Water Treatment formula solvers

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Acid Feed to Reduce Alkalinity

\dot m = \frac{\Delta \mathrm{Alk} \, Q \times \frac{\mathrm{EW}}{50.04}}{p/100\%}

Water TreatmentChemistrySizes the acid feed needed to knock a target amount of alkalinity out of a stream, correcting for the acid's equivalent weight and its commercial strength.

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.

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.

Blowdown Rate from Cycles

B = \frac{E}{\text{COC} - 1}

Water TreatmentFluid MechanicsBlowdown a cooling tower must bleed to hold a target cycles of concentration, given its evaporation rate.

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.

Boiler Blowdown Percent

\%B = \frac{\text{TDS}_{fw}}{\text{TDS}_b} \times 100

Water TreatmentChemistryBoiler blowdown as a percentage of feedwater, set by the ratio of feedwater TDS to the maximum TDS allowed in the drum.

Boiler Blowdown Rate from Steam Rate

B = \frac{S}{\text{COC} - 1}

Water TreatmentThermodynamicsContinuous blowdown a steam boiler must carry, in pounds per hour, from its steam production rate and target cycles of concentration.

Boiler Cycles of Concentration

\text{COC} = \frac{\text{TDS}_b}{\text{TDS}_{fw}}

Water TreatmentChemistryCycles of concentration in a steam boiler: boiler water TDS divided by feedwater TDS, since steam leaves the dissolved solids behind.

Boiler Horsepower to Heat Output

Q = 33{,}475 \; \text{BHP}

Water TreatmentThermodynamicsConverts boiler horsepower to heat output using the ASME definition of 33,475 BTU per hour per boiler horsepower.

Boiler Horsepower to Steam Rate

S = 34.5 \; \text{BHP}

Water TreatmentThermodynamicsSteam output of a boiler from its horsepower rating, at the ASME definition of 34.5 lb/h of steam from and at 212 °F per BHP.

Boiler Makeup from Condensate Return

M = S\left(1 - \frac{\%CR}{100}\right)

Water TreatmentThermodynamicsFresh makeup water a steam plant must treat, from the steam production rate and the fraction of condensate that comes back.

Breakpoint Chlorine-to-Ammonia Ratio

R = \frac{\mathrm{Cl_2}}{\mathrm{NH_3\text{-}N}}

Water TreatmentChemistryThe weight ratio of chlorine dose to ammonia nitrogen, which must reach about 7.6 to 1 to pass breakpoint and produce a free chlorine residual.

Chemical Feed Rate (lb/day = mg/L × MGD × 8.34)

\dot m = C \, Q

Water TreatmentChemistryConverts a target chemical dose and a plant flow into a mass feed rate, the classic pounds-per-day formula built on water weighing 8.34 lb per gallon.

Chemical Feed Rate from Dose

W = C \, Q \, \rho_w

Water TreatmentChemistryChemical feed rate in pounds per day from a ppm dose and a water flow, using the trade density of 8.34 lb per US gallon.

Chemical Mass Consumed Over a Period

m = W \, t

Water TreatmentChemistryTreatment chemical a feed rate consumes over a period — the step that turns pounds per day into the annual tonnage a contract is priced on.

Chemical Treatment Cost

C_p = m \, p_c

Water TreatmentChemistryInvoice for a treatment chemical: the mass of product consumed over a period times its unit price, the second line of a water budget.

Chemical-Consuming Loss Rate

L = B + D

Water TreatmentChemistryFluid MechanicsFlow that actually carries treatment out of a cooling tower — blowdown plus drift, because evaporation leaves every molecule of inhibitor behind.

Chick–Watson Inactivation

\log_{10}\!\left(\frac{N_0}{N}\right) = k \, C^{\,n} \, t

Water TreatmentChick's 1908 first-order disinfection law with Watson's concentration exponent: the log reduction achieved rises with the disinfectant concentration raised to a dilution coefficient n, and linearly with contact time. When n = 1 it reduces to the familiar CT dose law. It is an idealisation — real curves show a shoulder at the start and a tail at the end.

Chiller Heat Rejection

Q_r = Q_e \, \mathrm{HRF}

Water TreatmentThermodynamicsHVAC & HydronicsHeat a chiller's tower has to reject: the evaporator load times the heat rejection factor that adds the compressor's own work to the load.

