Wastewater Treatment Mathematical Formulas - Tennessee

Wastewater Treatment Mathematical Formulas

Second Edition

Fleming Training Center Murfreesboro, TN

Updated January 13, 2011

Index

Activated Sludge .................................................................... 11, 12 Area ....................................................................................... 4 Chlorination ............................................................................ 9 Conversion Factors ................................................................ 1, 2 Converting lbs/gal to mg/mL................................................... 2 Depth/Diameter Table ............................................................ 18 Dosage, general ..................................................................... 5 Flow ....................................................................................... 4 Flow Conversions Chart ......................................................... 3 Flow, Partially Full Pipe .......................................................... 18 Laboratory .............................................................................. 15, 16, 17 Metric Conversion .................................................................. 2 Pounds Formulas ................................................................... 5 Power ..................................................................................... 5 Preliminary Treatment ............................................................ 7 Pumps .................................................................................... 6, 7 Sedimentation ........................................................................ 8 Solution Preparation............................................................... 7 Sludge, Dewatering and Disposal .......................................... 14 Sludge, Digestion ................................................................... 12, 13 Sludge, Production and Thickening........................................ 13 Temperature........................................................................... 2 and 17 Trickling Filters ....................................................................... 9 Volume ................................................................................... 4 Waste Treatment Ponds......................................................... 14, 15

Wastewater Treatment Math Formulas

Conversion Factors

Length

1 foot (ft) ................................................... 12 inches (in)

1 yard (yd) ....................................................... 3 feet (ft)

1 mile (mi)................................................. 5,280 feet (ft)

Area

1 acre (ac) ................................. 43,560 square feet (ft2)

1 acre .............................................. 0.405 Hectare (Ha)

1 Hectare ....................................................... 2.47 acres 1 square foot (ft2) ....................... 144 square inches (in2)

Volume

1 cubic foot (ft3) .................................. 7.48 gallons (gal) 1 yd3 ...................................................................... 27 ft3 1 gallon ........................................ 231 cubic inches (in3) 1 gallon ........................................................... 0.1337 ft3

1 gallon .................................................. 3.785 Liters (L)

1 gallon ............................ 0.000001 Million Gallon (MG)

1 liter...............................................1,000 milliliters (mL)

1 liter..............................................................0.2642 gal 1 acre/foot (ac-ft) ..........................43,560 cubic feet (ft3)

1 acre-foot (ac-ft) ....................... 325,828.8 gallons (gal)

Flow

1 cubic foot per second (ft3/sec) .................. 449 gal/min 1 cubic foot per second (ft3/sec) ................ 0.6463 MGD

1 gal/min .................................................. 0.00144 MGD

Weight and Mass

1 gallon of water ................................. 8.34 pounds (lbs) 1 cubic foot of water (ft3).................................... 62.4 lbs

1 pound (lb) ......................................... 453.6 grams (g)

1 kilogram (kg)...................................... 1,000 grams (g)

1 kilogram ..................................................... 2.2 pounds

1 gram ......................................... 1,000 milligrams (mg)

1% ............................. 10,000 milligrams per liter (mg/L)

1 mg/L ..................................... 0.0584 grains per gallon

1 grain per gallon........................................17.118 mg/L

Wastewater Treatment Formulas

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Fleming Training Center Pressure and Head

1 foot of head.............. 0.433 pounds per square in (psi) 1 pound per square inch (psi) ..............2.31 feet of head Temperature Conversions C ............................................................ 0.556 (F-32) F...............................................................1.8(C) + 32

Converting lbs/gal to mg/mL

lbs

453.6

gram

1000

mg

gal

3.785

Liter

1000

mL

To use this diagram: First, find the box that coincides with the beginning unit (i.e. mg/mL). Then find the box that coincides with the desired ending units (i.e. lbs/gal). The numbers between the starting point and ending point are the conversion factors. When moving from a smaller box to a larger box, multiply by the factor between them. When moving from a larger box to a smaller box, divide by the factor between them. For the final number, divide the top number by the bottom number.

Metric Conversions

Primary Unit

mega . . . . kilo hecto deka no deci centi

(M) 1,000,000

(k) (h) (da) prefix (d)

(c)

1,000 100 10

1

1/10

1/100

meter ? linear measurement liter ? volume measurement gram ? weight measurement

milli . . . . micro

(m) 1/1,000

(?) 1/1,000,000

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Wastewater Treatment Formulas

Wastewater Treatment Math Formulas

Flow Conversions

cfm

cfs

60

1440

cfd

7.48

gps 60

7.48 gpm

7.48 MGD

1,000,000

gpd 1440

8.34

8.34

8.34

lb/sec

60

lb/min

1440

lb/day

cfs = cfm = cfd =

cubic feet per second cubic feet per minute cubic feet per day

gps = gpm = gpd =

gallons per second gallons per minute gallons per day

To use this diagram: First, find the box that coincides with the beginning units (i.e. gpm). Then, find the box that coincides with the desired ending units (i.e. cfs). The numbers between the starting point and ending point are the conversion factors. When moving from a smaller box to a larger box, multiply by the factor between them. When moving from a larger box to a smaller box, divide by the factor between them.

