VWEA Operations Challenge Roanoke, VA July 14, 2016

Basic Math Functions

• Addition & Multiplication– Order does not matter

– 2 x 3 or 3 x 2

• Subtraction & Division– Must be done in the order given

– Different order = different answer

– 5-3 = 2, but 3-5 = -2

– 8/4= 2, but 4/8 = 0.5

Wastewater Math

• Involves complex calculations– Based on basic math concepts

8.34)]mg/L?MGD(?8.34)mg/L?MGD[(?

8.34MG)?MG(?mg/L? X

21%,,,,,

Multiple Step Calculations

• Eliminate parentheses then brackets– Work “inside – out”

8.34)6(57)(66)(4

3,150]5.8)[(6,500

250.24224

3,150][37,700

250.266

40,850

368.7250.2618.9

Basic Concepts

.5050%50100= =

DecimalFractionPercent

Percent(%)

• Parts per 100 • Used in

• Expressing plant process performance• Solids treatment calculations

• Unless otherwise stated, convert percent to decimal percent BEFORE using in most wastewater treatment calculations.

Percent to Decimal

• Divide percent (%) by 100

0.50100

5050%

Decimal to Percent

• Move the decimal 2 places to the right and change the decimal to a % sign.

5 0%

Calculator Use

• Select based on needs• Read instructions• Practice using functions• Write down what you are

going to do– Start with small numbers– Do a piece at a time

Remember…

• Exam regulations DO NOT allow:– programmable

calculators

– calculators that have alpha-numeric keyboards

Problem Solving is easy if you follow these steps

Step 1:Understand

the problem

Step 1 - Understand the Problem

• The operator removes 5,400 gallons of sludge. The sludge contains 275 gallons of solids. What is the percent solids?

Percent Solids = ?

-Read the problem carefully-Identify what to solve


Step 2:Decide how

you’re going to solve theproblem

• The operator removes 5,400 gallons of sludge. The sludge contains 275 gallons of solids. What is the percent solids?

Step 2 – How to Solve the Problem

Total = 5,400 Quantity =275

-Find the formula

Percent Solids = ?

Step 2 - How to solve the problem

Fill in the required data in the correct positions!

100xQuantity Total

QuantityMeasured%

-Write down the formula

Step 3:Solve The

Problem


Step 3 - Solve the problem

% Solids = 0.0509 X 100

% Solids = 5.09 or 5.1%

% Solids =275 gallons

5,400 gallonsX 100


Step 4:Double-Check

Your Work

Determining Percent

• Example– Sludge volume = 5,400 gal

– Solids volume = 275 gal

5.1%or%5.09Solids%

100xgal5,400

gal275Solids%

What a % Equals

PercentDecimalxTotalQuantityMeasured

• Given:– %

– Total

• What quantity does the % equal

What does it Equal?

• Example:– Sludge volume = 5,400 gal

– Percent Solids = 5.1%

Quantity = 5,400 gallonsx 0.051

= 275.4 gallons

Determining the Total

• Given– Percent

– What the percent equals

• Find the total

%Decimal

QuantityMeasuredTotal

What is the Total?

• Example:– 275 gallons of solids

– Percent Solids = 5.1%

Total, gallons =275.4 gallons

0.051

= 5,400 gallons

Circumference, Area, Volume

Plants are made up of tanks and channels

It will be necessary to calculate

14163Π

A constant Used for:

Circles Cylinders Cones Spheres

Needed when calculating Circumference Area Volume

Not This

(Pie)

Distance around an object

Expressed in linear units

Circumference & Perimeter

Circumference of a Circle

Diameter

DiameterxΠC

80 ft

ft251ft80x3.1416C

Circumference of a Circle Example

Perimeter of a Rectangle or Square

LW

)Wx2()Lx2(Perimeter

Length & width must be same units

Rectangle PerimeterExample

L =90 ft

W = 45 ft

ft270

ft452ft902Perimeter

The surface of an object

Measured in square units

Requires 2 dimensions

Area

Area of a Circle

DiameterDiameter4

ΠA

Diameter

0.7854

3.1416

Calculation Shortcut

For area & volume calculations

Area of a CircleExample

2ft9,499

ft110ft110x0.785A

110 ft

WxLA

Area –Rectangle/Square

Length & width must be same units!

