
Hydrology Teaching Notes/Handouts
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 Hydrology Teaching Notes/Handouts
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 Parker, Garald G. (Garald Gordon)
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 Aquifers  Hydrogeology  Everglades (Fla.) ( lcsh )
Hydrology  Florida  Biscayne Aquifer (Fla.) ( lcsh )
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 University of South Florida
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 University of South Florida
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891343127 ( OCLC ) G1600660 ( USFLDC DOI ) g16.660 ( USFLDC Handle )
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â€¢ â€¢ â€¢ "" 0 6 J , j ' c 8 s.. ft4 0 Q) I I L co ' ft4 0 Hydrol. l Zones or subsurf'ace water, arterTerzagbiY Verslya~ Belt or spil water Intermediate belt (vadose water) Capillary fringe (Fringe water; p <.. atm) LAND SURFACE .Zone or discontinuous capillary saturation (Mainly separate rings and envelopes; p â€¢ atm) Zone ot semicontinuous capillary saturation (Larger openings~' unsaturated; p atm) Pendular stage Ftmicular stage/ (p â€¢ ata) +l Zone or continuous capillary saturation (p <:, atm) Capillary stage I (p â€¢ ata)6f+WATER TABIE +__J Grotmd water (phreatic water, pleurotic water; p > atm) Internal water (Juvenile water, magmatic water; may be wholly Ground water 1/ 11e1nzer, 0. E â€¢ : U. S. Geol. Survey 'laterSupply Paper 494, p. 23, 1923. Y Terzaghi, Karl: Soil moisture and capillary phencaena in soils, chap. 9a in Hydrology, edited by 0. E. Meinzer McGrawHill, pp. 331363, 1942. , Versluys, J., Die Kapillari tat der boden: Internat. Mitt. Bodenlrunde vol. 7, pp. 117140, 1917. , I in chemical union) 6/ Hubbert, King, Theory or groundwater aotion: Jour. Geol., vol. 48, no. 8, pp. 785944, Hov.Dec. 1940. I
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â€¢ â€¢ â€¢ Hydrol. 2 Surface tension and capillary rise At an interface between two fluids, molecular forces create a tensile stress in tbe surface or separationthis stress is known as surface tension. For water against air, this stress is f'airly large (0.073 g/em. at 200C); thus, water can resist hydrostatic tensile stresses or many atmospheres without losing its continuity. If the lower end or a vertical tube or very sâ€¢ll (capillary) diameter is dipped into a liquid, the liquid comes to rest within the tube with its surf'ace either above or below the free liquid surf'ace outside the tube, depending on the canposition of the liquid, the â€¢terial of the tube, and impurities in the liquid or on the tube. If tpe liquid is clean water and tbe "tube" is glass or one or the common earth â€¢terials, the water will rise in the tube, as in the sketch below. he o( / / / 2r 2r â€¢ diameter of tube heâ€¢ capillary rise "'â€¢ "contact angle" between edge of meniscus and wall of tube Here, pressure is atmospheric at the level or the free water surface both outside and inside the tube; pressure also is atmospheric on the water meniscus within the tube. Thus, weight of the water within the tube is sustained by surface tension in the meniscus, and the raised water column is under tensionthat is, the pressure is less than atmospheric. At equilibrium if r2 T he :s T 21rr cos ot (Weight) s (Lift by surface tension) where 1' s density of water at the particular teaperature T s surface tension in g/em Then he â€¢ r 2.1 coaoC (1) (2) For pure water in clean glass, a( = O and cos o( = l; for roan temperature or 20 c, T â€¢ o.b~ 1 ~~â€¢ ~~;ce {}) ~ J ~IJt
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â€¢ â€¢ â€¢ Hydrol. 2cont â€¢ For natural earth mterials there are too many variables to express capillary raise in precise terms, but in general it increases as grain size decreases. Terzaghi ("Hydrology," cha.pt. 9) cites experimental measure ments by Atterberg or capillary rise in seven sands at a temperature or 17oC over a term or 72 days. Porosities and void ratios were essentially the same in all seven41 percent and 0.69, respectiYely. The measurements, given below,show that capillary rise increased nearly in inverse proportion to the grain size. Grain size, mm he, cm 52 21 10.5 0.50.2 0.20.1 0.10.05 0.050.02 2.5 6.5 13.5 24.6 42.8 105.5 200M* Still rising after 72 days. If the capillary tube or the preceding sketch is raised vertically from the liquid, drainage will cease when the meniscus falls to a point about he above the lower end or the tube. At the same time a permanent droplet will form at the lower end or the tube as in the sketch at the left. As before, \ surface tension in the meniscus sustains the weight of the liquid column he. Near the lower end or the tube, stress h C _ droplet. Tension in the surface or the droplet acts like ),~\changes fran tension in the column to cOlll)ression in the 1an elastic container and transfers the weight of' the drop1 let to the lower end of' the tube. Conditions analogous to . this example exist in stratified, granular earth materials which are not continuously saturated and in which water is percolatbg downward from a finegrained material above to a coarsergrained material below. P=atm Let the sketch at the lef't represent an idealized section across the wall of' a well that taps unconfined ground water, with the waterbearing material replaced by a bundle or vertical capillary tubes or h c various diameters. Then, the upper surface or the "zone of' sat]mation" in the bundle Pâ€¢
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)) â€¢
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â€¢ â€¢ â€¢ llydrol. 2a Unit cross sectional area Piezomefric surface ~=~=Unit decline in ~~â€¢ piezometric surface~ , r:~~===Unit decline of water table I ~::__:.__.. _:___ I: t:_____:__. ::_:ConTfiiin9=:..=:.~ : : ~=~nial4rTaT.= :...:=====::, , , 1______ = ::::: :: :â€¢::. :::: : =:=:.:.::\ :. :::: :: .:.::Confinil}Jl_ :~__ _:_____: malerial :_: A . ARTESIAN AQUIFER :..:Con f i ning_.:::=______ material=_:~ 8. WATERTABLE AQUIFER Figure 2 Diagrams for explaining the coefficient of storage for artesian and for watertable aquifers GPO IJ5'40
