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
3
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
5
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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