Energy Transformation 1 Caloria of heat = energy necessary to raise the temperature of one gram of pure water from 14.5 – 15.5 o C Latent Heat of vaporization Hv = – 0.564T (Cal./g) Latent Heat of condensation

Energy Transformation, Cont. Latent heat of fusion – Hf – 1 g of ice at 0 o C => ~80 cal of heat must be added to melt ice. Resulting water has same temperature. Sublimation – Water passes directly from a solid state to a vapor state. Energy = Hf + Hv => 677 cal/g at 0 o C. Hv > 6Hf > 5 x amt. to warm water from 0 o C -> 100 o C

Hydrologic Equation Inflow = outflow +/- Changes in storage Equation is simple statement of mass conservation

Condensation Condensation occurs when air mass can no longer hold all of its humidity. Temperature drops => saturation humidity drops. If absolute humidity remains constant => relative humidity rises. Relative humidity reaches 100% => condensation => Dew point temperature.

Cool, moist Warm, dry Limited soil-moisture storage

Effective uniform depth (EUD) of precipitation Arithmetic mean method – the rain gauge network is of uniform density. Isohyetal line method. Thiessen method. - construct polygons - weighted by polygon areas

All infiltrate some water always on the surface Puddles and overland flow

Q0Q0

Increase of Recharge find t 1 tc = t 1 find Q A & Q B  V tp = Q B t 1 /2.3 – Q A t 1 /2.3 G = 2  V tp

low overland and return flows; high baseflow; strong water retaining (unconsolidated sand is thick). High overland and return flows; low baseflow; little water retaining (soils are thin).

Manning equation V = 1.49 R 2/3 S 1/2 /n or R 2/3 S 1/2 /n V – average velocity (L/T; ft/s or m/s). R – hydraulic radius; or ratio of the cross- sectional area of flow in square feet to the wetted perimeter (L; ft or m). S – energy gradient or slope of the water surface. n – the Manning roughness coefficient.

Determining ground water recharge from baseflow (1) Meyboom method (Seasonal recession method): utilizes stream hydrographs from two or more consecutive years. Assumptions: the catchment area has no dams or other method of streamflow regulation; snowmelt contributes little to the runoff.

Determining ground water recharge from baseflow (2) Rorabaugh method (Recession curve displacement method): utilizes stream hydrograph during one season.

d 60 d 10

Sediment Classification Sediments are classified on basis of size of individual grains Grain size distribution curve Uniformity coefficient C u = d 60 /d 10 d 60 = grain size that is 60% finer by weight. d 10 = grain size that is 10% finer by weight. C u = 4 => well sorted; C u > 6 => poorly sorted.

Specific Yield and Retention Specific yield – S y : ratio of volume of water that drains from a saturated rock owing to the attraction of gravity to the total volume of the rock. Specific retention – S r : ratio of the volume of water in a rock can retain against gravity drainage to the total volume of the rock. n = S y + S r. S r increases with decreasing grain size.

Darcy ’ s Law Q = -KA(dh/dl). dh/dl = Hydraulic gradient. dh = change in head between two points separated by small distance dl.

Laminar flow (Small R < 10) Turbulent flow (Large R) Flow lines Darcy ’ s Law: Yes Darcy ’ s Law: No

Hydraulic conductivity K = hydraulic conductivity (L/T). K is also referred to as the coefficient of permeability. K = -Q[A(dh/dl)] [ L 3 /T/[L 2 (L/L)] = L/T] V = Q/A = -K(dh/dl) = specific discharge or Darcian velocity.

Intrinsic Permeability Intrinsic permeability K i = Cd 2 (L 2 ). K = K i (γ/μ) or K = K i (ρg/ μ) Petroleum industry 1 Darcy = unit of intrinsic permeability K i 1 darcy = 1 cP x 1 cm 3 /s / (1 atm/ 1 cm). cP – centipoise dyn s/cm 2 atm – atmospheric pressure – x dyn/cm 2 1 darcy = 9.87 x cm 2 ~ cm 2

Factors affecting permeability of sediments Grain size increases permeability increases. S. Dev. Of particle size increase poor sorting => permeability decrease. Coarse samples show a greater decrease of permeability as S. Dev. Of particle size increases. Unimodal samples (one dominant size) vs. bimodal samples.