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â€¢ â€¢ â€¢ Hydrol. 3 Movement of ground water Critical velocity.Index camaonly used to determine it flow is laminar or turbulent is the socalled Reynolds number where R dy.l' six fa y d â€¢ mean diameter or grains v â€¢ mean velocity or the moving fluid JJ â€¢ density or the fluid .P â€¢ dynamic viscosity or the fiuid y â€¢ kinematic viscosity or the rluid Ir R is less than about 1, the flow is "viscous" or laminar and velocity varies as the first power or the h1draulic gradient. Ir R is greater than about 10, the flow is turbulent and velocity varies as the onehalt power ( square root) or the h1draulic gradient â€¢ At values or R between 1 and 10, flow â€¢Y be either Jaminar or turbulent, depending on the range in si2:e and shape or grains. Darcy's lay.For steadystate laminar flow in pel'lleable media (when dh/dt â€¢ O) Darcy's law may be written where Q â€¢ k â€¢ A a I â€¢ hl and h2 â€¢ 1 s t Q .. kAI kA ( hl112) â€¢ kA dh/d quantity ~f/low in a given interval or time a constan~ crosssectional area through which now takes place h1draul1c gradient h1drostatic heads at either end or the flow reach length or the reach time Because movement is in the direction or diminishing head, dh/d is considered negative and Darcy's law ror unit crosssectional area may be generalized q â€¢ f â€¢ k dh/d:! when dh/dt â€¢ 0 l./ In the remainder or Hydrol. 3, k denotes coefficient or permeability in consistent units; P denotes coefficient or permeability in Geological Survey units. cf/~1 (4) (;) (6)
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â€¢ â€¢ â€¢ Hydrol. 3cont â€¢ Coefficient or permeability.In equation (5) the constant k is the coefficient of permeability or the transmission constant, a characteristic of the permeable medium. Then k â€¢ Q Ae].t2) or k = g dh/d 1 Thus, k has the dimensions or T Lf L/L â€¢ ; wb:l.ch is a velocity. where Meinzer' a coefficient or permeability p = l. gpd/rt Q â€¢ quantity of flow in gallons a day, at 600F I â€¢ hydraulic gradient (1) as a ratio 6h/.O.i or (2) in feet per mile A â€¢ crosssectional area in (1) square feet or (2) footlliles Thus, P has dimensions or (gal/day/rt2(rt/tt) â€¢ (gal/day)/rt2 It (gal/day/rtmile(rt/mile) T which again is a velocity. In the above equation of dimensions, rt/tt is unity or 100 percent hydraulic gradient. Slichter's trapapdssion constant (k, WaterSupplf Paper 140, p. 11) differs fran ~inzer's coefficient or permeability (PJ only in that Q is expressed in cubic feet a minute. Thus, using subscripts s and m to identify the Slichter and Meinzer units, respectively, we may write (7) Pm â€¢ 1.077 x 104 Pa (9)
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T Li. (l/L) ~!:!:1~ ,o"2~ 4/UC.~,, (d~/~) .;. .â€¢ â€¢ .' .. :,._.,..J. ~: â€¢â€¢ ~::: : â€¢ â€¢ â€¢
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â€¢ â€¢ â€¢ Hydrol. 3cont â€¢ Coefficient or trgpsmissibility.The coefficient of tr8D.Sllissibilit or trnnSJPissiyity (Theis) measures the capacity or an entire aquif'er to tr8DS11lit water at the prevailing temperature. In simplest terme it is Yeinzer's coefficient of peraeability (corrected for teaperature) aultiplied by the saturated thickness of the aquifer, thus where m â€¢ thickness or the aquifer, in feet W â€¢ width or aquifer, in feet Thus, T has dimensions of' (gal/day)/:rt(rt/tt) â€¢ (gal/day)/tt i,:. â€¢ T The coefficients P and T now are well entrenched in 2m:. literature. (10) However, they conform to neither the tootpoundsecond nor the centimetergr .. second systems. Other workers who deal with movement or fluids through per.able media have established other units of permeability, some or which introduce properties of the fluid (such as viscosity). Sane of' these units are more logical than ours; therefore, we should not quarrel with their use. Relation or ;permeability to grain size.According to Jacob (Engineering Hydrology, cbapt. 5, p. 324, 1950), a coefficient or permeability (k) may be expressed in the fora where Qd2Y k â€¢ ,M C â€¢ a dimensionless constant depending on physical characteristics or the permeable medium (porosity, range and distribution or grain sizes, shapes of grains, etc.) d â€¢ mean diameter or grains Y â€¢ specif'ic weight (density) or the fluid )A â€¢ viscosity of the fluid Ignoring properties or fluid ( Y and)A) , permeability or medium alone may be regarded as (11) (12) which is another wa:y of saying that the permeability varies as the square or the grain d;temter, and thus has the dimensions 1 2 â€¢ This is in agreement with S. I:rmay (On the hydraulic conductivity of unsaturated soils: Am. Geophys. Union Trans., vol. 35, no. 3, equation (12) p. 465, June 1954) â€¢
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â€¢ â€¢ Bydrol. 3cont â€¢ Relation or coefficient of permeability to velocity.Darcy's law may be written Q â€¢ kIA â€¢ pAv k â€¢ ll (13) I where where p â€¢ porosity v :s velocity In Geological Survey units, equation (1:5) may be written p â€¢ 1,4~ PY gpd/rt v â€¢ velocity, in rt per day Relation or Darcy's law to Thiem equation.Let the following sketch represent half the cross section or the cone of depression around a well that has been pumped long enough for the essential establishment or steadystate flow (equilibrium; dh/dt â€¢ 0) (14} If the material is homogeneous and if the base or the aquifer and the undisturbed water table are assumed to be parallel and horizontal; then, by Darcy's law, equal quantities or water flow through any two concentric cylinders as at r1 and r2, and the quantity or flow is equal to the discharge or the well. Under the assumed conditions of steadystate flow, Darcy's law may be expressed as a differential equation in cylindrical coordinates k>J~. . q = 211'krh dh/dr â€¢ collecting constants and separating variables 91:. â€¢ 21l'k h dh r q (15)