LW

2ft5,175

ft45ft115A

Rectangle AreaExample

L=115 ft

W=45 ft

How much an object will hold

Measured in cubic units

Uses 3 dimensions

Volume

Volume of a Cylinder

depthxDiameterxDiameterx0.785

depthDiameterDiameter4

3.1416Volume

Cylinder VolumeExample

3

2

ft141,693

ft20ft95ft950.785

dxDx0.785Volume

Depth = 20 ft

Diameter =95 ft

Volume of aRectangular Tank

depthxWidthxLengthVolume

Length, width & depth must be same units!

W

L

d

Rectangle VolumeExample

3ft148,500

ft22ft45ft150

depthxWidthxLengthVolume

45 ft

150 ft

22 ft

Conversion Factors

• Type 1 - Conversion from one unit to another– Feet to inches

– Gallons to pounds

– Cubic feet to gallons

• Type 2 - Conversion to metric system– Gallons to liters

– Pounds to grams

Basic Conversions

• Conversion by multiplying or dividing by a conversion factor– Feet x 12 inches/foot

– Gallons x 8.34 lbs./gal

Reference Chart Handout

Back PageLeft Column to Right Column

Multiply

Right Column to Left ColumnDivide

Cubic Feet to Gallons

From chart:

Cubic Feet 7.48 Gallons

Gallons = Cubic Feet x 7.48 gal/ft3

Example

How many gallons of sludge can be pumped to a digester with 3,240 cubic feet of volume available?

3,240 ft3x 7.48 gal/ft3

=24,235 gallons

Type equation here.

Gallons to Cubic Feet

From chart:

Cubic Feet 7.48 Gallons

Cubic feet = Gallons7.48 gal/ft3

Example

• How many cubic feet of sludge are removed when 15,500 gallons are withdrawn?

Cubic feet = 15,500 gallons7.48 gal/ft3

= 2,072 ft3

Gallons to Pounds

From chart:

Gallon 8.34 Pounds

Pounds = Gallons x 8.34 lbs/gallon

Example

If 1,235 gallons of solids are removed from the primary settling tank, how many pounds of solids are removed?

Pounds = 1,235 gallons x 8.34 lbs/gallon

= 10,300 pounds

Pounds to gallons

From chart:

Gallon 8.34 Pounds

Gallons = pounds

8.34 pounds/gallon

Example

• How many gallons of water are required to fill a tank which holds 6,458 pounds of water?

Gallons = 6,458 lbs

8.34 pounds/gallons

= 774 gallons

Liters to Gallons

Gallons 3.785 Liters

From the chart:

Gallons = Liters

3.785 L/gallon

Example

Convert 231,500 liters to gallons

Gallons = 231,500 Liters3.785 L/gallon

= 61,163 gallons

Flow Rates

• Use conversion chart

• Million Gallons per Day (MGD)– Gallons per day (gpd)

– Gallons per hour (gph)

– Gallons per minute (gpm)

– Cubic feet per second (cfs)

– Liters per second (Lps)

– Cubic meters per day (m3/day)

cfs to MGD

From the table:

MGD 1.55 Cubic feet/second

MGD =Flow, CFS

1.55 cfs/MG

Example

The flow in a channel is 3.45 cfs. What is the flow rate in MGD?

MGD =3.45 cfs

1.55 cfs/MG

= 2.23 MGD

MGD to cfs

From the table:

MGD 1.55 Cubic feet/second

cfs = MGD x 1.55 cfs/MGD

Example

The flow entering the grit channel is 2.95 MGD. What is the flow rate in cubic feet per second?