Chlorine Dose from a Weight of Product

C = \frac{m \, p}{V}

Water TreatmentChemistryGives the free chlorine concentration produced by dissolving a known weight of hypochlorite product of known strength in a known volume of water.

Chlorine Dose, Demand and Residual

D = C_{\text{demand}} + C_{\text{res}}

Water TreatmentChemistryThe fundamental chlorination balance: the dose applied equals the chlorine consumed by the water's demand plus the residual left for disinfection.

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.

Closed Loop Slug Dose Volume

V_p = \frac{C \, V_s \, \rho_w}{\rho_p}

Water TreatmentChemistryVolume of liquid product needed for a one-shot slug dose to hit a target ppm in a closed loop of known volume and product density.

Condensate Return Percentage

\%CR = \frac{S_c}{S} \times 100

Water TreatmentThermodynamicsPercentage of generated steam that comes back to the boiler house as condensate — the headline efficiency number for any steam plant.

Condenser Water Flow Rate

\dot{V} = \frac{\dot{Q} \cdot \mathrm{HRF}}{\rho_w c_w \, \Delta T}

HVAC & HydronicsFluid MechanicsWater TreatmentTower water flow needed to reject a chiller's load plus compressor heat, the physics behind the 3 gpm per ton at 10 °F rule of thumb.

Continuity Equation (A₁v₁ = A₂v₂)

A_1 v_1 = A_2 v_2

Fluid MechanicsWater TreatmentPhysicsFor incompressible flow, the same volume per second passes every cross-section of the pipe.

Cooling Tower Approach

A = T_c - T_{wb}

Water TreatmentThermodynamicsCooling tower approach: how many degrees the cold basin water sits above the ambient wet-bulb temperature, the true measure of tower performance.

Cooling Tower Drift Loss

D = \frac{d}{100} \, R

Water TreatmentFluid MechanicsDrift (windage) loss from a cooling tower as a percentage of the recirculation rate, the fraction of basin water blown out as droplets.

Cooling Tower Evaporation Rate

E = 0.001 \, R \, \Delta T

Water TreatmentFluid MechanicsThermodynamicsEvaporation loss from a cooling tower using the industry rule of 0.1% of recirculation per degree Fahrenheit of range.

Cooling Tower Heat Rejection

Q = 500 \, R \, \Delta T

Water TreatmentThermodynamicsFluid MechanicsHeat a cooling tower rejects from flow and range using the trade constant 500 = 8.34 lb/gal × 60 min/h × 1 BTU/(lb·°F).

Cooling Tower LSI at Cycles of Concentration

\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}\left(T_s,\ N\,\mathrm{Ca_m},\ N\,\mathrm{Alk_m},\ N\,\mathrm{TDS_m}\right)

Water TreatmentChemistryThe rigorous Langelier index of recirculating water: makeup calcium, alkalinity and TDS multiplied by the cycles, evaluated at the measured tower pH and the hottest surface temperature.

Cooling Tower Makeup Water Rate

M = E + B + D

Water TreatmentFluid MechanicsTotal makeup water a cooling tower needs: the sum of evaporation, blowdown to drain, and drift carried out in the air stream.

Cooling Tower Range

\Delta T = T_h - T_c

Water TreatmentThermodynamicsCooling tower range: the temperature drop the tower achieves between the hot water returning from the plant and the cold basin water.

Corrosion Rate from Coupon Weight Loss

P = \frac{m \, Y}{\rho \, A \, t}

Water TreatmentChemistryUniform corrosion rate as metal thickness lost per year, from a coupon's weight loss, density, exposed area and exposure time.

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.

CT Achieved (Disinfectant Residual × Contact Time)

\text{CT} = C \, T_{10}

Water TreatmentThe disinfection CT: the residual concentration a pathogen is exposed to multiplied by the time it is exposed for, returned in the regulatory unit of mg·min/L. This is the CT your plant ACHIEVED. Whether it is enough is a separate question, answered by your regulator's table for your pathogen, disinfectant, temperature and pH — never by this page.

Cycles of Concentration (COC = M/B)

\text{COC} = \frac{M}{B}

Water TreatmentFluid MechanicsCycles of concentration for a cooling tower from the makeup and blowdown flows — the master number every treatment program is built around.

