Formula

Volume of Sphere

V=\frac{4\pi r^3}{3}

BOD formula: Volume, Seeding, Ultimate BOD

BOD=D_1-D_2\cdot\frac{BODVolume}{SampleVolume}

BOD=\frac{\left(D_1-D_2\right)\cdot\left(B_1-B_2\right)f}{P}

BOD_{t}=BOD_{u}\left(1-e^{-kt}\right)

k_{T}=k_{20}\left(1.047\right)^{T-20}

Mass Balance

Qc = Qa + Qb

QcCc = QaCa + QbCb

mass density

\rho=\frac{P}{RT}

viscosity, \mu

\mu=\frac{\tau y}{V} dynamic/absolute

\omega=\frac{\mu}{\rho} kinematic

surface tension,  \sigma

\sigma=\frac{F}{L_{Total}}

P=\frac{4\sigma}{D}

adhesion > cohesion = rise

capillarity, h

h=\frac{4\sigma\cos\beta}{\gamma D}

Bulk Modulus, Eb

E_{B}=\frac{\Delta P}{-\frac{\Delta V}{V_1}}

Compressibility

reciprocal of Eb

Mass Loading (BOD, COD, TSS)

concentration (mg/L) * flow (gpd) 

unit: lb/day or kg/day

F/M Ratio

= BOD or COD (lb/day) / MLVSS (lb/day)

= (BOD or COD mg/L) x Flow / (MLVSS mg/L) x Volume

unit: lb BOD or COD / lb MLVSS

Waste or WAS (lb/day)

Actual MLVSS in aeration tank (lb/day) - Desired MLVSS in aeration tank (lb/day)

Waste Rate (gpd)

derived from the mass loading formula

= WAS (lb/day) / waste concentration (mg/L)

MCRT or SRT (days)

\frac{MLSS_{Volume},gal}{\left(Waste,\frac{mg}{L}\cdot Flow,gpd\right)+\left(Effluent,\frac{mg}{L}\cdot Flow,gpd\right)}

unit analysis: gallons will be cancelled, leaving “days”

SVI (Sludge Volume Index) 

= SSV (mL/L) / MLSS (g/L)

unit: mL/g

%SSV (Settled Sludge Volume)

= Settled Sludge (mL) / 1000 mL

unit: mL/L

Simple Interest

I = Pni

F = P+I

Compound Interest

I = P (1+i)^nm

i = r/m

Annuities

F=A\left\lbrack\frac{\left(1+i\right)^{nm}-1}{i}\right\rbrack

P=A\left\lbrack\frac{1-\left(1+i\right)^{-nm}}{i}\right\rbrack

Depreciation

d=\frac{C_{o}-C_{L}}{L}

Dn = dn

Cn = Co - Dn

Pace Factor

PF=distance/no. of paces

%Error = Measured Value - True Value / True Value

Stadia Method

D=ks+c

D=ks(cos)+c

k-stadia factor, usually 100

c-stadia constant

Subtense Bar Method

D=\frac{\frac{s}{2}}{\tan\frac{\theta}{2}}

s=2m

Correction in Taping

Corr. = TL - ML

\frac{cor.}{NL}=\frac{x}{ML}

CorrectedLength=ML\pm x

Correction due to Tension

C_{P}=\frac{\left(Pm-Ps\right)L}{AE}

A=\frac{W}{\gamma L}

gamma=unit weight

Correction due to Temperature

C_{T}=\alpha L\left(T-Ts\right)

Correction due to Sagging

C_{s}=\frac{\omega^2L^3}{24P^2}

\omega=\frac{W}{L}

Levelling

BM+BS = HI

HI-FS = TP Elev