a t very high frequencies.


44/54

A38 CONTRIBUTIONS TO GENERAL GE.~W)GY

FIGURE9.-Theoretical curves showing incressed sensitivity of measurement of the geometric standarddeviation by using a higher reference transducer lreqnency, for d l equal to 150 microns.

The sensitivity of the apparatus to concentration measurementdepends mainly on the accuracy of readings, the frequency, thegcorrletric mean size, and to a lesser degree on the dispersion param-eter. The inherent inaccuracy of reading the apparatus is consider-ably greater for the larger particle sizes because of the unsteadinessof the echo. If the transducer frequency is 25 mc and the geometricstandard deviation is 1.0, the attenuation coefficient at a d, of 500microns may be read within 0.15 db per in. to give an accuracy of


45/54

FIGURE0.-Theoretical curves showing Inmeased sensltivit3 of measurem ent of the geometric standarddeviation b y using a higher reference transducer frequency , for d, equal to 200 microns.

f 250 ppm, and at a d, of 100 microns the attenuation coefficientreadings are within f .05 db per in. for a sensitivity of f 2 0 ppm.The greatest sensitivity is given by the highest frequency, whichtherefore should be used for determining concentration. The concen-tration measurement is then very sensitive for the srnaller sizes. Theslopes of the attenuation-concentration lines for the six experimentalfrequencies indicate the sensitivity of the concentration rneasureinent(fig. 21).


46/54

A40 CONTRIBUTIONS TO GENERAL GE,OWGY


47/54

Before the constructioh of the variable-frequency equ ipm ent,some preliminary tests were made of the effects of different typ esof sedim ent on th e relation of at ten ua tion to particle diam eter.These tests were run at 5 and 25 mc, and their results are plotted onfigures 22, 23, and 24.Figure 22 shows the resu lts of tests a t 25 inc made on six sandsfrom different sources. T he solid line is the theoretical curve fordiffraction loss. The respective best-fit diffraction-loss curveswould be in rath er close agreem ent except for those of the Cheyenneand R epublican River sands.


48/54

A42 WNTRIBUTION~STO GERERAL C:EOU)GY

FIGURE 3.-Attenuation-wefiicient relation for different sands and materials at 25 mc.

Figure 23 shows the attenuation-diameter relation at 25 mc ofM.S. mixture sand, Minnesota silica sand, glass beads, and aluminumoxide abrasive grits. Plotted points for the Minnesota silica sandand glass beads appear to scatter around virtually the same curve.Plotted points for the M.S. mixture and aluminum oxide grit fallabout a curve that is of the same slope as the curve for the othertwo materials but a t a different intercept.

The attenuation coefficients for 3 of the 9 sands or other materialsbegan to deviate from their straight-line diffraction-loss curves forsizes larger than 500 microns (figs. 2 and 23). The deviation notedon figure 3 was also for sizes larger than 500 microns. Because thedeviation appeared for only three of the sands, some sediment prop-


49/54

P A R T I C L E D I A M E T E R , I N M I C R O N SFIGURE4.-Attenuation-wefRcient relation for different materials at 5 mc.

erty must be involved rather than any nonlinearity in the attenuation-concentration relation. The conclusion is that if nonlinearity causedby a high concentration of particles were involved, all the sands and~naterialswould show the same deviation. Further study is neededto determine the reasons for the deviation. However, the deviationis not a serious problem in most laboratory or field testing becauseonly small amounts of the larger sizes are present in most suspendedsamples and because the attenuation coefficient for the larger sizesis considerably less than that for the sizes smaller than 500 microns.Thus the part of the total attenuation coefficient contributed by thelarge sizes is usually insignificant.


50/54

A44 GONT~IBUTION.~O GENERAL G E O G YFigure 23 indicates that at tenuation is affected only slightly bydensity. Shap e factors might have some effect, although the turhu -lence in the chamber would cause all particles to rotate rather thanfall with an y given orientation. T he rotary mo tion would tend togive a shadow in the diffraction-loss range t h a t would even ou t someof th e angularities except, of course, for elongated particles. Of thematerials tested , the abrasive is th e mo st angular, and the glass beadsare th e most spherical. M ore work needs to be done to determ ineth e effect of sh ap e factors. O ther properties relating to th e soniccharacter istics (such as the modu lus of ela sticity ) of a m ater ial alsoshould he considered. An imp or tan t aspect of fut ur e research onth is subje ct is th e determ ination of the influence of different sediment