Cycles of Concentration from Chloride

\text{COC} = \frac{\mathrm{Cl}_t}{\mathrm{Cl}_m}

Water TreatmentChemistryCycles of concentration from a chloride titration — the conservative tracer that neither precipitates nor gets dosed into the system.

Cycles of Concentration from Conductivity

\text{COC} = \frac{\sigma_t}{\sigma_m}

Water TreatmentChemistryCycles of concentration read straight off a conductivity meter: tower water conductivity divided by makeup water conductivity.

Cylinder Volume

V = \pi r^{2} h

GeometryWater TreatmentVolume of a right circular cylinder from its radius and height, using π ≈ 3.14159265.

D-Value (Decimal Reduction Time)

D = \frac{t}{\mathrm{LR}}

Water TreatmentThe decimal reduction time: how long at a fixed temperature it takes to reduce a population by one log — a factor of ten. It is the slope of the straight survival line on semi-log paper, and it is meaningless without the temperature it was measured at, which is why it is always written with one attached, as D₁₂₁.

Days Between Softener Regenerations

t = \frac{m_{\text{cap}}}{C \, Q}

Water TreatmentChemistryGives the run time a softener achieves between regenerations from its rated hardness capacity, the raw water hardness and the average water usage rate.

Degrees of Superheat

\Delta T_{sh} = T - T_s(p)

ThermodynamicsWater TreatmentHVAC & HydronicsHow many degrees a steam temperature sits above saturation at its own pressure, with the saturation temperature taken from IAPWS-IF97 Region 4.

Density

\rho = \tfrac{m}{V}

PhysicsChemistryWater TreatmentMass per unit volume.

Desuperheater Water Injection Rate

\dot{m}_w = \dot{m}_1 \, \frac{h_1 - h_2}{h_2 - h_w}

ThermodynamicsWater TreatmentHVAC & HydronicsSpray water a desuperheater needs to bring superheated steam down to a target enthalpy, straight from the mass and energy balance across the station.

Dilution Equation (C1V1 = C2V2)

C_1 V_1 = C_2 V_2

ChemistryWater TreatmentStates that concentration times volume is conserved when a solution is diluted, since the moles of solute do not change.

Dose Achieved from Chemical Added

C = \frac{m}{V \, \rho_w}

Water TreatmentChemistryConcentration reached in a system of known volume after adding a measured mass of chemical, at 8.34 lb of water per US gallon.

Effective Contact Time from Baffling Factor

T_{10} = \theta \times \mathrm{BF}

Water TreatmentThe effective contact time a basin actually delivers: its theoretical detention time multiplied by a baffling factor. T₁₀ is the time by which only 10% of a tracer has reached the outlet, so 90% of the water has had at least that much contact. This, and not the detention time, is the T in CT.

Energy Cost from a Utility Rate

C_e = E \, p_e

Water TreatmentThermodynamicsHVAC & HydronicsCost of the energy a system consumes: kilowatt-hours or fuel BTUs times the utility rate, for tower fans, pumps and boiler gas.

Equivalent Length of a Fitting

L_{eq} = \frac{K D}{f}

HVAC & HydronicsFluid MechanicsWater TreatmentConverts a fitting's K factor into the length of straight pipe that would cause the same friction loss at the same friction factor.

Equivalent Weight from Molar Mass and Valence

\mathrm{EW} = \frac{M}{z}

Water TreatmentChemistryGives the gram-equivalent weight of an ion or compound as its molar mass divided by the number of charges or replaceable hydrogens it carries.

F-Value (Equivalent Time at Reference Temperature)

F = t \times 10^{\,(T - T_{ref})/z}

Water TreatmentThe F-value: time spent at one temperature expressed as the equivalent time at a reference temperature. F₀ is the special case with the reference at 121.1 °C and z at 10 C°, the convention for spore-forming bacteria in thermal food processing. It is a bookkeeping conversion, and it lets the come-up, hold and cool-down of a whole cycle be added into one number.

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.

First-Order Chlorine Decay

C = C_0 \, e^{-k t}

Water TreatmentFree chlorine decays exponentially as it reacts with organics, biofilm and pipe wall. The bulk decay coefficient k is measured in a bottle test on your own water; the residual falls by the same fraction in every equal interval of time.