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â€¢ â€¢ â€¢ Integrating between the limits r2 and r , and~ and hi Solving fork, and converting to common logarithms k =2.303 q log1o r2/r1 1t(~2h12) (16) (17) Under artesian conditions (where there is no umratering} or in thick unconfined aquifers~ h 1 may be assumed essentially equal to 2 m. Then, inasmuch as ~2bi â€¢ (~+bi}(~bi) and s1s2 â€¢ ~bi, equation (17) may be rewritten k :s 2.303 q logia r2/r1 (s1s2 ) In Geological Survey units, noting that T == Pm, equation (18) may be written as the familiar Thiem equation (18) 528q log10 r2/r1 T â€¢ gpd/f't (19) s1s2 In thin unconf'ined aquifers in which the drawdown (s} is an appreciable proportion of' the thickness (m), however, C. E. Jacob (Notes on determining permeability by pumping tests under watertable conditions: u. s. Geol. Survey processed report, 25 pp., 1944) has shown that the observed drawdowns should be corrected as follows. Note frOll the sketch that 112 â€¢ m s2, and h 1 =m s 1 â€¢ Substituting these values in equation (17) and expanding k = (20)
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â€¢ â€¢ â€¢ Hydrol. 3cont â€¢ For convenience multiply both sides of equation (20) by 2m, which does not alter its value, and simplify k â€¢ In Geological Survey units, equation (21) may be written T = r2/ 528q log10 r1 gpd/:rt s1, s2' where s ' â€¢ corrected drawdown C = s 2m Equations (18) and (19) also may be derived directly from Theis' exponential integral {equation 23, Hydrol. 4) for long intervals of discharge (large values of~) â€¢ (21) (22)
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â€¢ â€¢ â€¢ Hydrol. 4 CgapressibilitY and elasticity or aquifers and nter Theis' coefficient or storage.In 1935 c. v. Theis (The relation between the lowering or the pies011etric surface and the rate and duration or discharge or a well using groundwater storage: Am. Geop~. Union Trans., 1935., p. 520) introduced for the first tille the variable t (time) and the constant S (coeft'icient or storage) in the following exponential integral (derived f'raa a heatflow equation) C. E. Jacob later ( On the flow or water in an elastic artesian aquifer: Am. Geophye. Union Trans., 1940, pp. 574586) confirmed Theis' equation (23) f'ran purely hprologic concepts. (23) The coefficient or storage (S) was defined by Theis (The significance and nature or the cone or depression in groundwater bodies: Econ. Geol., vol. 33, no. 8, p. 894, December 1938) "as the volume or water, measured in cubic feet, released f'rom storage in each colUJID or the aquifer having a base 1 root square and a height. equal to the thickness or the aquifer, when the water table or other piesaaetric surface is lowered 1 root. In watertable bodies, this coefficient of storage for long ;periods of' pum.pipg is approximately the specific yield." (The coefficient or storage S,.is dilaensionless; it assumes the dimensions L3 only when multiplied by the change in head L and the area I,2) â€¢ For artesian aquit'ers the range in Sis perhaps 10, 103; for unconfined aquifers the corresponding range in specific yield is perhaps < O .1 0 .3+. A better understanding or the coefficient or storage S my be had f'rom analysis of the following equation or Jacob {op. cit., p. 577; also chapt â€¢ 5 in Engineering Hydraulics , ~~ley & Sons, Inc. , _ p. 334, 1950> Avrwhere 9 1 m â€¢ E,, b IS s,. 9flll(i; +~+t) (21,) porosity or aquifer specific weight of. water per unit area (62.4 lb tt3/144 in2tt2) thickness or aquifer, :rt bulk aodulus or elasticity or water (3:rlo5 lb 1n2) effective part or unit area or aquifer that responds elastically. For an uncemented granular aquifer, b is unity; for a solid aquifer, as a limestone having tubular channels, bis apparently equal to tbe porosity; for a cemented sandstone, b doubtless ranges between these lilli ts â€¢
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â€¢ â€¢ Bydrol. 4cont â€¢ A v'o E8 â€¢ bulk modulus ot elasticity or the aquifer C â€¢ a dimensionless quantity that depends largely on j )t'\' .vP the thickness, configuration, and distribution t ~A, or intercalated or adjacent clay beds. o1'" of" Ee â€¢ bulk modulus ot caa.pression ot the clay. . ~ti JJ' Within the parentheses or equation ( 24), the first term d~otes the ,pJ { release tran storage derived from elastic expansion or the water; the second term indicates that f'rom elastic coapression or the aquifer; the third term, where applicable, indicates that tran plastic deformation or clay. For practical applications to aquifers reasonably tree rrom clay the third tena within the parentheses ordinarily may be ignoredparticularly it the time intenal involved in determination of Sis suf'ticiently long. Then, for granular aquifers or loosely cemented sandstones for which b â€¢ 1 or appro:riaately 1, equation (24) can be sillplitied to s er 11 ( + }> s where p â€¢ i; = 3.3:rl06 in2 lb1 (25) For an exaaple of storage release tran expansion of water alone, assume 8 = 0.3 and m â€¢ 1 rt. T.ben S â€¢ 0.3 x (62.41b tt3/J.44in2tt2 ) x 1 ttx3.3:rl061Jl2lbl â€¢ 4.:,:r107 Similarly, tor m = 100 rt S = 4.:,x105 If multiplied by the d!fining conditions of unit change in bead (1 rt) over unit area (1 tt) each ot the above answers represents the fractional cubic foot of water released under the assumed conditions â€¢
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â€¢ "'I / . ( â€¢ Hydrol. 5 Subsidence resultipg from withdrawal or water or oil Subsidence of the land surface resulting from withdrawal of ground water or oil is a fairly cODDon phenomenon, but it is more apt to go on undetected in inland areas than along seacoastswhere danger of i't inundation soon becanes apparent. Among water fields, subsidence of il about 6 feet near San Jose, Calif'. and 4 feet near Texas City, Texas II L "" the Long Beach Harbor area, Calif. : Geol. Soc. America Bull., vol. . 60, pp. 461,30, 1949.) Subsidences of such magnitudes are believed to result mainly from plastic deformation of intercalated or adJacent clay beds. Lohman proposes a basis for coaputing the expected elastic subsidence as follows: Fran equation (25) Then, from Hooke's law that strain is prQportional to stress (within tbe elastic limit), we may write ~m â€¢ .Jll AP or .Jll â€¢ Am Ea Ea ~P where ~m z subsidence, in feet A p â€¢ duninutation of pressure, in lb in2 Then, combining equations (26) and (27) .611 â€¢ .6p <f emp ) Thus in a reasonably elastic artesian aquifer where Sis known from a pumping or flow test, e is known from core or sample tests, and m is known from a driller's log or electric log, it is possible to predict the subsidence for a given decline in artesian pressure. For example, from the following values for the Fox Hills sandstone in the Denver artesian basin: S â€¢ 2x104 o â€¢ m = 100 rt ( :~) e â€¢ o., â€¢ 100 lb 1n2 (231 ft of head; assumed) (26) (27) (28)
