Energy Transformation

• 1 Caloria of heat = energy necessary to raise the temperature of one gram of pure water from 14.5 – 15.5oC

• Latent Heat of vaporization

Hv = 597.3 – 0.564T (Cal./g)

• Latent Heat of condensation

Energy Transformation, Cont.

• Latent heat of fusion – Hf – 1 g of ice at 0oC => ~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 0oC.

• Hv > 6Hf > 5 x amt. to warm water from 0oC -> 100oC

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 Cool, moistWarm, 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

All infiltrate

some water always on the surface

Puddles and overland flow

Q0

Increase of Recharge

• find t1

• tc = 0.2144 t1

• find QA & QB

Vtp = QBt1/2.3 – QAt1/2.3

• G = 2 Vtp

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 R2/3 S1/2 /n or R2/3 S1/2 /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.

d60

d60

d10

d10

Sediment Classification

• Sediments are classified on basis of size of individual grains

• Grain size distribution curve• Uniformity coefficient Cu = d60/d10

• d60 = grain size that is 60% finer by weight.• d10 = grain size that is 10% finer by weight.• Cu = 4 => well sorted; Cu > 6 => poorly

sorted.

Specific Yield and Retention

• Specific yield – Sy: 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 – Sr: ratio of the volume of water in a rock can retain against gravity drainage to the total volume of the rock.

• n = Sy + Sr.• Sr 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

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)] [ L3/T/[L2(L/L)] = L/T]

• V = Q/A = -K(dh/dl) = specific discharge or Darcian velocity.

Intrinsic Permeability

• Intrinsic permeability Ki = Cd2 (L2).• K = Ki (γ/μ) or K = Ki (ρg/ μ)• Petroleum industry 1 Darcy = unit of intrinsic

permeability Ki

• 1 darcy = 1 cP x 1 cm3/s / (1 atm/ 1 cm). cP – centipoise - 0.01 dyn s/cm2

atm – atmospheric pressure – 1.0132 x 1016 dyn/cm2

• 1 darcy = 9.87 x 10-9 cm2 ~ 10-8 cm2

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(d10)2.

• K = hydraulic conductivity.

• d10 = effective grain size (0.1 – 3.0 mm).

• C = coefficient (see table on P 86).

Permeameters

• Constant-head permeameter

• Qt = -[KAt(ha-hb)]/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 = [dt2L/dc

2t]ln(h0/h).

• K = Hydraulic conductivity.• L = sample length.

• h0 = initial head in the falling tube.

• h = final head in the falling tube.

• t = time that it takes for head to go from h0 to h.

• dt = inside diameter of falling head tube.

• dc = 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 > 10-2 Darcy.

• Confining layer – unit with little or no permeability … < 10-2 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 => T1 + T2 + … + Tn

Specific Storage

• Specific storage Ss = 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).

• Ss = ρwg(α+nβ)• α = compressibiliy of aquifer skeleton.• n = porosity.• β = compressibility of water.

Storativity of confined Unit

S = b Ss

• Ss = 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 Sy and specific storage Ss.

• S = Sy + b Ss

Volume of water drained from aquifer

• Vw = SAdh

• Vw = volume of water drained.

• S = storativity (dimensionless).

• A = area overlying drained aquifer.

• dh = average decline in head.

Average horizontal conductivity: Kh avg = m=1,n (Khmbm/b)

Kh avg

Kv avg

Average vertical conductivity:

Kv avg = b / m=1,n (bm /Kvm)

Hydraulic head, h

• Hydraulic head is energy per unit weight.

• h = v2/2g + z + P/gρ. [L].

• Unit: (L; ft or m).

• v ~ 10-6 m/s or 30 m/y for ground water flows.

• v2/2g ~ 10-12 m2/s2 / (2 x 9.8 m/s2) ~ 10-13 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

(L3/T; ft3/d or m3/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.