Hydrological Basic Concepts
AOM 4643 Principles and Issues in Environmental Hydrology
Structure and Properties of Water
Water is a held together by a covalent bond one side has a negative charge and the other a positive charge. The positive end of one H2O molecule attracts the negative end of another => called hydrogen bond
Polar covalent bond (strong)
H+
104.5o
O2-
H+
hydrogen bond is weaker than a covalent bond but very important. Hydrogen bond determines most of water's unique properties
Thermal Properties of Water
boiling point and freezing point are higher than expected for its molecular weight (because of intermolecular attraction i.e. hydrogen bonds) water exists in solid, liquid & gas phases on earth. maximum density @ 4oC ice floats, caused by hydrogen bonds forming tetrahedra at low temp; important in determining earth's climate high specific heat capacity a large input of energy raises the temperature a relatively small amount; energy goes into breaking hydrogen bonds rather than raising the temperature
Structural Properties of Water
cohesive, sticks to itself high surface tension drops of water are spherical. capillarity results of combination of adhesion to solid surfaces i.e. glass (water molecules are attracted to oxygen atoms in glass) by hydrogen bonds and cohesion to itself through surface tension; important for circulation of blood in body and water in soil capillary forces are what allow moist sand to maintain vertical trench walls, whereas dry sand can only maintain a slope of 30o tiny menisci hold sand grains together through the hydrogen bonds
Water as a Solvent
universal solvent given enough time only a few natural substances will not dissolve in water. water dissolves substances by:
forming hydrogen bonds with its molecules (polar molecules) surrounding individual ions of the substance (electrolytes)
water alone cannot carry an electrical current due to the hydrogen bonds which do not allow hydrogen and oxygen atoms to move around freely of one another. Electrolytes in water can cause the solution to carry a charge. The higher the salt content the higher the electrical conductivity.
Basic Hydrologic Concepts
Hydrologic cycle describes the continuous circulation of water from land and sea to the atmosphere and back again. Concept is based on mass balance and is simply that water changes state and is transported in a closed system Hydrologic cycle is closed only globally, not on a watershed or continental scale. Hydrologic phenomena (precipitation, ET, infiltration, groundwater, overland, streamflow) are extremely complex and although quantifiable at lab scale, may never be fully predictable at the watershed scale. Thus we represent them in a simplified way by means of the systems concept.
Definition
A hydrologic system is defined as a structure (surface or subsurface) or volume (atmospheric) in space, surrounded by a boundary, that accepts water and other inputs (such as air or heat energy), operates (physical, chemical, biological) on them internally and produces them as outputs. We treat the hydrologic cycle as a system whose components are precipitation, evapotranspiration, interception, runoff, infiltration, etc.. We give up the quest to know the precise spatiotemporal water flow patterns within the system and settle instead for knowing total water storage, and spatially averaged water fluxes in and out of the control volume.
Example
overland flow
ET(t) surface runoff
groundwater discharge
Q(t)
The basic relations of physical hydrology this for system are derived from fundamental laws of classical physics. Particularly: Conservation of mass (m = mass of water) Conservation of energy (internal energy, kinetic energy and potential energy of the fluid)
Conservation of Mass
The most useful principal in hydrologic analysis and is required in almost all problems. Stated mathematically: dS + Q(t ) - I (t ) dt For our watershed problem: dS = P (t ) - Q(t ) - G (t ) - ET (t ) dt If have a steady flow problem, inflows=outflows:
P (t ) = Q(t ) + G (t ) + ET
dS =0 dt
Conservation of Energy
Second fundamental physical law utilized in physical hydrology is the conservation of energy. Total energy =internal energy + kinetic energy +potential energy Total Energy E = Eu + 1/2 mV2 + mgz
Energy per unit mass
e
=
eu
+
1/2 V2
+
gz
Internal Energy
Internal energy is the sum of sensible heat and latent heat. Sensible heat is that part of the internal energy that is proportional to the substance's temperature, i.e. deu = CpdT
Latent heat - Amount of heat exchange required for inducing a phase change per gram of substance without a change in temperature. Usually a function of temperature.
Latent Heat Values for Water
liquid water to vapor
Le = latent heat of evaporation = 597.3 - 0.57 T cal/g (2.5x106 - 2370T J/kg) This is heat absorbed (by vaporized water from surroundings) to break H bonds so evaporation can take place evaporation always accompanied by transfer of heat out of water body or surroundings to vapor latent heat transfer
vapor to liquid water
Lc = latent heat of condensation = -597.3 + 0.57 T cal/g (-2.5x106 + 2370T J/kg) This is heat released to surroundings when H bonds formed during condensation
Latent Heat Values for Water
ice to liquid
Lm = latent heat of melting = 79.7 cal/g ( 0.33 * 106 J/kg) This is energy required to disrupt tetrahedral molecular structure.
liquid to ice
Lf = latent heat of fusion = -79.7 cal/g ( 0.33 * 106 J/kg) This is energy released as tetrahedral molecular structure is formed.
ice to vapor
Ls = latent heat of sublimation = 677 - 0.07 T cal/g This is energy needed to a) disrupt molecular structure then b) break H bonds
Latent Heat Values for Water
At typical atmospheric temp. and pressure on earth, energy required to sublimate ice to vapor generally greater than that required to melt ice through evaporation. Therefore, usually water goes through liquid phase first.
Temp (oC) -10 0 10
Ls = 677 - 0.07 T (cal/g) 677.7 677 676.6
Lm + Le = 79.7 + 597.3 - 0.57 T (cal/g) 682.7 677 671.3
Latent Heat Transfer
1952 J/kg K latent heat of evaporation 539 cal/g at 100 C 2.3*106 J/kg at 100 C
Internal energy
latent heat of fusion = 80 cal/g = 0.33*106 J/kg
specific heat Cp = 1 cal/gC =4183 J/kgK
ice 2106 J/kg K 0
liquid water 100
water vapor
Temp C
Jumps in curve latent heat transfer to water Slope in curve sensible heat transfer to water
Examples of Use of Latent Heat Properties
In the SW use the latent heat of evaporation for airconditioning houses water and air is run into evaporative cooler on roofs of houses -- as water evaporates absorbs heat from air. Cooled air is returned to house. Irrigation of plants to protect from freezing. when irrigation water freezes it releases heat to the environment which increases air temperature slightly and protects plant. Latent heat transfer is the dominant cause of internal energy change for water in most hydrologic applications temperatures usually only change a few degrees C so sensible heat transfer is small.