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Soils & Hydrology Math
Soils & Hydrology Math
98
Science
Undergraduate 3
03/15/2016

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Cards

Term
how to calculate mass of horizon in lbs/a
Definition

BD x (62.4lb/ft3) x (5280ft2/mile) x (1 mile/(640 (a/mile))) x (in/(12in/ft)) = lbs/a

 

BD= bulk density (g/cm3)

Term
Map has a scale of 1:20,000. How many acres per square inch on map?
Definition

1in on map= (20,000in/(12in/ft))= 1,667ft

 

((1,667ft2)ft2)/(43,560ft2/a)= 63.79 acres

Term
how to calculate ppm of P in the soil (mg/kg soil) from the solution concentration (mg P/L)
Definition

((mg P/L) x L)/(kg soil)= mg/kg= ppm

 

to find lbs/a, multiply both the neumerator and the denominator by 2, since an acre has 2 million lbs of soil to a 6" depth

Term
base saturation
Definition
% of cations in soil that are bases, that is, (sum of the basic cations)/CEC
Term
how to calculate exchangeable acidity
Definition

N(acid) x V(acid)= N(base) x V(base)

solve for N(acid)

N(meq/mL) x ((mL acid before titration)/(g of soil sample))= meq/g

(meq/g) x 100= meq/100g

Term
how to measure exchangeable cations
Definition

(meq/L) x (L/(g of soil sample))= meq/g

(meq/g) x 100= meq/100g

meq/L measured by AA

Term
how to convert AA absorbance to meq/L
Definition
meq/L= slope x absorbance
Term
how to convert meq/100g to lbs/acre
Definition

(meq/100g) x (1/valence) x (((g/mol)mg)/1mg) x (1000g/1kg)= mg/kg= lbs/million lbs

(lbs/million lbs) x (2/2)= lbs/acre

Term
how to calculate lbs of nutrient
Definition
lbs nutrient= (lbs fert) x (analysis/100)
Term
how to figure out how much actual fertilizer to add
Definition

(lbs nutrient recommended)= (fert analysis as decimal) x (lbs fert to apply)

or

(lbs nutrient recommended)/(fert analysis as decimal)= lbs fert to apply

Term
how to convert between volumetric and gravimetric water content
Definition

using soil bulk density

 

θv= θg x BD

 

works because each cm3 of water weighs 1g

Term
gravimetric water content (θg)
Definition
θg= (g water)/(g soil)= g/g
Term
volumetric water content (θv)
Definition
θv= (cm3 water)/(cm3 soil)= cm3/cm3
Term
how to determine depth of water in soil (Dw)
Definition

Dw= θv x Ds

Dw= depth of water in soil (cm)

Ds= soil depth (cm)

θv= volumetric water content (cm3)

Term
how to calculate field capacity (FCg)
Definition

FCg= Mw/Ms

Mw= mass water

Ms= mass soil

Term
how to calculate plant available water (AWg)
Definition

AWg= FCg - WPg

FCg= field capacity

WPg= water content at wilting point

Term
how to convert gravimetric water content into volumetric water content
Definition
(gravimetric water content) x BD= volumetric water content
Term
how to convert volumetric water content into depth of water per depth of soil
Definition

Dw= θv x Ds

Dw= depth of water

Ds= depth of soil

θv= volumetric water content

Term
how to calculate capillary pore size
Definition

capillary rise equation

 

h= (2σ cos α)/(γr)= (0.15/r) cm

 

h= capillary rise

r= pore radius

σ= surface tension of water

α= air-water-soil contact angle

γ= specific weight of water

Term
how to calculate residence time
Definition

T= V/Q

T= residence time

V= volume of revervoir

Q= flow through reservoir

Term
how to calculate capillary rise
Definition

h= (2σ cos α)/(γr)= (0.15/r) cm

 

h= capillary rise

r= pore radius

σ= surface tension of water

α= air-water-soil contact angle

γ= specific weight of water

 

for glass and most soils: h= (0.15/r)cm

Term
how to calculate total energy of a moving fluid
Definition

E= GE + PE + KE

E= energy

GE= gravitational energy

PE= pressure energy

KE= kinetic energy

Term
another way to calculate total energy of a moving fluid
Definition

E= (mgz) + (p) + ((1/2)mv2)

m= mass

g= gravitational constant (9.8m/s2)

z= elevation

p= fluid pressure

v= velocity

Term
how to calculate hydraulic head of a fluid, that is, total head
Definition

h= (E/Vγ)= z + p + (v2/2g)

h= hydraulic head, the energy of an equivalent height of water

v= volume

γ= specific weight of water

z= elevation

p= pressure head

(v2/2g)= velocity head, usually ignored in soils

Term
how to calculate hydraulic head (simplified)
Definition

h= z + p

 

H= hydraulic head of a fluid

z= elevation

p= pressure head

Term
how to calculate porosity
Definition
PS= (volume voids)/(volume soil)= cm3/cm3
Term
how to calculate bulk density
Definition
BD= (g soil)/(cm3 soil)= g/cm3
Term
combined equation for particle density and bulk density
Definition

PS= 1- (BD/PD)

PD= particle density

Term
how to convert between volumetric water content and gravimetric water content
Definition
θv= θg x BD
Term
how to calculate relative saturation
Definition

Θ= (cm3 water)/(cm3 pores)= θv/PS

Θ= capital theta

θ= lower case theta

Term
plant vailable water (AW)
Definition

AW= FC - WP

AW= plant available water

FC= field capacity

WP= wilting point

Term
hydraulic head
Definition

a measure of the potential energy of water

h= z+p

h= hydraulic head

z= elevation head

p= pressure head

Term
how to calculate hydraulic gradient
Definition

G= (Δh/Δx)