Flash Steam Mass Rate

\dot{m}_f = \frac{\%F}{100} \, \dot{m}_c

ThermodynamicsWater TreatmentFlash steam a condensate stream releases when it is let down to a lower pressure, from the flash percentage and the condensate rate through the trap.

Flash Steam Percentage

\%F = \frac{h_{f1} - h_{f2}}{h_{fg2}} \times 100

Water TreatmentThermodynamicsPercentage of hot condensate that flashes to steam when let down to a lower pressure, from the saturated liquid and latent enthalpies.

Flow-Weighted Blending Concentration

C = \frac{Q_1 C_1 + Q_2 C_2}{Q_1 + Q_2}

Water & WastewaterWater TreatmentChemistryThe concentration you land on when two streams of known flow and known strength join — each stream's mass rate added, then divided by the combined flow. It is the arithmetic behind blending a hard well against a soft surface source, and behind every question about what a side stream does to a plant's influent.

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.

Glycol Dilution

C_1 V_1 = C_2 V_2

Water TreatmentChemistryDilution equation for mixing glycol (or any concentrate) to a target strength.

Glycol Loop Heat Transfer (Capacity Derate)

\dot{Q} = \rho c \dot{V} \, \Delta T

HVAC & HydronicsThermodynamicsWater TreatmentHeat carried by a glycol loop using the actual mix density and specific heat, which is how the 500 constant derates for antifreeze.

Grains per Gallon ↔ ppm Hardness

H = 17.118\,G

Water TreatmentChemistryConverts water hardness between grains per US gallon and mg/L as CaCO₃ using the exact 17.118 mg/L per grain trade factor.

Hardness Load Removed per Regeneration

m = C \, V

Water TreatmentChemistryGives the mass of hardness as CaCO₃ a softener must remove between regenerations from the raw hardness and the volume of water treated.

Hardness Removal Efficiency and Leakage

R = \frac{C_{\text{in}} - C_{\text{out}}}{C_{\text{in}}}

Water TreatmentChemistryGives the fraction of hardness a softener or membrane removes from the inlet and outlet concentrations, with the remainder being leakage to service.

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.

Hazen–Williams Head Loss

h_f = \frac{10.67 \, L \, Q^{1.852}}{C^{1.852} D^{4.8704}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe waterworks head-loss equation in SI form, with Q in m³/s and D in m; the 10.67 constant is 4.727 when working in feet and cubic feet per second.

Hazen–Williams Velocity

v = 0.849 \, C \, R^{0.63} S^{0.54}

HVAC & HydronicsFluid MechanicsWater TreatmentMean water velocity from hydraulic radius and hydraulic gradient; the 0.849 SI constant becomes 1.318 when R is in feet and v in feet per second.

Holding Time Index

\text{HTI} = \frac{\ln 2 \; V}{B}

Water TreatmentChemistryHolding time index: the half-life of a chemical in a bled system, the time for half the treatment to wash out at a given blowdown 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.

Hydraulic Power (P = ρgQh)

P = \rho g Q h

Fluid MechanicsWater TreatmentPhysicsPower needed to lift a flow Q through a head h, with g = 9.80665 m/s².

Hydrostatic Pressure (P = ρgh)

P = \rho g h

MechanicsPhysicsWater TreatmentGauge pressure at depth h in a fluid of density ρ, using g = 9.80665 m/s².

Hypochlorite Product Mass from Available Chlorine

m_{\text{prod}} = \frac{m_{\mathrm{Cl}} \times 100\%}{p}

Water TreatmentChemistryConverts a required mass of available chlorine into the mass of hypochlorite product to weigh out, given the product's percent available chlorine.

Ion Concentration as CaCO₃ Equivalent

C_{\mathrm{CaCO_3}} = C_{\mathrm{ion}} \times \frac{50.04}{\mathrm{EW}}

Water TreatmentChemistryRestates any ion's concentration in the trade's common currency of CaCO₃ by scaling with the ratio of equivalent weights, 50.04 over the ion's own.

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.

Langelier Saturation Index (LSI)

\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}

Water TreatmentChemistryThe classic calcium-carbonate scaling index: measured pH minus the saturation pH, positive for scaling and negative for corrosive water.