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â€¢ â€¢ â€¢ â€¢ Hydrol. 5cont â€¢ ~m â€¢ . 1021b in2(2xl04x2,31 :rt in2lbl 0.3xla2tt x 3.3:xl06in2lbl) â€¢ 1a21b in2(4 .62x104rt in2lbl 104rt in2lbl) â€¢ 3.6x10, say 0.04 rt Assume a thick artesian bed in a water or oil f'ield having the following values: S â€¢ 103 9 â€¢ o., m â€¢ 1,000 ft Ap â€¢ 1,000 lb in2 Then 6m â€¢ lcYlb in2(lcYx2.3lft in2lbl 0.3xlcY:rt x 3.3xl06in2lb1 ) â€¢ 1<9lb in2(2.:,1x1a':rt 1n21bl 1a'rt 1n21bl) â€¢ 1., rt These are believed to be reasonable values for expected subsidence resulting fran purely elastic caapreseion of the aquifer and elastic expansion of the water. The actual subsidence might be considerably greater owing to plastic deformation of any intercalated or adJacent clay. If an elastic subsidence bas been identified and measured, its value can be inserted into equation (27) to detera:lne the value or E8 â€¢ If the latter value proves to be of reasonable magnitude, then elastic ecapression or the strata becaaes a competent explanation of tbe measured subsidence. Es also may be determined directly from equation ( 25) or ( 26) â€¢ ftrA â€¢ ' 1.' k' "' I(:) 1 'l., ,o" 'ft.J. ,01,,'f. { s1r,i,___) ' .,.........,... J
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t . â€¢ â€¢ â€¢
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â€¢ ! :,: ... j â€¢ â€¢ Uniform and flashy stream flow from adjacent terranes Hydrol. 6 t5~::~....,,""T'",,,., ;..,o , :xi ~'f IIIO IUI 11,U IIIJ 1114 IIIJ /Ill 1117 IUI lln 1g,o IIJI 1g.,z /gJJ 1gu /gJJ /gJI IIIJT IUI Fig. 2Accumulated monthly deviations from uniform flow in three streams of central Oregon, in percentage of the mean for the 25 years ending September 30, 19211945
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â€¢ â€¢ â€¢ Hydrol. 6cont â€¢ or the preceding two diagrus, the upper ( after Lohman, s. W., Sand Hills area, Nebraska, chapt. 5 in The physical and econoaic foundation or natmal resources, pt. 'IV, subsurface facilities or water management and patterns of supplytype area studies: Interior and Insular Affairs Camnittee, House o:f' Bepresentatives, United States Congress, fig. 5.7, 1953) contrasts relatively unitora flow or the Jliddle Loup River, Nebr., with the nae~ flow of the White River, s. Dak. The Middle Loup is one of several branches of a streaa that drains the Sand Hills, a grO\Uldwater reservoir or great volume, whereas the White drains a shale terrane. The two streams are in the same climatic environment, yet during much or the year the flow of the Middle Loup is 10 times the greater. The ratio or greatest flow to least flow (during the year shown) is 1.6 to 1 for the Jliddle Loup, but is 'i?!'l .5 to 1 tor the lhi te. The lower diagraa (after Piper, A. M.: Am. Geophysical Union Trans., vol. 29, pp. 511520, 1948) contrasts the John Day, Deschutes, and Metolius Rivers of central Oregon. The John Day drains 7,580 sq mi of rather iJllpermeable terrane. Its now fiuctuates considerably each year and diminished progressively during the recurrent droughts of 19291941; its minimum now has been less than 1 percent of its mean flow. The Deschutes drains 10,500 sq Iii. Its flow is strikingly unifora, the â€¢ minimum of record having been 58 percent of the mean; this uniformity is an effect of large perennial groundwater runoff. The groundwater runoff of the Deschutes caaes largely fran a part of its basin that is exceptionally permeable. This part is drained largely by a tributary stream., the Metolius River, whose minimum now of record is 76 percent of the mean. In this tributary, flow seems to lag at least 5 years af'ter fluctuations or precipitation; it actually increased slightly from 1933 into 1938, during a prolonged drought â€¢
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â€¢ â€¢ â€¢ Hydrol. 7 Relation of fresh grotmd water to salt water along sea coasts GltybenHerzberg principle.Small oceanic islands and coastal spits, if formed of material that is continuously and moderately permeable, canmonly are tmderlain by a lensshaped mass or fresh ground water "floating" upon underlying salt water. If hydrostatic equilibrium were attained, the form of the freshwater mass would accord with Archimedes' principle tl'lt~ a floating l;>Qdy displaces its own weight of liquid. Thus, Badon Ghyben.w and HerzbergsF fotmd, apparently independently, that the l/ Badon Ghyben, W., Nota in verband me~ de voorgenanen put boring nabiJ Amsterdam: K. Inst. Ind. Tijdschr, 188889, p. 21, The Hague, 1889. g/ Herzberg, Baurat, Die Wasserversorgung einiger Nordseebader: Jour. Gasbeleuchtung tmd Wasserversorgung, Jahrg. 44, Munich, 1901. depth to salt water was roughly a ftmction of the he~ght of the water table above mean sea level, and of the density of the sea water. In the sketch below, Mean sea level let Then whence and ' ' ' \ \ ' ' ' ' ' ' H = total thickness of fresh water h 1 = depth of fresh water below mean sea level s height of fresh water above mean sea level 1 â€¢ specific gravity of sea water (specific gravity of fresh ground water assl)pled to be 1) H â€¢ h1 + â€¢ "'flhl r;: 112 = y h1 h1 â€¢ h1(_!!l) .. p.1 =iw h,. r~ hi fy (29) (30) (31)
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â€¢ â€¢ _!)~ \ \:? " \ I \ / ~t/ \ \ X b~ tr, ) I r.,_Y, I â€¢
