hydrology midterm 2

fluid statics through groundwater units

flow

based on a force balance, imbalance can lead to flow

speed of flow depends on

steepness and properties of fluid

fluid

substance that continuously deforms (changes shape when subjected to a shear stress)

body force

forces that act at a distance and do not require contact (eg: gravity)

surface force

forces caused by direct contact between two fluid particles (eg: pressure)

pressure

surface force that holds normal to the surface, also a stress (force/area)

shear force

a frictional surface force that acts tangentially
resistance to flow/deformation

units of pascals

1 Pa = 1 kg m-1 s-2

roughness

other source of resistance, property of the fluid environment

rate of deformation equation

where:
f = force
A = area
miu = fluid viscosity
u = tangent object
d = depth

fluid statics

a special case of fluid at rest
if not moving, shear stresses are absent
only consider pressure and elevation

hydrostatic equation

describes variation of pressure with depth in a fluid at rest
where density and gravitational acceleration are constants so pressure increases linearly with depth

pressure head

p/(rho*g) = d

fluid dynamics

assuming flow rate is steady with time, elevation and pressure plus a term that describes the F/A in the system associated with water movement through a system

faster moving fluid

relieves pressure, lower pressure

velocity and pressure are

inverse/compensatory

Bernoulli Equation

constant rate of flow, frictionless

continuity equation

steady flow is a hose, no changes in the amount of water in any segment at any time (inflow=outflow)
conservation of mass/volume

flow constriction

if area increases, velocity must decrease

head loss

an empirical way of dealing with fluid friction that is dissipating energy as it flows
depends on: viscosity of the fluid/flow, diameter of pipe, length of pipe section, and roughness

laminar flow

nonturbulent streamline flow in parallel layers, experiences less energy loss because less energy is transferred via vertical motion

turbulent flow

flow in which the velocity at any point varies erratically

Reynold's number

describes which fluid type is likely in a given set of conditions

open channel hydraulics

unbounded at the top, free water surface open to atmospheric pressure where pressure changes with depth

friction slope

the head loss per unit length along a channel
slops of energy surface, generally analogous with water bed

head loss in terms of friction slope

friction slope with hydraulic radius

open channel flow

for a rectangular cross section

with w= width
h= height
and a wetted perimeter of 2h+w

Chezy formula

c is a resistance factor… large for smooth objects, small for rough
S is the slope of the bed, representative of the friction slope
R is the hydraulic radius… the ratio of cross-sectional area to perimeter

Manning equation

k is equal to 1 m1/3 s-1 in SI units

Manning n

the inverse of the Chezy c parameter, non-linearly inverse due to different powers of Rh
larger for surfaces

smoother flow environment

faster flow, less frictional dissipation of energy

empirical relationship for roughness

includes friction factor, water depth, and D84, the size of bed material of which 84% of bed material is finer
Determined by measuring lots of diameters of the bed material, sorting the data from smallest to largest, and picking out the 84th percentile

bank full

fully filled to banks

floodplain

overflowing bank

terrace

where you want to build a house/overflow least likley to reach

as depth gets bigger, discharge gets...

bigger faster (h to the 1.5 power)

Manning relationship (stage-discharge)

Discharge can be related to depth of flow, or stage of flow

If we measure depth and know how that translates to discharge we have an easy measure of discharge

in open channels, total head

decreases in a downstream direction at a rate determined by the slope of the channels

slope determines rate of

elevation loss

hydrograph

graph of a continuous record of river stage or discharge versus time for a particular point

rating curve

plot of discharge versus stage and the associated equation for a functional form relating them

floods

an increase in discharge following the input of water from a rain or snowmelth

attenuated

reduced in peak

baseflow

background low-flow conditions in a stream, characterized by flow between flood events and supplied inflow of groundwater

porous medium

a rock, sediment, or soil that contains pores or void sections

Poiseuille's Law

defines the average velocity through a tube for a flow of a viscous fluid through a capillary tube
where h is the hydraulic head =

dh/dl

difference in hydraulic head over difference in length (slope)

key points of groundwater hydraulics

1. flow is down the hydraulic head gradient
2. discharge is directly proportional to the hydraulic head gradient
3. flow is inversely proportional to fluid viscosity

Darcy's law

Q is directly proportional to dl, where k is a constant of pro

specific discharge

discharge per unit cross-sectional area of a flow through the porous medium (units in m/s)

hydraulic conductivity (K)

describes how Q changes with fluid weight (rho*g), fluid viscosity (miu), and the aggregate effect of pipe diameters (D^2/32)

intrinsic permeability (k)

ability of a porous medium to transmit fluid, independent of the fluid properties (dimensions in length^2)

porosity

the fraction of the total volume of a porous medium occupied by void space (dimensionless on a scale of 0 to 1)
note: v is always greater than Q

aquifer

a saturated geologic formation that contains and transmits significant quantities of w

aquifuge

a formation that neither contains nor transmits water

aquiclude

can contain but doesn't transmit water

aquitard

general term describing formations of low permeability (aquifuge and

wells & piezometers

are used to measure the hydraulic head in an aquifer

piezometer

a tube or pipe that measures the pressure head at a point in the surface

piezometric surface

sum of elevation head and pressure head

unconfined aquifer

a permeable formation whose upper bound is the water table

confined aquifer

upper band is an aquitard where water is typically under pressure

flow net

simplified approach to calculating flow (direction), constitutes of mapped streamlines and equipotentials

angle at which equipotentials and streamlines intersect

90°

equipotentials

gradient of steepest descent

streamtube

space between streamlines, volume discharged is equal through all streamtubes

where spacing between the streamtubes is narrow, flow is

fastest

procedure for calculating discharge

1. isolate a (perfect) square
2. use Darcy's law to calculate discharge through these squares
3. extend to get discharge for the entire aquifer

Qs

discharge of a streamtube

K*b

transmissivity

recharge zone

zones with an angle

discharge zone

zones with an angle >90° contribute to discharge

hinge

where discharge and recharge are separated, demarcated by the location where equipotential lines are exactly perpendicular to the local water table

what is a flow net really displaying?

a solution to the steady-state flow in a particular basin geometry, can be written as specific discharge

aspect ratio

basin length to depth ratio

large aspect ratio

shallow basin

small aspect ratio

deeper basin, has more dischage/flow because of a high number of streamflow tubes

what is the most common cause of variation in hydraulic head and groundwater flow?

topographic relief

shallow topography

the regional flow is attenuated relative to dominant influence of the local flow systems

deep topography

regional transport emerges/ local (L), intermediate (I), and regional (R) flow systems

geological heterogeneity

always exists and contrasts in physical properties
can drastically alter the situation from that which would be expected based on the table, with high flow areas capturing and focusing flow

specific yield (Sy)

the volume of water per unit aquifer area per unit decline in hydraulic head
- less than porosity
- ranges from 0.01 to 0.3 (unitless)

unconfined aquifer cone of depression

shape and expansion of the cone depends on pumping rate, Sy, & transmissivity

storativity (S)

volume of water per unit aquifer area per unit decline in potentiometric surface
- ranges from 0.005 to 0.05
- S << Sy

confined aquifer cone of depression

shape and rate of expansion of aquifer depends on pumping rate, storativity (S), and transmissivity

leaky aquitards

increases b (thickness of aquifer) a little with low increase in K

Chezy U

cross-sectional average velocity