pesky cet Bua. Kea. Gtr TP TP 77-2 Stilling Well Design for Accurate Water Level Measurement by William N. Seelig TECHNICAL PAPER NO. 77-2 JANUARY 1977 Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING RESEARCH CENTER Kingman Building Fort Belvoir, Va. 22060 Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from: National Technical Information Service ATTN: Operations Division 5285 Port Royal Road Springfield, Virginia 22151 The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. qua oO t- ——— up oa wT — a) ho =~ = a Mn wh UN SSIF SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE RE AU NSERUCTIONS BEFORE COMPLETING FORM T. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER Paar 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED STILLING WELL DESIGN FOR ACCURATE WATER LEVEL MEASUREMENT Technical Paper 6. PERFORMING ORG. REPORT NUMBER 7. AUTHOR(S) 8. CONTRACT OR GRANT NUMBER(s) William N. Seelig 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS Department of the Army Coastal Engineering Research Center (CERRE-CS) Kingman Building, Fort Belvoir, Virginia 22060 A31220 » CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Department of the Army January 1977 Coastal Engineering Research Center 13. NUMBER OF PAGES Kingman Building, Fort Belvoir, Virginia 22060 21 - MONITORING AGENCY NAME & ADDRESS(If different from Controlling Office) 1S. SECURITY CLASS. (of this report) UNCLASSIFIED 15a. DECLASSIFICATION/ DOWNGRADING SCHEDULE DISTRIBUTION STATEMENT (of this Report) Approved for public release; distribution unlimited. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) - SUPPLEMENTARY NOTES KEY WORDS (Continue on reverse side if necessary and identify by block number) Long waves Stilling well Water level measurement ABSTRACT (Continue on reverse side if necesaary and identify by block number) A method is presented for the design of stilling wells based on the work by Noye (1974a, 1974b, 1974c). A step-by-step procedure is out- lined, design curves are presented, and an example is given to illustrate the procedure. DD ion", 1473. cprtion oF t Nov 65 Is OBSOLETE a UNCLASSIFIED C SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) Ge atk ute Wes Y nt pee eye Gis A a oe rea ie ai Seve i PREFACE This report provides coastal engineers with a method for designing stilling wells to accurately measure coastal water level fluctuations, based on the theoretical and laboratory work of Noye (1974a, 1974b, 1974c). The work was carried out under the coastal structures program of the U.S. Army Coastal Engineering Research Center (CERC). The report was prepared by William N. Seelig, Research Hydraulic Engineer, Coastal Structures Branch, under the general supervision of Dr. R.M. Sorensen, Chief, Coastal Structures Branch. Comments on this publication are invited. Approved for publication in accordance with Public Law 166, 79th Congress, approved 31 July 1945, as supplemented by Public Law 172, 88th Congress, approved 7 November 1963. OHN H. COUSINS Colonel, Corps of Engineers Commander and Director CONTENTS CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI). I INTRODUCTION . II LINEAR DAMPING STILLING WELLS. III DESIGN OF THE WATER LEVEL RECORDER . IV A SAMPLE DESIGN. V CONCLUSION . LITERATURE CITED . FIGURES 1 Approximate distribution of ocean surface wave energy illustrating the classification of surface waves . 2 The linear stilling well . 3 Response characteristics of a linear stilling well 4 Theoretical linear stilling well design to obtain 90 percent of a l-hour wave . 5 Theoretical linear stilling well design to dampen 95 percent of a 10-second wave. 900i 6 Amplitude response of the Pentwater stilling well predicted from the drainage test. SUNT Ace oL mG Royton ros neice nigl 70 7 Pentwater water levels, November 1974. 8 Spectra of water levels for Pentwater Lake, Michigan, for November 1974 . Page 18 21 19 20 CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) UNITS OF MEASUREMENT U.S. customary units of measurement used in this report can be converted to metric (SI) units as follows: Multiply by inches 25.4 2.54 square inches 6.452 cubic inches 16.39 feet 30.48 0.3048 square feet 0.0929 cubic feet 0.0283 yards 0.9144 square yards 0.836 cubic yards 0.7646 miles 1.6093 square miles 259.0 knots 1.8532 acres 0.4047 foot-pounds 1.3558 millibars 1.0197 X 10°? ounces 28.35 pounds 453.6 0.4536 ton, long 1.0160 ton, short 0.9072 degrees (angle) 0.1745 Fahrenheit degrees 5/9 To obtain millimeters centimeters square centimeters