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â€¢ â€¢ â€¢ Hydrol. 7cant. ( An average value of Y is about l. 025, whence h1 = about 40 112 ) The foregoing assumes hydrostatic equilibrium, which applies approximately near the center of the lens but does not apply near points of freshwater discharge into wells or at the coast. Actually, a dynamic equilibrium exists between recharge and discharge, with fresh water moving over the body of salt waterV. 'V Hubbert, M. K'.., The theory of grotmdwater motion: Jour. Geol., vol. 481 pp. 8828841 924926, 1940. Effect of pumping wells.A well drilled into a "GhybenHerzberg" lens may or may not yield fresh water, depending on the depth of the well and or its cone or depression when pumping. The following diagrams show the probable relations between fresh and salt water in a coastal area (after Lohman, S. w., Geo~ogy and grotmdwater resources of the Elizabeth City area, North Carolina: U. S. Geol. Survey WaterSupply Paper 773A, fig. 3, 1936). C Water table . Little River S~ ltwel a C b C Pigure 5. DiagrlUIUII showing probable relations between f'reah and salt water 1n the Elizabeth Cit7 area, it it 1a assumed that the waterbearing materials are homogeneous and permeable both lateral.17 toward the Pasquotank and Little Rivers and downward to considerable depth. (Not drawn to scale.) Diagram a shows theoretical relations between treah and salt water betore pumping. A shallow well, A, near either river may encounter salt water even without pumping. Diagram b shows that when well B 1a pumped, onl7 a moderate lowering ot the head ma7 result in drawing in salt water, whereas in well Can equal loweringot head ma7 not result in drawing in salt water. Diagram c shows that too great a lowering ot the head in wel.l C ma7 also reaul.t in drawing in salt water.
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â€¢ / â€¢ / ci,7r l, ) l U 2, \,Yv L , â€¢
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â€¢ â€¢ â€¢ Hydrol. 7cont â€¢ Artesian aquifer cropping out along continental sbelf'.In the sketch below, let the artesian aquiter extend to an of'f'shore outcrop. Being under greater bead, the fresh water in that aquifer would extend beyond the Gbyben Herzberg interface in the encloaing mterials â€¢ Ir tbe well shown were allowed to flow or were pUJllPed, the treshwater head in the aquif'er would be diainiehed and the interface with salt water would move landward. If draft is excessive and continual, the intertace eventually will reach the well, which then will becane salted. wat~r r11/,Je '. .... Sur~ce / / / ./ I Sea level
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â€¢ â€¢ â€¢ Hydrol. 7cont â€¢ stratification or salt water and fresh water in sed1mnts (Arter Williams, C. C., and Lohman, S. W., Geology and groundwater resources of' a part of' southcentral Kansas, with special reference to tbe Wichita llUDicipal water supply: ~~ol. ___ ~'!'ftY Bull.J&_Pâ€¢ 181, 1949.) The f'olloring results were obtained f'raa a driven well put down to a depth of' 44 f'eet at a point 2,0 f'eet downstream f'raa an "evaporation" pond contai.Jd.ng brine with a chloride content or 51,~ parts per million. Chloride concentrations at given depths in alluviua 250 reet C:Sli an "euporatign" pond. Depth (f'eet) 23 25 28 30 33 35 38 40 41 43 43 44 (Depth to water level, 9 .5 f'eet) (Impervious stratUll) I' Chloride concentration (parts per aillion) 1,900 6,800 39,000 50,300 50,900 The boundary between the fresh and salty waters was f'o\Dld to be much sharper at greater distances f'rca the source of' intrusion, as indicated in the following analyses. Chloride concentrations at given depths in alluvium 750 feet b:911 an "evaporation" pond. Depth (f'eet) 28 30 33 35 38 40 43 45 47 49 49 50 (Depth to water level, 9 f'eet) (Iapervious stratum) " Chloride concentration (parts per aillion) 6g 69 71 70 2,240 b"~ ~,r CMC~
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â€¢ ) â€¢
PAGE 28
â€¢ â€¢ â€¢ Hydrol. 8 "The source or water derived from wells" . Under the above title c. :r. Theis (Civil Eng., vol. 10, pp. 277280, 1940) has stated concisely the h1'drologic principles upon which depend much or our present quantitative approach to groundwater probleu. The statements that follow are sU11111&rized f"ran these principles. T.be essential factors that determine the response or an aquifer to developaent by wells are: â€¢l. Distance to, and character or, the recharge 2. Distance to the locality or natural discharge 3 . Character of' the cone or depression in the aquifer, which depends upon coefficients of' trannissibility (T) and of storage (S) Prior to any developaent by wells, an aquifer is in a state of approximate d~amic equilibrium in that over the years recharge and discharge essentially balance. Pumping fran wells upsets this condition of' equilibriua, but unless the draft is excessive,a new dynamic equilibriua may be established by: 1. Loss of groundwater storage 2. Increase in recharge (natural or artificial) 3. Decrease in natural discharge 4. Combination of these Fran equation 2, (Bydrol. 4) it follows that the drawdown (a) is directly proportional to the rate of discharge (Q) and inversely proportional to the coefficient of transaissibility (T); thus (using k as a constant of proportionality): s kQ s k T (32) (33) Furthermore, after any given interval of pumping ( t), excepting very short intervals, the spread of the radius of the cone of depression (r) is independent of the rate of discharge and inversely proportional to the coefficient of storage (S), thus: (34) In an artesian aquifer the coefficient of storage is no more than a small fraction of that in an unconfined aquifer; hence, the cone of depression in an artesian aquifer â€¢Y spread f"rODl a hundred to several thousand times faster tban in an unconfined aquifer. Thus, excepting aquifers that are very extensive, a new equ:J.libriua in an arte,sian aquifer may be established soon after development begins. Accordingly, sueh an artesian aquifer generally can be treated essentially as a unit in any measures for conservation of ground water.
