S09.323.L8

Topics

Ch. 3

Properties of aquifers

Sediment characteristics

Equations of energy

Hydraulic Conductivity

Darcy’s Law

Equations of Energy

Energy (E) = the ability to do work

Potential E (pE)= stored energy =energy of position or resting energy. (e.g. water at highest elevation in the watershed has the potential to do work if it is permitted to flow downstream).

Kinetic Energy (kE) = energy of motion (e.g. when that water is permitted to flow downstream it converts gravitational potential energy into kE).

Equations:

F= ma Force = mass x acceleration

Weight = common force

1) W = mg

Where weight (Newtons) = mass (kg) x acceleration due to gravity (= g = 9.81 m/sec²)

Note that 1 kg = mass, which = 9.81 N (its weight)

Our scales are set up to measure mass under the assumption that it is being weighed in a gravitational force = g.

For English system, mass = slug

weight = pound (lb) = 1 slug-ft/sec²

2) Density (r) = mass/volume (m/V)

3) Specific weight (g) = weight/volume (= w/V) which equals

4) Pressure = Force / Area (F/A)

For Hydrology Pressure measured relative to atmospheric pressure

Metric = 1.013 X 10⁵ Pascals (Pa) = N/m²

English = 2116 Lb/ft²

Viscosity = resistance to flow

Dynamic Viscosity = µ = N sec / m² = lb sec / ft²

Bulk modulus

Water is compressible fluid; its density increases with increasing pressure.

The constant of proportionality of compressibility = bulk modulus (units = N/m² or lb/ft²)

Properties of aquifers

Porosity

Last time :

Porosity (n) = V_voids / V_sample x 100

Effective porosity = pore volume able to transmit fluid

Total porosity = 100 [1-(r_b /r_d)]

where

r_b = bulk density of aquifer

r_d = density of the particle material.

Sediment packing

Uniform grain size =

Cubic packing =each sphere sits directly on crest of underlying sphere. If clasts are uniform and well rounded, porosity = 47.65%.

Rhombohedral packing = sphere sits in the hollow created by four adjacent spheres of underlying layer = 25.95%.

Sorting

See fig. 3.4 for semilog chart of grain size distribution

Variable grain size = lower porosity as small clasts will settle into voids between larger clasts.

How sorting determined = using standard sieves and weighing each fraction

Sieve scales = based on fractions of mm

Phi units (f) = D = D₀ x 2^-f

where D₀ = 1 mm

Uniformity coefficient (C_u) = d₆₀/d₁₀

Where d ₆₀ and d₁₀ = percent of sample finer by weight

If C_u < 4 = well sorted

Effective grain size = d₁₀ on the grainsize curve

Porosity

Diagenesis = all the things that happen after burial = compaction, removal of material, addition of material, crystallization and cementation.

Primary porosity = pores left between grains

Secondary porosity = fractures, dissolution features in carbonate rocks