cubic centimeters centimeters meters square meters cubic meters meters square meters cubic meters kilometers hectares kilometers per hour hectares newton meters kilograms per square centimeter grams grams kilograms metric tons metric tons radians Celsius degrees or Kelvins’ ‘To obtain Celsius (C) temperature readings from Fahrenheit (F) readings, use formula: C = (5/9) (F — 32). To obtain Kelvin (K) readings, use formula: K = (5/9) (F — 32) + 273.15. (Re); ee oY n AMMO meats Sie stamens fh ‘cet ans enna cea teem ; ae TIF) Bs Ge OF Tips binomials Hee ty ids gyntoun ce BE A vo ® a ae et ¢ . otitamtifsayy raatipe FC GRELIR Mk ) xpos ob Fi Rests es it4 11 eRe Dib aration ae Wt a REN ae : RSID in ONAL 2 exdo.e | ei a Mir Sc ee De ae ah iy ve ays i ; casas Aig 4 hh Fi ene Hh se aa igh ne A herein 4s iH om ee. i) be it ae it wigs Lien mds diet 3h cael ieee aay ri ay Aid ' Bi) Det ie eer nade weil? ny wed Rey aa ae F (: cotstom Wana eas Cc) hes wy : ua) hve s ¢ oat, SRRIVERACRT: eb ies Vat er ® a S © Weeret ite \Snemsnatei ) : ‘esis bea 50 porcpin 7 a Ow mV « | ie “6.068 of Co. s iy oe ite Masha slate ne tet og ZARB. Hatin oh OS Ten aes ametooh D atk sink.o r 1,8 oe Yin vet aceon oO! GE MALT st See - ivi Pee “adit ae ponent pee ot weuie ett iene ie a) x Ce | ana a : ' Hite 2: mata 4% eves ved mt lator hee ‘Bei ie - 7 | ft i’ r eu, i a Pt wit ro aru rae By, eb ti ue ee - dynes Psat - p | hee ee . aug ie ee rete a — } awe oitoar Sl ce ae | ai0e ae 7 ee a aauibny lestviaAl ww! yongniy’ nasbots) ee we. maT =e sor esi nme SC crises bape dabilinicl ain (ck 4) iy P= LD. sadtaerel bad mean CR Sywhctond? ; - : Let (ah, i “aioeet® - 7 i ahve be seus STILLING WELL DESIGN FOR ACCURATE WATER LEVEL MEASUREMENT by Welitam N. Seeltg I. INTRODUCTION Coastal engineers and scientists have a frequent need for accurate measurements of long-period water level fluctuations (periods longer than about 5 minutes). Important long waves may include astronomical or meteor- Ological tides, seiching of lakes and harbors, and tsunamis. The approxi- mate distribution of ocean surface waves is shown in Figure 1. A problem in measuring water level has been that the long-period wave of interest, the stgnal, is often of much smaller amplitude than the short- period wind waves that act as notse. For example, on the Great Lakes a seiche important to inlet hydraulics may have an amplitude on the order of 0.1 foot, while wind waves may be several feet high. In this type of Situation where the signal-to-noise ratio is small, a carefully designed system is needed to dampen or eliminate noise while recording the important long waves. This paper presents a method of designing a water level recording system for accurately measuring water level fluctuations of interest by dampening or eliminating undesirable short-period fluctuations. The unique aspect of this design is that water level fluctuations inside the well are linearly related to fluctuations outside the well, so no nonlinear water level amplifications occur. The linear stilling well design presented requires that the well be free from fouling. Even a small piece of debris in the orifice will dis- rupt the response characteristics of the well, so this type of well is recommended for short-term operation in clear water areas. II. LINEAR DAMPING STILLING WELLS Noye (1974a), using laboratory tests, showed that the conventional stilling well, consisting of a well and orifice, will respond to a broad spectrum of waves and a response of this type may confuse the record of interest. Cross (1968) reported that this type of well system may intro- duce higher harmonics of waves into the well and that wind waves, through nonlinear effects, can cause a net displacement of the mean water level inside the well as compared with the mean water level outside the well. A recommended stilling well system for accurately measuring long waves is the linear damping stilling well which has a pipe or tube as an orifice (Fig. 2) (Noye, 1974b, 1974c). This system can be designed to record the important long waves and eliminate undesirable noise. A disadvantage of the system is the critical diameter of the intake pipe. Dirt or other foreign matter entering the pipe will disrupt cali- brated response characteristics. For this reason, the intake to the well should be carefully sited, preferably in an area where fouling will not affect the operation of the well. *9010J SutTIO}SOI ALeUTId pue ‘g010j} SuTyNqta4stp AreutTid ‘pueq oAemM AG SOACM BOEFANS JO UOTIEITFISSe[I 