Formula solver index — formula.expert

Cost of Water Over a Period

C_w = V \, p_w

Water TreatmentFluid MechanicsWater & WastewaterCost of the water a system buys over a period: the metered volume times the utility's rate, in whatever currency that rate was in.

Sewer Credit for Evaporated Water

C_c = V_e \, p_s

Water TreatmentFluid MechanicsWater & WastewaterSewer credit for water a tower evaporates: the volume that never reaches the drain, valued at the municipal sewer rate.

Net Water and Sewer Cost of a Cooling Tower

C = V_m \, p_w + (V_m - V_e) \, p_s

Water TreatmentFluid MechanicsWater & WastewaterFull water and sewer bill for a cooling tower: makeup charged at the water rate, plus only the volume actually discharged at the sewer rate.

Hydraulic Detention Time

t = \frac{V}{Q}

Water & WastewaterWater TreatmentFluid MechanicsTheoretical detention time of a tank, clarifier or contact basin: the working volume divided by the flow passing through it.

Surface Overflow Rate

v_o = \frac{Q}{A}

Water & WastewaterWater TreatmentFluid MechanicsSurface overflow (surface loading) rate of a settling basin — flow divided by plan area, reported here in metres per day.

Filtration Rate (Filter Loading Rate)

v_f = \frac{Q}{A}

Water & WastewaterWater TreatmentFluid MechanicsFiltration rate through a granular media filter: flow divided by filter bed area, the approach velocity reported in metres per day.

Backwash Water Volume

V_{bw} = v_b \, A \, t

Water & WastewaterWater TreatmentFluid MechanicsWater consumed by one filter backwash, from the backwash rise rate, the filter bed area and the duration of the wash.

Percent Backwash Water

\%BW = \frac{V_{bw}}{V_f} \times 100

Water & WastewaterWater TreatmentShare of a filter's production consumed by its own backwash, the housekeeping ratio that flags short runs and poor coagulation.

CT Value for Disinfection Credit

\text{CT} = C \, t

Water & WastewaterWater TreatmentChemistryDisinfection CT: residual concentration multiplied by contact time, returned in the regulatory unit of mg·min/L.

BOD Mass Loading

W = Q \, C

Water & WastewaterWater TreatmentChemistryMass of BOD, COD or solids arriving per unit time from a flow and its concentration, on the sanitary basis of 1 mg/L = 1 g/m³.

BOD Removal Efficiency

E = \frac{C_i - C_e}{C_i} \times 100

Water & WastewaterWater TreatmentPercent removal across a treatment unit or a whole plant, from the influent and effluent concentrations of BOD, TSS or any pollutant.

Volumetric Organic Loading Rate

L_v = \frac{Q \, S_0}{V}

Water & WastewaterWater TreatmentOrganic load applied per unit of reactor volume, returned in kg BOD per cubic metre per day — the sizing number for basins and digesters.

Food-to-Microorganism (F/M) Ratio

\frac{F}{M} = \frac{Q \, S_0}{V \, X}

Water & WastewaterWater TreatmentFood-to-microorganism ratio: BOD applied per day divided by the mass of mixed liquor solids holding it, in kg BOD per kg MLVSS per day.

Mean Cell Residence Time (Sludge Age)

\text{SRT} = \frac{V \, X}{Q_w \, X_w}

Water & WastewaterWater TreatmentSolids retention time of an activated sludge plant: the mass of solids under aeration divided by the mass wasted each day.

Sludge Volume Index (SVI)

\text{SVI} = \frac{SV_{30}}{X}

Water & WastewaterWater TreatmentSludge volume index in mL/g: the volume a gram of mixed liquor solids occupies after settling thirty minutes in a litre cylinder.

Return Activated Sludge Rate

Q_r = \frac{Q \, X}{X_r - X}

Water & WastewaterWater TreatmentReturn sludge flow needed to hold a target mixed liquor concentration, from a solids balance around the aeration basin.

Clarifier Solids Loading Rate

\text{SLR} = \frac{(Q + Q_r) \, X}{A}

Water & WastewaterWater TreatmentSolids applied to a secondary clarifier per unit of surface area, in kg of MLSS per square metre per day, including the return flow.

Sludge Volume from Dry Solids

V = \frac{m}{S \, \rho_w \, (P/100)}

Water & WastewaterWater TreatmentVolume of wet sludge holding a given mass of dry solids, from the solids percentage and the sludge specific gravity, at 1000 kg/m³ water.