2.95 MGD x 1.55 cfs/MGD

= 4.57 cfs

MGD to gpd

From the chart:

MGD 1,000,000 Gallons

gpd = MGD x 1,000,000 gallons/MG

Example

The flow meter reads 27.5 MGD. What is the flow in gallons per day?

gpd = 27.5 MGD x 1,000,000 gallons/MG

= 27,5000,000 gpd

gpd to MGD

From the chart:

MGD 1,000,000 Gallons

MGD =Flow, gpd

1,000,000 gallons/MGD

Example

The return pump flow meter reads 45, 700 gallons per day. What is the current flow rate in million gallons per day?

MGD =45,700 gpd

1,000,000 gallons/MGD

= 0.0457 MGD

MGD to gpm

• Two steps– Convert million gallons to gallons

(x 1,000,000)

– Convert days to minutes (/1,440)

gpm =MGD x 1,000,000 gallons/MG

1,440 minutes per day

Example

The current pump rate is 2.65 MGD. What is the flow rate in gallons per minute?

Step 1:Million gallons per day must be converted to gallons per day

Flow, gpd = 2.65 MGD x 1,000,000 = 2,650,000 gpd

Example

Flow, gpm =2,650,000 gallons per day

1,440 minutes per day

= 1,841 gallons per minute

Step 2:Divide gallons per day by 1,440 minutes/day

gpm to MGD

• Two steps– Convert gallons/minute to gallons/day

(x 1,440)

– Convert gallons to million gallons (/1,000,000)

MGD =gpm x 1,440 minutes per day

1,000,000 gal/MG

Example

The current flow is 1,259 gpm. What is the flow in million gallons per day?

MGD =1,259 gpm x 1,440 minutes per day

1,000,000 gal/MG

= 1.81 MGD

Complex Conversions

• Using weight, concentration & flow

• Two or more measurements

• One or more conversion factors

• Can be rearranged to solve for any of the measured items

Davidson Pie• Think “inside the circle”

lbs./ lbs. per day

8.34

lbs/gallon

Vol./MGD mg/L

Pounds

• Numbers in bottom half are multiplied

Pounds

8.34

lbs/gallon

Volume, MG mg/L

Pounds Example

• Volume = 0.9 MG

• MLSS= 2,580 mg/L

• Pounds = ?

? pounds

8.34 lbs/gallon

0.9 MG 2,580mg/L

19,366 pounds

Pounds = 2,580 mg/L x 0.90 MG x 8.34= 19,366 lbs

Pounds/day

• Numbers in bottom half are multiplied

lbs per day

8.34 lbs/gallon

MGD mg/L

Pounds/day Example

• Flow = 6 MGD

• Inf. TSS = 260 mg/L

• lbs./day = ?

? lbs per day

8.34 lbs/gallon

MGD mg/L6 MGD 260mg/L

13,010 lbs/day

6.0 MGD x 8.34 lbs./gallon x 260 mg/L=13,010.4 lbs/day

MG or MGD or mg/L

• If lbs./lbs. per day is known

• Multiply bottom numbers together

• Divide into top half

lbs./lbs. per day

8.34 lbs/gallon

MG OR MGD mg/L

Pounds to mg/L

• Quantity, lbs. = 3,529

• Volume = 0.25

• MLSS, mg/L= ?

lbs

8.34

lbs./gallon

MGD ? mg/L0.25 MG 1,693mg/L

3,529 Pounds

Conc., mg/L =3,529 lbs

0.25 MG x 8.34= 1,693 mg/L

Pounds/day to MGD

• Inf. BOD = 186 mg/L

• BOD, lbs/day = 8,956

• Flow = ? MGD

lbs per day

8.34 lbs/gallon

? MGD mg/L186mg/L

8,956 lbs/day

5.77MGD

8,956 lbs/day186 mg/L x 8.34

= 5.77 MGD

• Read the question

• Choose the right formula

• Make necessary conversions

• Double check work

• And relax…

In Review

VWEA Operations Challenge Roanoke, VA July 14, 2016

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Transcript of VWEA Operations Challenge Roanoke, VA July 14, 2016