94} SUTJeIYSNT[ IL ABSLOUS OAM 9deFINS UkdDO FO UOTINGTI4STp oqeutxorddy ‘[ sAnsTy (U/sa|oK9 ) ‘bas sOl pOl ¢ Ol 20 01 9Ol ,;-Ol 2-01 ¢-Ol (aID9S AaDayiquy) (3) Absaug SS SSS Ss Ooo db aua§ 5 18S SSS SS SSS Ss SS SHS SSS SOS SO SO SOS SS SoS S55 =! = SSS 9 9 SS SST eo : a \ 30404 | | \ i | | Bursoysay | L-——uo1suay 200j1ng¢_———-»J ! ' [gee 9108) SI}01409 ei eee oe Aapwiig ! ae ponen aa 4a2--- 2222 = b= 2 = =P oo a pp I ' 20404 ——_—_N pt emmiuoaly ‘unS—s, | PUIM i | Buiqanisig | ! ' I ' arene *sumayskS soi ++ Aipwidd I peeniee Saeaae a a A a eee ee 3 das aieeeaabosassos | |! =SanDdM SOaADM 6 ! SaADM j + S2n0m kane —maaiseae ee A9019 “ear nosDujaT S8ADM POlsad-bu07 aire | pug ee $10 sO'l SOE UIWG u2l Ube Ppolaad ——————— SaydiaS saxo] 4D919 Recorder d= Water Depth of Orifice D,=Inside Diameter of Orifice Pipe D,,=Inside Well Diameter 3S Length of Pipe Stilling Well Water Level to be Measured 1 : p Orifice Pipe aaré “$F Bottom L L | Sealed p Figure 2. The linear stilling well. The well is especially useful for short-term operations in measuring harbor response to long-wave forcing and long-wave conditions outside the harbor. On the Great Lakes, forced pumping mode oscillations near or longer than the natural pumping mode (''Helmholtz mode'') of the inlet-harbor system are generally the most important in producing reversing inlet cur- rents and harbor oscillations. If the gage is to be placed in a harbor and the geometry of the harbor and inlets are known, a formula can be used to predict the Helmholtz period (Seelig and Sorensen, 1976) or a simple numerical model can be used to show which long waves will be important to the harbor (Seelig, Harris, and Herchenroder, 1976). Typical Helmholtz periods for Great Lakes harbors range from 10 minutes to 5 hours. Once these potentially important periods have been determined, the stilling well system and recorder can be designed to record the waves. The linear stilling well consists of two basic components: (a) A well of inside diameter, D,,, which provides the stillwater level to be meas- ured; and (b) an orifice consisting of a pipe of length, L,, and inside diameter, D,,. Both the well and pipe should be smooth and free of ob- structions. Common materials are plastic or metal. The bottom of the well is sealed so that the water can only enter the well through the orifice pipe. Friction in the pipe due to laminar flow, in conjunction with the continuity of flow between the small orifice pipe and the relativly larger well, determines how the stilling well will respond to long-wave forcing. The variables that can be changed in well design are the diameter of the well, the diameter and length of the intake pipe, and the depth of the orifice pipe entrance below the water level. Noye (1974b, 1974c) has theoretically and experimentally shown that two dimensionless param- eters (8, and N) can be used to design a linear stilling well. 8, is a dimensionless frequency; N describes the amplitude modulation and phase lag of the long wave inside the well as compared with the wave outside the well. The parameters are given by Noye as: 128 v2 Ly Dy? and 32 v lp Dee \ 2a a g Dot | a (2) where v = the kinematic viscosity of water (about 107° feet squared per second) Lr = the pipe length (feet) D,, = the inside diameter of the well (feet) 10 g = the acceleration of gravity (32.2 feet per second squared) Dp T = the wave period (seconds). the inside diameter of the orifice pipe (feet) The theoretical dimensionless response characteristics of the linear stilling well as functions of N and 8») are shown in Figure 3. It is frequently best to design a well with a value of N_ greater than 5 because the well can be tested using a drainage test to determine the actual response characteristics of the well (Noye, 1974b). Wells with a value of N less than 5 are more difficult to test. A value of N = 0.33 gives the sharpest distinction between measured and dampened waves; however, this type of well is difficult to build of common materials and even more dif- ficult to test. It is desirable to have 0 < 8 < 0.4 for the long-period waves to be measured so that the long-wave amplitude in the well is approx- imately equal to the long-wave amplitude outside the well (Fig. 3). At the same time the value of 8, should be 10 or greater for the short- period wind waves and other noise for these to be thoroughly dampened by the well. Simplifying equations (1) and (2): ye 32975 X 10719 Lp Dy? and 2 Boy = Oo BA LOT sd (4) p for English units. Solving for the