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.
Limited soil-moisture storage
Cool, moist
Warm, dry
Cool, moist
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
All infiltrate
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 crosssectional 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.
Darcy’s Law:
Yes
Darcy’s Law: No
Laminar flow (Small R < 10)
Flow lines
Turbulent flow (Large R)
Flow lines
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/dc2t]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)
Kv avg
Kh 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.