characteristics on th e m easured results.Figure 24 shows the attenuation-diameter relation for the M.S.mixture, M innesota silica sand, an d glass beads a t 5 mc. T h e slopeof M inn eso ta silica san d in th e diffraction-loss range is different fro mth e theoretical slope. Th e slopes for d l three materials differ in th etransition range.Although the ultrasonic method is promising for rapid and con-venient analysis of sediment concentration and particle size, thepresent form of the equipment is not very practical, especially whenfiner sediments are involved. Too much time is required for th esediment to se ttle ou t before the echo of the nex t frequency can headjusted to the zero-concentration level. Th e settleme nt time is sogrea t th a t drift can be a serious problem. I n fact, reproducible d a tawere difficult to obtain for sizes smaller than about 60 microns.Un fortun ately, eq uipm ent limitations and th e unavailability of sedi-men ts with v ery sm all, hu t know n, particle sizes prevented extensionof the s tu dy into the viscous-loss range .T o design a transm itter t h at would be free of t h ~ s e roblemsseems entirely possible. Ins tead of several plug-in un its th e tran s-mitter should be a single unit that has crystal-controlled channelsth a t are band-switched to ob tain the required frequencies. Becaused l tubes would be in co nstan t operation, the single un it would elim-inate the warmup time before each test and the associated drift.Also, the transm itter w ould be designed for higher power o u tp ut tha nth a t of th e present un its; thus higher frequencies could he used toiniprove the sensitivity of m easuremen t. A stable tran sm itter could h eadjusted at each frequency to give a certain exact output for zeroconcentration; thus, the zero-level adjustments would be eliminatedexcept for periodic checks. Rapid te sts on an y size of sed imen twould then he possible.An adequate ultrasonic method would he especially advantageousfor sediments finer than the sieve tange, because the ultrasonic


51/54

$b8 analysis could be completed in a few minutes, whereas a sediment*L tion-method analysis takes considerable time. The distribution forthe complete range of particle sizes could be determined with themethod if the experimental attenuation-diameter relations are ex-

tended into the viscous-loss range and if the procedures outlined inthis study are followed. Also, distributions other than log normalcould be determined with the method if they were used to plot curvescorresponding to those on figures 7 to 14.The ultrasonic method seems to be adaptable to a continuouslyrecording device for use in natural streams. The housing containingthe transducer could be suspended in the stream a t the desired pointof measurement. The equipment could operate principally a t onefrequency, for instance 50 mc, and could be made to scan the range offrequencies automatically a t preaet time intervals. Hence, a con-tinuous record of concentration with frequent size analyses could beread from the recorder graphs.Some method would have to be found for correcting the zero-concentration calibration of a field instrument for the effects oftemperature and entrained air. A possible solution would be totrap a sample of water, let the sediment settle out, and then makethe zero reading.Because the attenuation relations for light and sound differ onlyby a constant factor, the approach described in this study seems to beequally adaptable to light. However, the experimental curves forlight would probably differ more from one sediment to another thanthe curves for sound (fig. 3). Thus, quantitative measurement ofsize distribution and concentration probably could be obtained for agiven sediment by varying the wavelength of the light, as did Gambleand Barnett (1937).

CONCLUSION8 AND RECOMMENDATIONSA method was theoretically developed and experimentally verifiedfor measuring concentration and size distribution of a suspendedsediment with ultrasonic equipment.In the theoretical development, attenuation relations for soundwaves passing through suspensions of uniform-sized particles wereextended to include size-diitribution parameters describing mixturesof particle sizes having a log-normal distribution. From the relationsfor mixtures of particlesizes, the size-distribution parameters and theconcentration were determined uniquely by varying the frequency ofthe sound wave., The derived relations seem equally adaptable tomethods in which light waves are used. Furthermore, size distribu-tions other than log normal can be determined by following a methodsimilar to that described here.


52/54

A46 COiYTRIBUTIONlG TO GENERAL QEDLOI3YFor the diffraction-loss range, the theoretical attenuation is inde-pendent of frequency, but the experimental resulds show that attenu-ation is a function of the one-third power of frequency. No simple

theoretical relations are available for the attenuation coefficient inthe transition region between the scattering-loss and diffraction-lossranges. The experimental relations showed' about the same depend-ency on frequency as did those for light waves. The attenuationequation for' the M.S. mixture sand in the transition region wss

For light, the attenuation coefficient is proportional to K1, whereasfor sound it is proportional to I!?.'. Experimental relations for thescattering-loss and viscous-loss ranges were not found because ofequipment limitations. Sizes tested covered the sieve range only.Experimental results from artificially constructed log-normaldistributions were in close agreement with the theoretical results.The sensitivity of measuring the geometric mean size is high, butthat of measuring the geometric standard deviations should beincreased by using a frequency higher than 25 mc. The ultrasonictechnique is sensitive to concentration for the usual range of suspended-sediment sizes.The time required lor an ultrasonic annlysis in the laboratory willbe considerably shorter than that required for a sedimentation-methodanalysis, especially of sizes smaller than the minimum sieve size.However, the drift that occurs in the present equipment must bereduced before the equipment will be practical for h e sediments.Equipment limitations and the unavailability or fine sediments withknown particle sizes prevented adequate study of the viscous-lossrange.