length of pipe in feet, Ly» from equation (4): ae 5 89 Dpt T = 0.160 X 10 . (5) 1g D2 The theoretical length of pipe as functions of the inside pipe diameter and the well diamater is given in Figure 4. This design is for 90 percent of the forcing wave with a period of 1 hour measured by the well. Since = is linearly related to period from equation (5), the pipe length from igure 4 can be multiplied by the period (in hours) to estimate L re- quired for waves other than 1 hour. To obtain 95 percent or more of a l-hour wave, reduce the pipe length in Figure 4 by about one-half. If the period of the important long waves is unknown, an alternate method of well design is to dampen wind waves and record any longer period waves. Curves designed to dampen 95 percent of the amplitude of a 10- second wave are presented in Figure 5. The pipe length can also be i 8 wai 2 OQ | oF Ss Si ® i re ) rm) & e © wo re) og : — oe e £ z (a) S. (eo) ro) (e) wo oO wo = A = = ro) ° (2P1S4NO 44B19H/ 119M aut apisu; yyBiaH aADM) (20) asuodsay apnijduy 40 10 4.0 Dimensionless Freq. (85) 1.0 HSN AAI SUDIPDY *>) 6b] asvud 0.4 0.) Response characteristics of a linear stilling well (after Noye, 1974b). Ravougeres l2 0.60 0.80 1.00 1.20 1.40 1.60 Figure 4. Theoretical linear stilling well design to obtain 90 percent of a l-hour wave. Figure 5. Theoretical linear stilling well design to dampen 95 percent of a 10-second wave. multiplied by the period (in seconds) and divided by 10 to estimate required for other than 10-second waves. The recorded long waves of inter- est can then be corrected for the particular well damping that occurred. The drainage test is recommended to determine the actual hydraulic characteristics of a well designed to measure a specific long wave. If the alternate well design is used, a drainage test is unnecessary. The drainage test should be conducted after the stilling well and its com- ponents are assembled, but before the well is installed. To perform this test, partially fill the well and allow it to drain until the flow stops. Close off the orifice, then fill the well with a head of water, H (in feet), above the orifice pipe level of approximately: 8000 v2 lp _ 2.48 X 10> 2 Tt He es = 7 (6) 3 =p 2 but not higher, to assure laminar flow throughout the system. Tests by Noye (1974b) show that the time constant of the well, Ty, is the time that it takes for the head inside the well to fall to 0.37 (37 percent) Ott iSeintvall heady. GH One way of determining when 37 percent of the head has been lost is by measuring the volume of water coming out of the orifice pipe with a premeasured bucket or beaker. The value of T, is then used to deter- mine the amplitude response, a, (well amplitude divided by forcing amplitude), of the well from: ee el TOs ae (7) be 2m To\2 1.0 + ( uy T 27 To arctan T (8) In building a well, first determine the theoretical orifice pipe length, then build the well with a longer pipe length. Test the well several times, using the drainage test to determine the actual hydraulic characteristics of the well. If the well dampens too much of the important waves, cut off some of the orifice pipe and re-run the drainage test until the desired response characteristics are obtained. and the phase lag from: E90 The drainage test can be run at any time during the life of the well to determine if corrosion or other fouling has impaired the function of the well. III. DESIGN OF THE WATER LEVEL RECORDER Care must be taken to select a level recorder compatible with the stilling well and the waves to be measured. For economic reasons, it is generally best to select a standard unit. A number of types with different options are available. If a digital recorder is chosen, the sample rate should be such that at least 15 to 30 data points are taken over each important long-wave period. The level resolution should be less than one-tenth the long-wave height. Because a digital recorder makes only an instantaneous measurement at each sampling interval, it is especially important to design the still- ing well to eliminate high-frequency or short-period noise. An analog recorder should have a chart speed fast enough so each impor- tant long wave is long enough on the chart for an easy and accurate meas- urement. However, too fast a speed for longtime periods will lead to large volumes of paper and frequent maintenance checks to replace the chart paper. The height scale should adequately record the important waves and still allow sufficient space at the top and bottom of