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)

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

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

((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

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

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

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

meq/L measured by AA

(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

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

or

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

using soil bulk density

θ_v= θ_g x BD

works because each cm³ of water weighs 1g

D_w= θ_v x D_s

D_w= depth of water in soil (cm)

D_s= soil depth (cm)

θ_v= volumetric water content (cm³)

FC_g= M_w/M_s

M_w= mass water

M_s= mass soil

AW_g= FC_g - WP_g

FC_g= field capacity

WP_g= water content at wilting point

D_w= θ_v x D_s

D_w= depth of water

D_s= depth of soil

θ_v= volumetric water content

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

T= V/Q

T= residence time

V= volume of revervoir

Q= flow through reservoir

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

E= GE + PE + KE

E= energy

GE= gravitational energy

PE= pressure energy

KE= kinetic energy

E= (mgz) + (p) + ((1/2)mv²)

m= mass

g= gravitational constant (9.8m/s²)

z= elevation

p= fluid pressure

v= velocity

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

h= z + p

H= hydraulic head of a fluid

z= elevation

p= pressure head

PS= 1- (BD/PD)

PD= particle density

Θ= (cm³ water)/(cm³ pores)= θ_v/PS

Θ= capital theta

θ= lower case theta

AW= FC - WP

AW= plant available water

FC= field capacity

WP= wilting point

a measure of the potential energy of water

h= z+p

h= hydraulic head

z= elevation head

p= pressure head

G= (Δh/Δx)

G= slope between 2 points

Δh= change in hydraulic head

Δx= distance between 2 points

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

v= q/θ_v

v= water/pore velocity

q= water/darcian flux

θ_v= volumetric water content

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

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

Q= total flow

A= cross-sectional area

G= magnitude of driving force

q= -K_u x G= -K x K_r x G

q= water flux

K_u= unsaturated hydraulic conductivity

K_r= relative hydraulic conductivity

K= hydraulic conductivity or permeability

G= magnitude of driving force

K_r= K_u/K

K_u= unsaturated hydraulic conductivity

K= hydraulic conductivity or permeability

θ_v= θ_g x BD

θ_v= volumetric water content

θ_g= gravimetric water content

BD= bulk density

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

((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

((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

r= (0.15/h)

h= height (cm)

porosity= 1-(BD/PD)

BD= bulk density (g/cm³)

PD= particle density (usually 2.65 g/cm³)

v=((2r²g)/(9μ)) x (ρ_s-ρ_w)

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

r= particle radius (cm)

g= gravitational constant (9.8 cm/s²)

ρ_s= density of solid particle(g/cm³)

ρ_w= density of water (g/cm³)

μ= viscosity of the liquid (units of poise)

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

%WSA= % water stable aggregates