The ultrasonic method seems adaptable to continuously recordingand automatic field installations. Operation at one frequency,perhaps 50 mc, could be augmented by scanning the range ol lrequen-cies at preset time intervals to give a record of concentration withfrequent size analyses.Although experimentally verified, the ultrasonic method still requiresextensive research before it will be usable for routine work in thelaboratory or field. An extensive equipment-development program iis needed to improve the laboratory equipment and to design con- 1inuously recording field equipment. With improved laboratoryequipment, the experimental relations and theoretical curves can beextended into the viscous-lose range. The effects on the attenuation-coefficient equation of such factors ss shape, density, and thermal and


53/54

elastic properties of the particle should be studied for each loss range.Allowable limits of departure of size distribution from a log-normalcurve need to be studied.LITERATURE CITED

Anderson, V. C., 1960, Sound acattering by solid cylinders and spheres: AcousticalSoc. America Jour., v. 22, no. 4, p. 426-431.

Austin, J. B., 1939, Methoda of representing distribution of particle size: Indus.and Eng. Chemistry, Anal. Ed., v. 11, p. 334-339.Blench, Thomas, 1952, Normal size distribution found in samples of river bed

aand: Civil Eng., v. 22, no. 2, p. 147.Busby, J., and Richardson, E. G., 1966, The propagation of ultrasonics in sus-

pengiona of particles in a liquid: Phya. Soc. [London] Proc., v. 69, no. B,p. 193-202.Chow, Ven Te, 1954, The Log-probability Law and i ts engineering applications:

Am. Soc. Civil Engineers Proc., Separate no. 636, 26 p.Colby, B. R., and Hembree, C. H., 1965, Computatione of total sediment discharge,

Niobrara River near Cody, Nebraska: U.S. Geol. Survey Water-SupplyPaper 1367, 187 p.DallaValle, J. M., 1948, Micrometrics: New York, Pitman Pub. Co., 555 p.Einstein, H. A,, 1944, Bed load movement in Mountain Creek: U.S. Dept. Agr.,

Soil Conserv. Service, SCS-TP-65, 54 p.Epatein, P. S., 1941, On the absorption of aound waves in suspensions andemulaions (Theodore von Karman Anniv. volume): California Inst. Tech-nology, Paaadena, Calif., p. 162-188.

Faran, J. J., 1961, Sound acattering by solid cylinders and spheres: Acou8ticalSoc. America Jour., v. 23, no. 4, p. 406-417. , ,Gamble, D. L., and Bamett, C. E., 1937, Scattering in thc near infrared-a

measure of particle aise and size distribution: Indus, and Eng. Chemiatry.Anal. Ed., v. 9, p. 310-314.Grassy, R. G., 1941, Use of turbidity determinations in estimating the auepended

load of natural streams: Am. Water Works Asaoc. Jour., v. 36, no. 4, p.439-463.Hatch, Thcodore, and Choate, 9. P., 1929, Statistical description of aize propertieaof non-uniform particulate substances: Franklin Inet. Jour., v. 207, p.369-387.Lord Rayleigh, 1037, The theory of aound, 2d ed.: New York, Dover Pub.,

v. 2, 504 p.Morse, P. M., 1048, Vibration and sound, 2d ed.: New York, McGraw-Hill

Book Co., 468 p.Morse, P. M., and others, 1946, Scattering and radiation from circular cylinders

and spheres: U.S. Navy Dept.. Ofice of Reaearch and Inventions,washington, D.c., 129 p.-Sewell, C. J . T.. 1010. The extinction of aound in a viscoue atmoa~her e y smallobstacles of oylindrical or spherical form: Royal SOC. [~ondonlPhilos.Tram. (A), v. 210, p. 230-270.

Smoltc~yk, . U., 1065, Beitrag sur ermittlung der feingeschiebe mengenganglinie:Inst. fur Waaserbau Mitt. 43, Technischen Univ. Berlin-Chariottenburg[in German], p. 25-60.


54/54

Documents

USGS Bulletin 1141-A