Langelier Saturation Index from a Full Water Analysis

\mathrm{LSI} = \mathrm{pH} - \left(\mathrm{p}K_2 - \mathrm{p}K_{sp} + \mathrm{p[Ca^{2+}]} + \mathrm{p[HCO_3^-]} + 5\,\mathrm{p}f_m\right)

Water TreatmentChemistryLSI in one step from pH, temperature, calcium, total alkalinity and TDS, with temperature-dependent equilibria, activity correction and the alkalinity corrected for carbonate and hydroxide.

Larson–Skold Index

\mathrm{LS} = \dfrac{\frac{\mathrm{Cl}}{35.45} + \frac{\mathrm{SO_4}}{48.03}}{\frac{\mathrm{Alk}}{50.04}}

Water TreatmentChemistryRatio of aggressive chloride and sulphate equivalents to protective bicarbonate alkalinity, predicting pitting of mild steel in distribution water.

Lime Dose for Softening (as CaCO₃)

L = \mathrm{CO_2} + \mathrm{Alk} + \mathrm{Mg} + \mathrm{Ex}

Water TreatmentChemistryWater & WastewaterThe stoichiometric lime requirement for excess-lime softening, in mg/L as CaCO₃: every acid the lime has to neutralise before it can precipitate anything, plus the magnesium it must convert, plus the excess that makes the reaction finish in a real basin.

Log Inactivation from Counts

\mathrm{LR} = \log_{10}\!\left(\frac{N_0}{N}\right)

Water TreatmentThe log reduction actually measured: the base-10 logarithm of the count before a process divided by the count after. This is the reduction observed, not the reduction credited — regulatory credit is granted for a demonstrated CT or an approved process, not for a favourable pair of samples.

Log Reduction to Percent Kill

P = 1 - 10^{-\mathrm{LR}}

Water TreatmentThe conversion between a log reduction and a percent kill. They are the same statement: 1-log is 90%, 2-log is 99%, 3-log is 99.9%, 4-log is 99.99%. Percent enters and leaves as a percentage when you pick the % unit; internally it is a fraction between 0 and 1.

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.

Minor Loss from K Factor

h_L = K \, \frac{v^{2}}{2g}

HVAC & HydronicsFluid MechanicsWater TreatmentHead lost through a valve or fitting as a multiple of velocity head, with g = 9.80665 m/s² and K taken from a fitting table.

Mixing Two Solutions (C₁V₁ + C₂V₂ = C_f V_f)

C_f = \frac{C_1 V_1 + C_2 V_2}{V_1 + V_2}

ChemistryWater TreatmentGives the concentration you land on when two solutions of known strength and volume are poured together, by conserving the moles of solute and letting the volumes add.

Napier's Steam Leak Rate

\dot{m} = \frac{A \, P}{70}

ThermodynamicsWater TreatmentFluid MechanicsSteam lost through a hole, a blowing trap or a lifted relief valve by Napier's rule — pounds per second from square inches times psia, over 70.

Net Positive Suction Head Available (NPSHa)

NPSH_a = h_{atm} + h_s - h_f - h_{vp}

HVAC & HydronicsFluid MechanicsWater TreatmentAbsolute head available at the pump suction above the liquid's vapour pressure — the margin that keeps a pump from cavitating.

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.

Pasteurisation Units (PU)

\mathrm{PU} = t \times 10^{\,(T - T_{\mathrm{ref}})/7}

Brewing & FermentationWater TreatmentOne pasteurisation unit is one minute held at 60 °C, and every other temperature is converted to that currency by a factor of ten for each 7 C°. It is how a tunnel pasteuriser is specified, how a flash unit is verified, and the number a brewery's quality system is written around.

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.

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.

Percent Blowdown

\%B = \frac{B}{M} \times 100

Water TreatmentFluid MechanicsBlowdown expressed as a percentage of makeup water — the share of purchased water that goes straight to the sewer.

pH from Hydrogen Ion Concentration

\mathrm{pH} = -\log_{10}\,[\mathrm{H^+}]

ChemistryWater TreatmentExpresses acidity as the negative base-10 logarithm of the hydrogen ion concentration in mol/L.