PAGE 29
~'f':) ~s~\J ~L~ 1J.J1 irt , T&'E! M &TTEN, sre~ ~M â€¢
PAGE 30
â€¢ â€¢ â€¢ Hydrol. 8cOJlt â€¢ Conversel.y, in an extensive \Ulcontined aquiter where tbe develoiaent occurs at great distances :rraa the areas ot recharge and ot natural discharge, for a considerable period of t1aost ot the water is derived traa storage and equilibriua is reestablished very slowly. A large \Ulcontined aquifer or this type generally oaxmot be treated as a unit tor conservation measures; rather, it be treated generally as a nuaber ot distinct subunits. Thorough knowledge of these hydrologic principles plus the gathering and proper interpretation of the pertinent field data should perait the solution of virtually any quantitative groundwater problems, although in sane areas tbe solution â€¢Y be very difticult â€¢
PAGE 31

PAGE 32
â€¢ Hydrol.l/J Records or wells Fill out f'orm 9185 as completely as possible; try to get all available information on first visit. On reverse side sketch location with respect to nearby geography; also sketch closeup or well and its 11.P. Test or good description: so stranger can find well and M.P. with aid or only the well schedule and base map. (A..!;!t~NI) UNITED STATES DEPARTMENT OF THE INTERIOR O GEOLOCICAL SURVEY ,,:J,,,2.1_IJ WATER RESOURCES DIVISION_..~ WELL SCHEDULE ,,i,3. Date â€¢.â€¢.â€¢ .. JL _____ 1~ Field No. ./J/!_ Record by ZIL.~ .. .. dRJ Office â€¢No.Source of datal'!/MtS.Mreinlnr. ... E. .. 0/N.nlC:. 1. Loca.tiox : State . C!IJL4Cl!ldlJ....... . ... County ..L!f4r:14 ___ _ ,,,,,o.sof.~ "'â€¢â€¢ Zrrâ€¢ r'#â€¢~iâ€¢L_ â€¢~ er,,.,, ~,., KapsW ... JJ. 4 ... 1aec. .. L4 ... T .J~ ... ~~d> 2. Owfler: WJJIJM.r.. .. la/kr.L. Address ...... ~/.Jh __ _ â€¢ Tenant '' AddressDriller â€¢.. ,. Address .............. J a. TWJl'Ph11 ~llel/~4~..................... i i 4. Efiw0tiox~.,/_4o[..fft. .. _AL1k....... !! 5. Trpe: Dug,c!!'i"jdriven,bored.Jetted ...... 1J..7 ! i 6. Dept&: Rept. â€¢.. ..~ ft. Meas . ............... ft. j â€¢ ! 7. Cuiag: Diam. /J... in., to_!_().. in., Type,k'IL) ..... : ...... j f)epth/iJ/1 .. ft., Finish . 11fl~'1 ... ~.1'1d.. ..... ... : 8. Chief Aquifer~nr.>t'. .. â€¢.. F!m .J.J?./J. ft. to J.: .. ft. Others~.. . r.. . .m .. ./J11k'l/'6 .. J~ . . .... tft:...~b. .......... . 9. Water level ,:Z . .'9./()_ .. ft.:!:;. _ ... 9...:.6..: .. 19.~,7~L'.f~ ... . I., dLOUL"'l, .... A/. .. .JL~. which i1 ... IJ.,S. .. ft.~aurface 10. hfflp: Ty~ â€¢..â€¢ .#.,_IJ.tt.. .......... CapacityG. M. Power: Kind â€¢.â€¢.... JI~Horsepower11. Yield : Flow ~tJ.!!.. G. M., Pump â€¢.... G. M., Meas., Bm. Eat. ........ . Drawdown â€¢â€¢..â€¢.... ft. afteihours pumpins.G. M. 12. Uae: Dom., ~PS., RR., Ind., I1r., Oba.Adeq;:;: permanence ~d4L ..... â€¢~13. Qualit11 â€¢â€¢â€¢â€¢â€¢â€¢â€¢ G.Jj.4.t/.................. . ............ Temp â€¢..â€¢.. â€¢ .:J.. ...... â€¢F. Taste, odor, color .. ./Y.#..11.~.. . .... . ............ Sample 1';,1 ...â€¢........... Unfit for â€¢......â€¢..â€¢.........â€¢...â€¢.................. ........................ ................. 14. Rt!rt1arl.a: (Log AnalyR1, etc.,$..41/..(J . .l, ~nd..2.":'.~ ... .Sll.,:,d .. r1'K..CKJJ. ,~~,?,. .. ~!Ml(. ~Ac:tl~C~,.,)_..4 _ ~ . .a2.<1. 4 .. S4nil.r~e.,f'../'&l J4.1> ..Jt/S:. ...... W.~':f'h.i~d..41!4'. d' ,.s cJ17, â€¢ (f/';;;;<;j,â€¢â€¢~t/J
PAGE 33
â€¢ 
PAGE 34
â€¢ â€¢ Hydrol. 10 Computing changes in groundwater storage from 1.Maps sbgpjng lines or equal t1bftnge in water level (After Williams, C. C. , and Lohman, S â€¢ W. , see reference on Hydrol. 7) i y I \ I . //~1'r~I â€¢. \ 13 I OCTottltt â€¢â€¢ ,,,.. I \ I I I ~ l T1 I Superposition of watertable contour maps made before pllllping began (June 1, 1940) and after 4 years or pumping (Oct. 1, 1944) allows construction or map at left showing lines of equal change in water level. Fran such maps and average value of specific yield, changes in groundwater storage are readily caaputed â€¢
PAGE 35
â€¢ â€¢ â€¢ Bydrol. 10cont â€¢ 2.Tbiessen polygons For ccaputing mean height of water table, change in groundwater storage, and the like, it is a COIIIJIK)Jl practice to weight the observed data rraa eachobservation well according to a polygonal area of influence for that well. "Thiessen polygons" are simple to construct, although procedures differ in sane details â€¢ A camaon method is as follows : A" / \ / " .,/1', / \ / k I <(I \ I I \ / I I \ I/ / \ \ I ,)Y In the typical array above, Join observation well~ by rays (dashed lines) dividing the area into a network or triangles whose sides are as short as possible, and whose angles ordinarily are not obtuse â€¢ At the midpoint or each ray, erect a perpendicular and extend these perpendiculars to intersect one another ( solid lines) â€¢ The intersecting perpendiculars define the polygon of influence around each well. Areas or the polygons are determined readily by plan1weter. Storage change in a given area may be coaputed at intervals such as a quarter, half year, or year. Here the same polygonal areas should be used in each successive caaputation, but a complication arises wherever an observation well is not represented in the observed data. In this event, it is convenient to interpolate the missing data fraa the observations at adJacent wells rather than to construct new polygons, as the end result generally is essentially the same. other caaplications arise where the water table or potentiaaetric surface is tmeven. Here, it is undesirable that a polygon span a sharp ridge or deep trough or that surface. Considerable Judgment can be exercised in building up the observationwell net to avoid this contingency â€¢
PAGE 36
â€¢ â€¢ â€¢ Bydrol. 10cont â€¢ An exaaple is given below ot a â€¢P or part 0 the San Luis Valley, Colorado, shoring changes in water level within such polygonal areas. (.A.tter Powell, W. J., Groundwater resources ot the San Luis Valley, Colorado: U. S. Geol. Suney WaterSupply Paper in press, pl. 10.) R .6. R.7E. R.8 . R . 9E. .... 1950 ... .... t 41 N. T. 40 N. T. 39 N.