the chart paper to record any extreme events which may occur. Some recorders offer a reversing pen when the chart paper width is exceeded. Analog recorders are available with either strip charts or drums. Strip charts are best for long-term operation; drums may be used for a short operation on the order of 1 day. Because analog recorders record the water level continuously, some water level fluctuations shorter in period than those of interest can be allowed to propagate into the well and this noise can be eliminated when digitiz- ing or analyzing the data. IV. A SAMPLE DESIGN The design of a stilling well at Pentwater, Michigan, is considered in measuring long-period waves potentially important to inlet hydraulics. A study of the Pentwater harbor indicates that waves with periods of between 1 to 2 hours will cause the largest reversing currents in the inlet (Seelig, Harris, and Herchenroder, 1976). Observation of the inlet also revealed that the water reversals have a period of about 1.5 hours. Figure 4 shows that a well with D,, = 0.83 foot (10 inches) and an orifice pipe of D, = 0.0208 foot (0.25 inch) should have an of about 7 feet to record 90 percent of a wave period, T = 1 hour, and about 11 feet for T = 1.5 hours. The well was constructed with an intake pipe length of 20 feet and several drainage tests were run. As predicted, the drainage test showed that this length dampened too much of the waves in the 1- to 2-hour range. The plastic orifice pipe was then cut back after several tries to a length of 15 feet. The drainage test showed that this well had a time constant, T, = 500 seconds; this well was selected for the final design. The predicted response characteristics of the well from equation (7) are shown in Figure 6. Note that for wind waves with a period of 10 seconds (0.003 hour) the amplitude response is 0.0003 which means that only 0.03 percent of wind- wave amplitudes are propagated into the well. 1.0 0.9 0.8 0.7 0.6 @20°5 04 0.3 0.2 0.I ae 020406 08 10 12 i4 16 18 2.0 Forcing Wave Period (h) Figure 6. Amplitude response of the Pentwater stilling well predicted from the drainage test. A further method of reducing wind-wave effects on the record inside the well is to put the orifice as deep as possible. As depth increases wave dynamic pressure attenuation increases and the wind waves become less noticeable. However, the orifice should not be put too close to the bottom where clogging may occur. The recorder for this system was a digital recorder with a sampling interval of 5 minutes and a sampling height resolution of 0.01 foot. The float was 5 inches in diameter. Figures 7 and 8 are examples of records and spectral analysis of records of water levels obtained at Pentwater, using this well. Note that several long waves are present simultaneously in the harbor at various periods of about 1 hour or longer. From Figure 6, 85 percent or more of the wave amplitudes are recorded and the particular percentages at each period can be used to obtain final amplitude values of the spectral com- ponents of interest. V. CONCLUSION A linear stilling well is recommended where accurate measurements of water level fluctuations are required and short-period noise must be dampened. 0.25 Height (ft) ro) 3 Nov i 2 we) on 0.25 Height (ft) ro) -0.25 4 Nov 0.25 Height (ft) ro) 5 Nov ! S Dw) n O 4 8 l2 16 20 24 Time (h) Figure 7. Pentwater water levels, November 1974. Spectral |.qe7 Peaks Period (h) 3 Nov (0000 h) to 4 Nov (1800 h) Normalized Variance 3 Ney (0) Wave Period (h) 1.3 4Nov (I8O00h) to 6 Nov (1300 h) Normalized Variance 3 215 1.0 Wave Period (h) Figure 8. Spectra of water levels for Pentwater Lake, Michigan, for November 1974. 20 LITERATURE CITED CROSS, R.H., "Tide Gage Frequency Response," Journal of the Waterways and Harbors Diviston, Vol. 94, No. 3, Aug. 1968, pp. 317-330. NOYE, B.J., "Tide-well Systems I: Some Non-linear Effects of the Conven- tional Tide Well," Journal of Marine Research, Vol. 32, No. 2, May 1974a, pp. 129-154. NOYE, B.J., ''Tide-well Systems II: The Frequency Response of a Linear Tide-well System," Journal of Marine Research, Vol. 32, No. 2, May 1974b, pp. 155-181. NOYE, B.J., "Tide-well Systems III: Improved Interpretation of Tide-well Records ,'' Journal of Marine Research, Vol. 32, No. 3, May 1974c, pp. 183-194. SEELIG, W.N., and SORENSEN, R.M., "Hydraulics of Great Lakes Inlets," draft report, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., in preparation, 1977. 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