Pipe Internal Volume

V = \frac{\pi D^{2}}{4} L

HVAC & HydronicsFluid MechanicsWater TreatmentThe liquid a run of pipe holds, from inside diameter and developed length — the starting point for every flush, fill or chemical dose.

Pipe Velocity from Flow and Diameter

v = \frac{4Q}{\pi D^{2}}

HVAC & HydronicsFluid MechanicsWater TreatmentAverage velocity in a full round pipe from volumetric flow and inside diameter — the first check on any piping design.

pOH from Hydroxide Ion Concentration

\mathrm{pOH} = -\log_{10}\,[\mathrm{OH^-}]

ChemistryWater TreatmentExpresses basicity as the negative base-10 logarithm of the hydroxide ion concentration in mol/L.

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.

Pounds of Active Chemical in a Tank

m = V \times \mathrm{SG} \times \rho_w \times p

Water TreatmentChemistryGives the mass of active chemical held in a storage tank from its volume, the solution's specific gravity and the percent active ingredient.

Predicted Cooling Tower LSI and Maximum Cycles, from the Makeup Analysis

\mathrm{LSI} = \mathrm{pH_{eq}} - \mathrm{pH_s}, \quad \mathrm{pH_{eq}} = 1.465\,\log_{10}(N\,\mathrm{Alk_m}) + 4.54

Water TreatmentChemistryProjects a tower's Langelier index from its makeup water and cycles, estimating tower pH from the cycled alkalinity, and solves for the cycles at which the index reaches a chosen limit.

Pressure Head (h = P/ρg)

h = \frac{P}{\rho g}

Fluid MechanicsWater TreatmentPhysicsConverts a pressure into the equivalent height of a fluid column, with g = 9.80665 m/s².

Product Dose from Active Strength

D_p = \frac{100 \, D_a}{A}

Water TreatmentChemistryConverts a required active-ingredient dose into the as-supplied product dose when the drum is only a given percent active.

Puckorius (Practical) Scaling Index

\mathrm{PSI} = 2\,\mathrm{pH_s} - \mathrm{pH_{eq}}, \quad \mathrm{pH_{eq}} = 1.465\,\log_{10}\mathrm{Alk} + 4.54

Water TreatmentChemistryA Ryznar variant that replaces measured pH with an equilibrium pH derived from alkalinity, giving a truer scaling call in poorly buffered cooling water.

Pump Affinity Law — Flow vs Impeller Diameter

\frac{Q_2}{Q_1} = \frac{D_2}{D_1}

HVAC & HydronicsFluid MechanicsWater TreatmentCapacity scales directly with trimmed impeller diameter at constant speed, the classic way to de-rate an oversized centrifugal pump permanently.

Pump Affinity Law — Flow vs Speed

\frac{Q_2}{Q_1} = \frac{N_2}{N_1}

HVAC & HydronicsFluid MechanicsWater TreatmentFirst affinity law: a centrifugal pump's capacity changes in direct proportion to shaft speed when the impeller diameter is unchanged.

Pump Affinity Law — Head vs Impeller Diameter

\frac{H_2}{H_1} = \left(\frac{D_2}{D_1}\right)^{2}

HVAC & HydronicsFluid MechanicsWater TreatmentDeveloped head falls with the square of the trimmed impeller diameter, so a 10% trim sheds about 19% of the head at constant speed.

Pump Affinity Law — Head vs Speed

\frac{H_2}{H_1} = \left(\frac{N_2}{N_1}\right)^{2}

HVAC & HydronicsFluid MechanicsWater TreatmentSecond affinity law: pump head varies with the square of shaft speed, so a 20% speed cut costs 36% of the developed head.

Pump Affinity Law — Power vs Speed

\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}

HVAC & HydronicsFluid MechanicsWater TreatmentThird affinity law: absorbed power varies with the cube of shaft speed — the single relation that pays for every variable-frequency drive.

Pump Brake Horsepower

BHP = \frac{Q \, H \, SG}{3960 \, \eta}

HVAC & HydronicsFluid MechanicsWater TreatmentShaft power the motor must actually supply; the 3960 constant assumes gpm, feet of head and horsepower, with efficiency as a fraction.