PAGE 37
â€¢ â€¢ â€¢ Depthtowater maps (After Fr;ye, J. C â€¢ , and Fishel, V. C. , Ground water in southwestern Kansas: Kans. Geol. Survey , fig. 5, 1949. ) r:!:rtr:~ liifail ifoiobj mffl ~)~t!rt$4~:"ttW! Figure 5. Map showing depths to water level below land surface in southwâ€¢tern Kansas. ( Compiled by W. W . Wilson ) Hydrol. ll
PAGE 38
â€¢ â€¢ â€¢ Hydrol. 12 llaps of bedrock topography (Arter Latta, B. F. , Geology and groundwater resources of Finney and Gray Counties, Kansas : Kans. Geol. Survey Bull. 55, fig. 7, 1944.) ,.. o l'1tt __ __J .dd" Iâ€¢ .. ' , ~ FIG. 7 . Map of Finney and Gray counties sho_wing by means o_f cont.ours ,. (I ( dashed lines) the shape and slope_ of the preTe~ surfae1:, location of test â€¢ â€¢ "\ bol .. (numbered cireles) , and II.ion of eroos seell0118 abown m figures 8 and 9c/ I. ( ~ua In some areas, particularly glaciated regions, such maps may show buried stream valleys that may contain productive aquifers. If aquifer lies above bedrock and is all waterbearing, superposition of watertable contour maps on contour maps of bedrock topography permits construction of saturatedthickness maps, such as shown on Hydrol. 13.
PAGE 39
â€¢ â€¢ â€¢ llaps shoring thickness or saturated â€¢terial (Af'ter FrJe, J. C., and Fishel, V. C., see reference on Bydrol. 11.) Figure 4. Map showing thickness of the Pleistocene and Ogallala deposits that are saturated with water in southwestern Kansas. Saturated sandstones of thâ€¢ Permian and Cretaceous rocks are not included. The quantity of water in atom.. ii, in 1â€¢eral, proportional to the saturated thickness of waNrmaterial. ( Compiled by Glenn Prescott ) Bydrol. 13 Such â€¢PB can be constructed fraa information given in driller's logs or electric logs, or in the 11&DDer described on Bydrol. 12. If' specific yield is known, such mps also can be used to determine quantity or ground water in storage.
PAGE 40
â€¢ â€¢ â€¢ Hydrol. 14 Maps shoring availability of ground water (After Lohman, S. w., and others, Groundwater supplies in Kansas available for national defense industries: Kans â€¢ Geol. Survey Bull. 41, pt. 2, fig. 2, 1942. See also Lohman , ... S. W., and Burtis., V. Jl., General availability of ground water and depth to water level in the Arkansas, White, and Red R1 ver Basins: U. S. Geol. Survey Hydrologic Investigations Atlas HA3., 1953.) . . Area in which large supplies of ground water ore available. Areas in which mod erately large supplies of ground water ore available Area ,n which moderately larae supptiet of ground wotâ€¢ ore available from wells 600 to 1500 feet dnp D Areas in which supof ground water adequate for industrial use generally cannot be obtained FIGUU 2. Map of Kansas showing by patterns the areas in which may be obtained supplies of ground water adequate for national defense industries. Areas designated by letters or numbers are discussed separately in the text.