Hazen method Estimate hydraulic conductivity in sandy sediments. K = C(d 10 ) 2. K = hydraulic conductivity. d 10 = effective grain size (0.1 – 3.0 mm). C = coefficient (see table on P 86).

Permeameters Constant-head permeameter Q t = -[KAt(h a -h b )]/L. K = VL/Ath. V = volume of water discharging in time. L = length of the sample. A = cross-sectional area of sample. h = hydraulic head. K = hydraulic conductivity

Falling head permeameter K = [d t 2 L/d c 2 t]ln(h 0 /h). K = Hydraulic conductivity. L = sample length. h 0 = initial head in the falling tube. h = final head in the falling tube. t = time that it takes for head to go from h 0 to h. d t = inside diameter of falling head tube. d c = inside diameter of sample chamber.

Aquifer Aquifer – geologic unit that can store and transmit water at rates fast enough to supply amounts to wells. Usually, intrinsic permeability > Darcy. Confining layer – unit with little or no permeability … < Darcy. aquifuge – absolutely impermeable unit. aquitard - a unit can store and transmit water slowly. Also called leaky confining layer. Raritan formation on Long Island. -- all these definitions are in a relative sense.

Transmissivity The amount of water that can be transmitted horizontally through a unit width by the full saturated thickness of the aquifer under a hydraulic gradient of 1. T = bK T = transmissivity. b = saturated thickness. K = hydraulic conductivity. Multilayer => T 1 + T 2 + … + T n

Specific Storage Specific storage S s = amount of water per unit volume stored or expelled owing to compressibility of mineral skeleton and pore water per unit change in head (1/L). S s = ρ w g(α+nβ) α = compressibiliy of aquifer skeleton. n = porosity. β = compressibility of water.

Storativity of confined Unit S = b S s S s = specific storage. b = aquifer thickness. All water released in confined, saturated aquifer comes from compressibility of mineral skeleton and pore water.

Storativity in Unconfined Unit Changes in saturation associated with changes in storage. Storage or release depends on specific yield S y and specific storage S s. S = S y + b S s

Volume of water drained from aquifer V w = SAdh V w = volume of water drained. S = storativity (dimensionless). A = area overlying drained aquifer. dh = average decline in head.

Average horizontal conductivity: K h avg =  m=1,n (K hm b m /b) K h avg K v avg Average vertical conductivity: K v avg = b /  m=1,n (b m /K vm )

Hydraulic head, h Hydraulic head is energy per unit weight. h = v 2 /2g + z + P/gρ. [L]. Unit: (L; ft or m). v ~ m/s or 30 m/y for ground water flows. v 2 /2g ~ m 2 /s 2 / (2 x 9.8 m/s 2 ) ~ m. h = z + P/gρ. [L].

Flow lines and flow nets A flow line is an imaginary line that traces the path that a particle of ground water would flow as it flows through an aquifer. A flow net is a network of equipotential lines and associated flow lines.

Boundary conditions No-flow boundary – flow line – parallel to the boundary. Equipotential line - intersect at right angle. Constant-head boundary – flow line – intersect at right angle. Equipotential line - parallel to the boundary. Water-table boundary – flow line – depends. Equipotential line - depends.

Estimate the quantity of water from flow net q ’ = Kph/f. q ’ – total volume discharge per unit width of aquifer (L 3 /T; ft 3 /d or m 3 /d). K – hydraulic conductivity (L/T; ft/d or m/d). p – number of flowtubes bounded by adjacent pairs of flow lines. h – total head loss over the length of flow lines (L; ft or m). f - number of squares bounded by any two adjacent flow lines and covering the entire length of flow.