Specific Gravity of Sludge

\frac{1}{S_{sl}} = \frac{P/100}{S_s} + \left(1 - \frac{P}{100}\right)

Water & WastewaterWater TreatmentSpecific gravity of a wet sludge from its percent solids and the specific gravity of the dry solids, by a reciprocal mass balance.

Solids Capture in Dewatering

R = \frac{C_c (C_f - C_{fil})}{C_f (C_c - C_{fil})} \times 100

Water & WastewaterWater TreatmentPercent solids capture of a belt press, centrifuge or filter from the feed, cake and filtrate solids concentrations by mass balance.

Van Kleeck Volatile Solids Reduction

R = \frac{V_{in} - V_{out}}{V_{in} - V_{in} V_{out}} \times 100

Water & WastewaterWater TreatmentPercent volatile solids destroyed in a digester by the Van Kleeck equation, using only the volatile fractions in and out.

Trickling Filter Hydraulic Loading

L_h = \frac{Q + Q_r}{A}

Water & WastewaterWater TreatmentFluid MechanicsHydraulic loading on a trickling filter including recirculation — total flow per unit of media surface area, in metres per day.

Trickling Filter Recirculation Factor

F = \frac{1 + R}{(1 + 0.1R)^2}

Water & WastewaterWater TreatmentNRC recirculation factor for trickling filter design, converting a recirculation ratio into the effective number of passes through the media.

Population Equivalent

PE = \frac{W}{w}

Water & WastewaterWater TreatmentPopulation equivalent of a waste stream: its pollutant load divided by the load one person contributes, typically 60 g BOD per day.

Per-Capita Wastewater Flow

q = \frac{Q}{P}

Water & WastewaterWater TreatmentFluid MechanicsAverage wastewater contributed per person per day, from the plant flow and the population served, reported in gallons per capita per day.

Harmon Peaking Factor

PF = 1 + \frac{14}{4 + \sqrt{P/1000}}

Water & WastewaterWater TreatmentFluid MechanicsHarmon peaking factor for sanitary sewer design: the ratio of peak hourly to average daily flow for a served population.

Manning's Equation for Velocity

v = \frac{1}{n} R^{2/3} S^{1/2}

Water & WastewaterFluid MechanicsOpen-channel velocity by Manning's equation in SI form, from the roughness coefficient, hydraulic radius and channel slope.

Manning's Equation for Flow

Q = \frac{1}{n} A R^{2/3} S^{1/2}

Water & WastewaterFluid MechanicsOpen-channel discharge by Manning's equation in SI form, from flow area, roughness, hydraulic radius and slope.

Francis Formula: Rectangular Weir

Q = 3.33 \, L \, H^{3/2}

Water & WastewaterFluid MechanicsFlow over a suppressed rectangular weir by the Francis formula, with the trade constant 3.33 for crest length and head in feet.

V-Notch (Triangular) Weir Flow

Q = \frac{8}{15} C_d \sqrt{2g} \, \tan\!\frac{\theta}{2} \, H^{5/2}

Water & WastewaterFluid MechanicsDischarge over a sharp-crested triangular weir from the notch angle, head and discharge coefficient, in the standard theoretical form.

Parshall Flume Free Flow

Q = 4 \, W \, H^{1.522 \, W^{0.026}}

Water & WastewaterFluid MechanicsFree-flow discharge through a Parshall flume of 1 to 8 ft throat width, with W and the head H in feet and Q in cubic feet per second.

Stokes Settling Velocity

v_s = \frac{g (\rho_s - \rho) d^2}{18 \mu}

Water & WastewaterFluid MechanicsTerminal settling velocity of a small sphere in laminar flow by Stokes' law — the grit chamber and clarifier design relation.

Jar Test Dose Scale-Up

D = \frac{V_{st} \, C_{st}}{V_{s}}

Water & WastewaterWater TreatmentChemistryConverts millilitres of stock solution added to a jar test beaker into the equivalent plant dose in mg/L of raw water.

Alkalinity Remaining After Alum

A_f = A_0 - 0.45 \, D

Water & WastewaterWater TreatmentChemistryAlkalinity left after coagulation, since each mg/L of alum destroys 0.45 mg/L of alkalinity as CaCO₃ in forming aluminium hydroxide floc.