PAGE 41
OIi .... .... c,,. ,0 .... â€¢ 0 0 â€¢ 0 0 0 0 0 0 HYDRAULIC CONVERSION TABLE EOl/lVALENT VALi/ES ARE SHOWN IN THE SAME HORIZONTAL LIN ACREFEEl /CREFEET GALLONS MILLION MILLION INCHESlW LITERS SECOND PER GALLONS 'CUBIC FEET ISO.MILE FEET PEROAY PERYEAR MINI.IT PER DAY PEROAY PER YEAR PER SEC ONE 1.9835 723.97 448.83 .646317 .086400 1.3.574 28 . .317 .50417 ONE 365 226.29 . .325851 ,043560 6.8438 14.276 .00138 .00274 ONE .6199 .00089.3 .000119 .01875 .03911 .00223 .00442 1.6129 ONE .001440 .000192 .03024 .06309 1 .. 5472 3.0689 I, 120.15 694.44 ONE .133681 21.0025 43.813 II. 574 22.957 8,379.2 5,194.8 7.4805 ONE 157.111 327.74 .07.367 .14612 53.333 33.065 .0476I .006364 ON 2.0860 .03531 .. 07004 25.566 15.850 .02282 .003051 .47937 ONE â€¢ tJâ€¢ '1 C') er' s:: 0 c+ '1 p. P> CD ..., :~ 0 0 c+ CD '1 er' 0 I '1 !>< p., :::t:! (l) =:, '1 c+ p., '1 ct> 0 I er' 0 0 tJâ€¢ tJâ€¢ c+ (') . 0 (') CD 8 0 ..., . '1 en Cl) ij tJâ€¢ < g CD ( ..... ::I: l 0 ..... . ..... \J\
PAGE 42
r~ QJ;.,,,,__.,...( 6 c..J ?,.ch.}1 â€¢ 1C@r O '(: (j_ d, jFr,.Js , cP. \.U.S 'P 4Q lf/ f ~"'1' ~. 0~/ /J.r+1 {;(.!.(~f r" CC~~ ~6'7, ' , Gutt:,, 't Tc,eir( E~1n,,,.c;. ,r~ I c. 1t' 
PAGE 43
MGD CFS Acreft/ day Acreft / year 3000 4.0 8 2.5 3.5 7 2500 2.0 3,0 6 1.9 1.8 2000 1.7 1900 2 . 5 5 1800 1.5 1700 1600 1.4 < 0 1500 0 1.3 2.0 4 z w 0 a: 1400 .... a: 1.9 < t2 0 ::, < w w i.8 w 1300 z 0 Q. (/) 1.1 1.7 a: (/) a: a::: 1200 z 1.6 w w w a: 0 Q. Q. LO Q. w ..J 1 . 5 3 1100 Q. ..J . 95 .... .... .... < w w .90 w 1.4 w (/) c., w w 1000 z .85 I I 950 0 z 1.3 w w ..J 0 0 0:: 900 .80 a: ..J 1 . 2 0 0 < ..J m < < 850 c., ..J .75 :::, 0 1.1 800 .70 750 .65 1.0 2 .95 700 .60 400 .90 650 . 55 .85 600 .so .50 550 .75 . 45 .70 500 300 .65 .40 450 .6() 250 400 .35 .55 .50 350 .30 200 .45 Nomograph for converting watermeasurement units. ,uu
PAGE 44
â€¢ WATE~ TABLE ~ .ffl,_ ...... :,... ___ MEAN SEA LEVEL _____ ~ FRESH WATER h J SEA WATER Figure 15r{)iagram . showing the relation between fresh water and sea water beneath a narrow peninsula; according to the GhybenHerzberg J!&lat icnsbj~. ...
PAGE 45
Fla.
PAGE 46
â€¢ â€¢ o .. a ~=_:i=:i=3::~=t= ::::::::::::= ___:__:__==___________: AOUICLUD E :____________ ___:_:_______~==i=~~~~~.::;._ ____________ _________________________________ _:__::~~Fi9. __ Generalized flow net showing streamlines and equipotential with fifty percent penetration in on isotropic sand. linu fn the vicinity of a dischar9in1 wel I â€¢ , . 0
PAGE 47
â€¢ â€¢ â€¢ W/ ?'LO~~â€¢ 0::~b 1 +~R I,() .... ..., ____ ,,,,_,_, t . ?" y~, ~l,L.C,,..,. "\A'1..a~~ .. ~~~' ~J ~,&..,,,, ~r,,,e......,. ~~ ~..c.zz.~ b,.1 ft
PAGE 48
e FIG. l:JPD / _,,,,,,. I / / \ \ / / \ \ \ \ \ I I I I I I â€¢ / I I I I I I \ \ \ \ \ \ ......... ___ .,,,,,,,,,. / I I / / FLOW NET IN A HOMOGENEOUS WATER TABLE AQUIFER BETWEEN PARALLEL EFFLUENT STREAMS WHEN RECHARGE TO THE AQUIFER IS UNIFORMLY DISTRIBUTED (AFTER HUBBERT).
PAGE 49
,â€¢ â€¢
PAGE 50
t ' .<"~ â€¢ 4 DEPTH, IN FEET REFERRED TO MEAN SEA LEVEL,U.S. COAST AND GEODETIC SURVEY DATUM 0 ;_; 0 0 8 g I a, UI â€¢ 0 0 0 I I I :,, N I 0 N 0 0 i5 0 0 I I I 4/ a, i tfJ: "" 00 ..,, ..,, \ â€¢â€¢~ J ~t ;e FI74 ;;o :r "" r c, lo :t Ir < < "" ,, ~ ~ .so __ ii~ J , : :::0 ri: ,.., l'T1 CD l> CD (/) rn ,.., l> < Tf z rm 0 J> ~o O C J> :::0 0 en r C 1,000........ ,6,ooo 16,000, nr ,., :c ; b > :II~~ :Om 4""'cn o"'~ 0, 0 " r ,., 0 z ....... ' '\ \ I / \ ' / ( \_ \ ' U' 0 5626 t "' :a.. 1,200 255 ::t 35848~ II) "' :a.. 157'5 .... "' " L F178 0196 FI72 FI75 FI62 V) FI82 r.,rFI63 f 1,i"" l\il,. o;:::,~ l:..~ FI64 FI79 FI76 F I8I FI65 F I83 F I46 FI54 V) FI70 F I77 F I66 :; :t V'I F173 ::t FI47 F155 ..._ FI67 :; h FI9I :t~ F 143 F 148 "'i 1F156 168 F158 F I C) i5 <2 J> z 0 .... rT1 .., ::c 0 s:: (./) ::r: 0 "'::c rT1 r z JT1 z "'I ::r: 0 C (./) J> z 0 (./) "0 .,, .,, ,.,, ,.,, I F188 V) ..._ ~ 48~~ ) lf1~UUf b , 'H/~~ 1~ â€¢ ~ ,,.. ? nr, F â€¢ 198 ....._ b. fN F159~::t F 202 F 149 ::t F 213 :i"" ")' :t,,. 160 G519 I c, IT1 . t 1' ~''l (.. 't I t "
PAGE 51
,,J. ,, .... .., N I ~ G 469 1 :::: l R!CHMONO ~OR j C U ir / zi., / Topography by Deportment of Engineering, Dode Coul\tY Contour interval I foot ..J 0 w > w ...J <[ w 20 (/) z <[ w :i: 0 40 lo w a:: a:: 60 w a:: ....... w w u.. 80 I ICl. 100 120 U S Coast and Geodetic Survey mean sea level datum of 1929 ATLANTIC COASTAL RIDGE ~ Land WATER , ~~~SILVER BLUFF TERRACE ,s.ooo EXPLANATION â€¢ Observation we! I 200lso'chlor â€¢â€¢ "::.)I

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