Pump Efficiency from Hydraulic and Shaft Power

\eta = \frac{P_{hyd}}{P_{shaft}}

HVAC & HydronicsFluid MechanicsWater TreatmentPump efficiency is the ratio of hydraulic power delivered to the liquid over the mechanical power absorbed at the shaft.

Pump Operating Point

Q_{op} = \sqrt{\frac{H_{0} - H_{st}}{k + c}}

HVAC & HydronicsFluid MechanicsWater TreatmentFlow at which a pump actually runs: the crossing of its own head curve, H = H₀ − cQ², with the system curve H = H_st + kQ².

Pump Specific Speed (Ns)

N_s = \frac{N \sqrt{Q}}{H^{0.75}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe dimensional index that classifies impeller type, evaluated in US units with N in rpm, Q in gpm and H in feet at the best efficiency point.

Pump System Curve

H = H_{st} + k Q^{2}

HVAC & HydronicsFluid MechanicsWater TreatmentHead a piping system demands at any flow: the static lift, which never changes, plus a friction term that grows as the square of the flow.

Pump Water Horsepower

WHP = \frac{Q \, H \, SG}{3960}

HVAC & HydronicsFluid MechanicsWater TreatmentUseful power delivered to the liquid; the 3960 divisor assumes US gallons per minute, feet of head and horsepower output.

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.

Ryznar Stability Index (RSI)

\mathrm{RSI} = 2\,\mathrm{pH_s} - \mathrm{pH}

Water TreatmentChemistryAn empirical scaling index scaled so that values below about 6 predict scale and values above about 7 predict corrosion in the same water.

Salt Dose per Regeneration

m_{\text{salt}} = D \, V

Water TreatmentChemistryGives the mass of sodium chloride a softener draws each regeneration from the resin volume and the programmed salt dosage per unit volume.

Saturation pH (pHs) for Langelier's Index

\mathrm{pH_s} = (9.3 + A + B) - (C + D)

Water TreatmentChemistryComputes the pH at which water is saturated with calcium carbonate from its TDS, temperature, calcium hardness and total alkalinity as CaCO₃.

Saturation pH (pHs), Rigorous — from the Carbonate Equilibria

\mathrm{pH_s} = \mathrm{p}K_2 - \mathrm{p}K_{sp} + \mathrm{p[Ca^{2+}]} + \mathrm{p[HCO_3^-]} + 5\,\mathrm{p}f_m

Water TreatmentChemistryThe pH at which water is exactly saturated with calcite, from temperature-dependent K₂ and Ksp and a Davies activity correction, not the four-term handbook shortcut.

Saturation Temperature and Pressure of Steam

T_{sat} = T_s(p_{sat}) \qquad p_{sat} = p_s(T_{sat})

ThermodynamicsWater TreatmentHVAC & HydronicsSaturation temperature from pressure and saturation pressure from temperature, on the IAPWS-IF97 Region 4 line the printed steam tables come from.

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.

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.

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.

Soda Ash Dose for Softening (as CaCO₃)

S = \mathrm{TH} - \mathrm{Alk}

Water TreatmentChemistryWater & WastewaterSoda ash makes up the difference between the hardness a water carries and the alkalinity it carries — the noncarbonate hardness, which lime cannot remove because no bicarbonate is paired with it. Expressed, as everything in softening is, in mg/L as CaCO₃.

Softener Resin Volume Required

V = \frac{m_{\text{cap}}}{q}

Water TreatmentChemistrySizes the ion-exchange resin bed from the hardness capacity required per regeneration and the resin's rated capacity per unit volume.

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.

Specific Gravity

SG = \frac{\rho}{\rho_{water}}

Fluid MechanicsWater TreatmentChemistryDensity expressed as a multiple of water's 1000 kg/m³.

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.

Steam Coil Condensate Load

\dot m = \frac{\dot Q}{h_{fg}}

HVAC & HydronicsThermodynamicsWater TreatmentSteam a coil condenses per unit time from its heat duty and the latent heat at the coil pressure — the same figure that sizes the trap and the condensate return.

Steam Quality from Enthalpy

x = \frac{h - h_f}{h_{fg}}

ThermodynamicsWater TreatmentDryness fraction of wet steam from its measured enthalpy, the saturated liquid enthalpy and the latent heat at the same pressure.

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.