Wastewater Treatment Formulas

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Rectangle: Circle:

Fleming Training Center

Area

Area, ft2 (Length, ft)(Width, ft) Area, ft2 (0.785)(Diameter, ft)2

Segment of a Circle, ft2

Volume, ft 3 1.333 (Height, ft)2

Diameter, ft 0.608

Height, ft

Rectangle, ft3:

Volume

Volume, ft3 (Length, ft)(Width, ft)(Depth, ft)

Cylinder, ft3:

Volume, ft3 (0.785)(Diameter, ft)2 (Depth or Length, ft)

Cone, ft3:

Volume, ft3 (0.785) (Diameter, ft)2 (Depth, ft) 3

3 Segment of Cylinder, ft :

Volume, ft 3

1.333

(Height)2

Diameter, ft Height, ft

0 .608

(Length,

ft)

3 Wedge, ft :

Volume,

ft 3

(Length,

ft)(Width, 2

ft)(Depth,

ft)

Volume, gallons

=

Volume, gal (Volume, ft3)(7.48gal/ft3)

Flow

Q AV OR Q (Area) (Velocity)

Q (Channel), ft3 / sec (Width, ft)(Depth, ft)(Velocity, ft/sec)

Q (Pipeline), ft3 / sec (0.785)(Diameter, ft)2 (Velocity, ft/sec)

Partially Full Pipe =

Flow,

ft

3

/sec

1.333

(Height)2

Diameter, ft Height, ft

0.608

(Velocity,

ft/sec)

Velocity,

ft/sec

Flow, ft3 /sec (0.785) (Diameter,

ft)2

Velocity, ft/sec Distance, ft Time, sec

Average Daily Flow, MGD Sum of All Daily Flows, MGD Number of Daily Flows

Annual Average Daily Flow, MGD Sum of All Monthly Average Daily Flows, MGD Number of Monthly Average Daily Flows

Daily Flow, gal/day/capita

Water Used, gal/day

Total Number of People Served

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Wastewater Treatment Formulas

Wastewater Treatment Math Formulas

Dosage

Dosage, mg/L Chemical Feed Rate, lbs/day (Flow, MGD) (8.34 lbs/gal)

Dosage, mg/L (Chemical Feed Rate, lbs/day) (Chemical Purity, %, expressed as a decimal) (Flow, MGD) (8.34 lbs/gal)

Dosage, mg/L (Feed Rate, grams/min) (1,000 mg/gram) (Flow, gal/min) (3.785 L/gal)

Pounds

Chemical Fed, lbs (Dose, mg/L) (Volume, MG) (8.34 lbs/gal)

Chemical Fed, lbs (Dose, mg/L) (Volume, MG) (8.34 lbs/gal) Chemical Purity, %, expressed as a decimal

Feed Rate, lbs/day (Dose, mg/L) (Flow, MGD) (8.34 lbs/gal)

Feed Rate, lbs/day (Dose, mg/L) (Flow, MGD) (8.34 lbs/gal) Chemical Purity, %, expressed as a decimal

Feed Rate, lbs/day (Concentration, mg/mL)(Vol ume Pumped, mL) (1,440 min/day) (Time Pumped, min) (1,000 mg/g) (453.6 g/lb)

Loading, lbs/day (Concentration, mg/L) (Flow, MGD) (8.34 lbs/gal)

Power

1 Horsepower = 746 watts or 0.746 kilowatts Power, watts (Volts) (Amps)

Amps, single - phase

(746 watts/HP) (Horsepower)

(Volts) (Efficiency, %, as decimal) (Power Factor)

Amps, three - phase

(746 watts/HP) (Horsepower)

(1.732)(Volts) (Efficiency, %, as decimal) (Power Factor)

Horsepower (Volts )(Amps) (746 watts/HP)

Kilowatts, single - phase (Volts) (Amps) (Power Factor) 1,000 watts/kilowatt

Kilowatts, three - phase (Volts) (Amps) (Power Factor) (1.732) 1,000 watts/kilowatt

Power Factor Watts (Volts)(Amps)

Wastewater Treatment Formulas

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MHP

Fleming Training Center

Pumps

Motor

BHP

Pump

WHP

% motor eff

Pumping Rate, gal/min Volume, gal Time, min

% pump eff

Pumping Rate, gal/min (Length, ft)(Width, ft)(Depth, ft)(7.48 gal/ ft3) Time, min

Pumping Rate, gal/min (0.785)(Diameter, ft)2 (Depth, ft)(7.48 gal/ ft3) Time, min

Time to Fill, min Tank Volume, gal Flow Rate, gal/min

Water HP (Flow, gal/min) (Head, ft) 3960

Brake HP

(Flow, gal/min) (Head, ft)

(3960) (Pump Efficiency, %, expressed as a decimal)

Motor HP

(Flow, gal/min) (Head, ft)

(3960) (Pump Eff., %, expressed as decimal) (Motor Eff., %,expressed as decimal)

Brake HP

(Water Horsepower)

Pump Efficiency, %, expressed as a decimal

Motor HP

(Brake Horsepower)

Motor Efficiency, %, expressed as a decimal

Motor Efficiency, % Brake Horsepower X 100% Motor Horsepower

Pump Efficiency, % Water Horsepower X 100% Brake Horsepower

Efficiency, % Horsepower Output X 100% Horsepower Supplied

Overall Efficiency, % Water Horsepower X 100% Motor Horsepower

Wire - to - Water Efficiency, % (Pump Eff., %, as decimal) (Motor Eff., %, as decimal) (100%)

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Wastewater Treatment Formulas

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