G= slope between 2 points

Δh= change in hydraulic head

Δx= distance between 2 points

Term
Darcy's Law equation
Definition

q= -K x (Δh/Δx)= -K x G

 

q= water flux aka darcian flux (cm/sec)

K= hydraulic conductivity

G= hydraulic gradient

Δh= change in hydraulic head

Δx= distance between 2 points

Term
pore velocity aka water velocity
Definition

v= q/θv

 

v= water/pore velocity

q= water/darcian flux

θv= volumetric water content

Term
how to calculate total flow
Definition

Q= q x A= -K x A x G

 

Q= total flow

q= water/darcian flux

K= hydraulic conductivity or permeability of soil

A= area of flow

G= magnitude of driving force

Term
how to find hydraulic conductivity (K)
Definition

K= -(Q/(A x G))

 

Q= total flow

A= cross-sectional area

G= magnitude of driving force

Term
how to use Darcy's Law for unsaturated flow
Definition

q= -Ku x G= -K x Kr x G

q= water flux

Ku= unsaturated hydraulic conductivity

Kr= relative hydraulic conductivity

K= hydraulic conductivity or permeability

G= magnitude of driving force

Term
how to calculate relative hydraulic conductivity (Kr)
Definition

Kr= Ku/K

Ku= unsaturated hydraulic conductivity

K= hydraulic conductivity or permeability

Term
how to find volumetric water content when given gravimetric water content and bulk density
Definition

θv= θg x BD

θv= volumetric water content

θg= gravimetric water content

BD= bulk density

Term
how to calculate exchangeable acidity
Definition

N(acid) x V(acid)= N(base) x V(base)

then

(N(base) x V(base))/V(acid)= N(acid)

then

N(acid) x ((total extraction volume before titration (mL))/(g soil used))= meq/g

then

(meq/g) x 100= meq/100g

Term
how to find % base saturation
Definition
(sum of bases)/(CEC (sum of all cations))= %BS
Term
how to find exchangeable bases
Definition

((meq base)/L) x ((total extraction volume (L))/(g soil sample))= (meq base)/g

 

multiply by 100 to get meq/100g

 

do this separately for each base

Term
how to change exchangeable element value to lbs/acre
Definition

((meq element)/100g) x (1/valence) x ((MW (mg))/1mg) x (1000g/1kg) = mg/kg= lbs/(million lbs)

 

(lbs/(million lbs)) x (2/2)= (lbs/(2 million lbs/acre))= lbs/acre

Term
how to find pore radius
Definition

r= (0.15/h)

h= height (cm)

Term
how to calculate porosity
Definition

porosity= 1-(BD/PD)

BD= bulk density (g/cm3)

PD= particle density (usually 2.65 g/cm3)

Term
1ft3= how many gallons?
Definition
7.48 gal
Term
1 gal= how many L?
Definition
3.78 L
Term
θg
Definition
gravimetric water content
Term
θv
Definition
volumetric water content
Term
Dw
Definition
depth of water in soil (cm)
Term
Ds
Definition
soil depth (cm)
Term
FCg
Definition
field capacity
Term
Dw
Definition
depth of water in soil (cm)
Term
Ds
Definition
soil depth (cm)
Term
FCg
Definition
field capacity
Term
Mw
Definition
mass water
Term
Ms
Definition
mass soil
Term
AWg
Definition
plant available water
Term
h
Definition
depending on context, can be capillary rise, hydraulic head, or height
Term
r
Definition
pore radius
Term
σ
Definition
surface tension of water
Term
α
Definition
air-water-soil contact angle
Term
γ
Definition
specific weight of water
Term
T
Definition
residence time
Term
V
Definition
volume of reservoir
Term
Q
Definition
flow through reservoir or total flow
Term
g
Definition
gravitational constant (9.8m/s2)
Term
z
Definition
elevation
Term
p
Definition
fluid pressure
Term
v
Definition
velocity or water/pore velocity
Term
v2/2g
Definition
velocity head, usually ignored in soils
Term
PS
Definition
porosity
Term
PD
Definition
particle density
Term
Θ (capital theta)
Definition
relative saturation
Term
q
Definition
water flux aka darcian flux
Term
K
Definition
hydraulic conductivity
Term
G
Definition
depending on context, this can be hydraulic gradient or magnitude of driving force
Term
Q
Definition
total flow
Term
K
Definition
hydraulic conductivity or permeability of soil
Term
A
Definition
area of flow or cross-sectional area
Term
Ku
Definition
unsaturated hydraulic conductivity
Term
Kr
Definition
relative hydraulic conductivity
Term
%BS
Definition
% base saturation
Term
GE
Definition
gravitational energy
Term
PE
Definition
pressure energy
Term
KE
Definition
kinetic energy
Term
Stokes's Law equation
Definition

v=((2r2g)/(9μ)) x (ρsw)

v= velocity of fall of particle (cm/sec)

r= particle radius (cm)

g= gravitational constant (9.8 cm/s2)

ρs= density of solid particle(g/cm3)

ρw= density of water (g/cm3)

μ= viscosity of the liquid (units of poise)

Term
Stokes's Law equation (simplified)
Definition
v= 8950r2
Term
how to calculate aggregate stability
Definition

%WSA=((final aggregate weight)/(initial aggregate weight)) x 100%

%WSA= % water stable aggregates

Term
L
Definition
Change in elevation
Term
ψ (Greek letter psi)
Definition
Pressure head
Term
How to calculate water holding capacity
Definition
water holding capacity= FC-WP
Term
units involved in hydraulic head
Definition
units of length
Term
water flow related to hydraulic head
Definition
flows from high hydraulic head to low hydraulic head
Term
another way to write pressure head (p)
Definition
Term
μ
Definition
viscosity of the liquid (units of poise)
Term
Δx
Definition
distance between 2 points
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