System Volume from Turnover Time

V = R \, t

Water TreatmentFluid MechanicsSystem water volume estimated from the recirculation rate and the measured turnover time — the field method when no drawings exist.

TDS Estimated from Conductivity (TDS = k × EC)

\mathrm{TDS} = k \times \mathrm{EC}

Water TreatmentChemistryEstimates total dissolved solids in mg/L from a conductivity reading in µS/cm using an empirical factor k, typically 0.55 to 0.70 for natural waters.

Torricelli's Law (v = √(2gh))

v = \sqrt{2 g h}

Fluid MechanicsWater TreatmentPhysicsSpeed of fluid jetting from an opening a depth h below the free surface, with g = 9.80665 m/s².

Total Alkalinity as CaCO₃ from Species

\mathrm{TA} = 0.8202\,\mathrm{HCO_3} + 1.6679\,\mathrm{CO_3} + 2.9425\,\mathrm{OH}

Water TreatmentChemistrySums bicarbonate, carbonate and hydroxide reported as their own ions into one total alkalinity expressed as milligrams per litre of CaCO₃.

Total Dynamic Head

TDH = h_s + h_f + h_v

HVAC & HydronicsFluid MechanicsWater TreatmentThe head a pump must develop: static lift plus friction losses plus velocity head, all expressed in feet or metres of the pumped liquid.

Total Hardness as CaCO₃

\mathrm{TH} = 2.497\,\mathrm{Ca} + 4.118\,\mathrm{Mg}

Water TreatmentChemistryConverts a lab report's calcium and magnesium ion results into a single total hardness expressed as milligrams per litre of CaCO₃.

Total Water Treatment Program Cost

C = C_w + C_p + C_e

Water TreatmentChemistryFluid MechanicsTotal operating cost of a treated cooling system: the water and sewer bill, the chemical invoice and the energy bill added together.

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.

Valve Flow Coefficient (Cv)

Q = C_v \sqrt{\frac{\Delta P}{SG}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe US valve-sizing relation: Cv is the gpm of 60 °F water a valve passes at 1 psi drop, so Q is in gpm and ΔP in psi.

Valve Flow Coefficient (Kv, metric)

Q = K_v \sqrt{\frac{\Delta p}{SG}}

HVAC & HydronicsFluid MechanicsWater TreatmentThe metric valve-sizing relation: Kv is the m³/h of water a valve passes at 1 bar drop, related to Cv by Cv ≈ 1.156 Kv.

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.

Velocity Head (h = v²/2g)

h_v = \frac{v^{2}}{2g}

Fluid MechanicsWater TreatmentPhysicsThe kinetic energy of a flow expressed as an equivalent column height, with g = 9.80665 m/s².

Volume of Water Over a Period

V = Q \, t

Water TreatmentFluid MechanicsWater a flow delivers over a period — the step that turns a makeup or blowdown rate into the daily or annual volume a customer is billed for.

Volumetric Flow Rate (Q = Av)

Q = A v

Fluid MechanicsWater TreatmentPhysicsFlow through a duct or pipe: cross-sectional area times average flow velocity.

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.

Water Resistivity and Conductivity

\rho = \frac{1}{\sigma}

Water TreatmentChemistryRelates the resistivity and conductivity of ultrapure and deionized water as exact reciprocals, the pair of scales used on DI and RO polishing loops.

Weir Loading Rate (Weir Overflow Rate)

W_L = \frac{Q}{L_w}

Water & WastewaterWater TreatmentFluid MechanicsFlow divided by the total length of weir crest it leaves over — the loading on a clarifier's collection weirs, reported here in cubic metres per day per metre of weir, which is numerically a square metre per day.

Wet Steam Enthalpy from h_f and h_g

h = (1 - x) \, h_f + x \, h_g

ThermodynamicsWater TreatmentEnthalpy of a wet steam mixture as the mass-weighted blend of saturated water and dry saturated steam — the lever rule on the h_f and h_g columns.

z-Value (Thermal Resistance Constant)

z = \frac{T_2 - T_1}{\log_{10} D_1 - \log_{10} D_2}

Water TreatmentThe z-value: the temperature change that moves the D-value by a factor of ten. It is the slope of Bigelow's thermal death-time curve, and it is a temperature DIFFERENCE, not a temperature — 10 C° of z is an interval, and it is not 10 °C.