Basic Math Midterm ReviewBasic Math Midterm Review

Math for Water TechnologyMTH 082-2

Math for Water TechnologyMTH 082-2

RULES FOR MIDTERMRULES FOR MIDTERM1.DRAW AND LABEL DIAGRAM

2.LIST FORMULAS

3 SOLVE EACH FORMULA INDIVIDUALLY

4. ISOLATE THE PARAMETERS NECESSARY

5. USE YOUR UNITS TO GUIDE YOU

6. SOLVE THE PROBLEM

1.DRAW AND LABEL DIAGRAM

2.LIST FORMULAS

3 SOLVE EACH FORMULA INDIVIDUALLY

4. ISOLATE THE PARAMETERS NECESSARY

5. USE YOUR UNITS TO GUIDE YOU

6. SOLVE THE PROBLEM

Chlorine ConcentrationsHypochlorite or Available Purity = DIVIDE

1.Sodium hypochlorite 5 to 15% available chlorine

2. Calcium hypochlorite (HTH) 65-70% available chlorine

3. Chlorine gas100% available chlorine or

100% active chlorine

1.Sodium hypochlorite 5 to 15% available chlorine

2. Calcium hypochlorite (HTH) 65-70% available chlorine

3. Chlorine gas100% available chlorine or

100% active chlorine

% Dry Strength of Solution1. Dry chlorine % Chlorine Strength= Chlorine (lbs) X 100

Solution(lbs)

1. Dry chlorine % Chlorine Strength= Chlorine (lbs) X 100

Solution(lbs)

2. Dry chlorine % Chlorine Strength= Chlorine (lbs) X 100

Water, Lbs + Chlorine(lbs)

2. Dry chlorine % Chlorine Strength= Chlorine (lbs) X 100

Water, Lbs + Chlorine(lbs)

3. Dry chlorine % Chlorine Strength= Hypo(lbs)(% available Cl) X

100 100 Water, Lbs+ hypo(lbs) (% available Cl)

100

3. Dry chlorine % Chlorine Strength= Hypo(lbs)(% available Cl) X

100 100 Water, Lbs+ hypo(lbs) (% available Cl)

100

Dry Hypochlorite Feed Rate

1.Hypochlorite (lb/day)=lbs/day chlorine % available

chlorine100

2. Hypochlorite (lb/day)= (mg/L chlorine)(MGD)(8.34) %strength hypochl

100

3. Hypochlorite (lbs)= (mg/L chlorine)(MG tank Vol)(8.34) %strength hypochl

100

1.Hypochlorite (lb/day)=lbs/day chlorine % available

chlorine100

2. Hypochlorite (lb/day)= (mg/L chlorine)(MGD)(8.34) %strength hypochl

100

3. Hypochlorite (lbs)= (mg/L chlorine)(MG tank Vol)(8.34) %strength hypochl

100

% Liquid Strength of Solution1. Liquid chlorineLbs Cl in liq. hypo= Lbs of chlorine in hypochlorite solution1. Liquid chlorineLbs Cl in liq. hypo= Lbs of chlorine in hypochlorite solution

2. Liquid chlorine (liq. Hypo lbs)(%Strength liq. Hyo) = (hypo Sol lbs) (% Strength liq. hyp)

100 100

2. Liquid chlorine (liq. Hypo lbs)(%Strength liq. Hyo) = (hypo Sol lbs) (% Strength liq. hyp)

100 100

3. Liquid chlorine(liq. Hypo gal)(8.34)(%Strength liq. Hyo)=(hypo Sol gal)(8.34)(%Strength liq. Hyp)

100 100

3. Liquid chlorine(liq. Hypo gal)(8.34)(%Strength liq. Hyo)=(hypo Sol gal)(8.34)(%Strength liq. Hyp)

100 100

Lbs/dayWhen do you multiply?

Available to Active (multiply)

Twenty 20 pounds of 50% available chlorine equals

10 lbs pounds of 100% active chlorine?Twenty 20 pounds of 50% available chlorine equals

10 lbs pounds of 100% active chlorine?

20 lbs20 lbs

10 lbs10 lbs

Active is pureActive is pureAvailable is unpureAvailable is unpure

20 lbs (0.50)= 10 lbs20 lbs (0.50)= 10 lbs

Lbs/dayWhen do you divide?

Active to Available

Forty 40 pounds of 100% active chlorine (chlorine gas) has the same disinfection power as 61 lbs

pounds of 65% available HTH chlorine?

Forty 40 pounds of 100% active chlorine (chlorine gas) has the same disinfection power as 61 lbs

pounds of 65% available HTH chlorine?40 lbs40 lbs 61 lbs61 lbs

Active is pureActive is pure Available is unpureAvailable is unpure

40 lbs = 61 lbs(.65)

Lbs/dayWhen do you multiply?

Available to Active (multiply)HW #4 Problem 3

Twenty two 22 pounds of 65% available chlorine equals 14.3 lbs pounds of 100% active chlorine!

HW #4 Problem 3

Twenty two 22 pounds of 65% available chlorine equals 14.3 lbs pounds of 100% active chlorine!

22 lbs22 lbs

14.3 lbs14.3 lbs

Active is pureActive is pureAvailable is unpureAvailable is unpure

22 lbs (0.65)= 14.3 lbs22 lbs (0.65)= 14.3 lbs

Lbs/dayWhen do you multiply?

Available to Available (multiply)HW #3 Problem 3

How many pounds of available chlorine are in 2 pounds of 65% powdered dry (available) chlorine?

HW #3 Problem 3

How many pounds of available chlorine are in 2 pounds of 65% powdered dry (available) chlorine?

2 lbs of 65% ava2 lbs of 65% ava

1.3 lbs is available1.3 lbs is available

Available is unpureAvailable is unpure

Available is unpureAvailable is unpure

2 lbs (0.65)= 1.3 lbs2 lbs (0.65)= 1.3 lbs

Lbs/dayWhen do you divide?

When do you multiply?PURITY IS THE KEY!!!!!

Lbs/dayWhen do you divide?

When do you multiply?PURITY IS THE KEY!!!!!

If you have a certain amount of <100% chlorine (available) and you want to know how much pure (active chlorine) that is you multiply!!!! (Need less of a more pure substance)

If you have a certain amount of <100% chlorine (available) and you want to know how much pure (active chlorine) that is you multiply!!!! (Need less of a more pure substance)

When using hypochlorite, more lbs/day must be used because it is not pure! Hypochlorite is “available” chlorine

When using hypochlorite, more lbs/day must be used because it is not pure! Hypochlorite is “available” chlorine

If you have a certain # of lbs of 100% pure chlorine (active) and what you need is a certain percentage (available) then you divide (its not pure so you will need more of it!)

If you have a certain # of lbs of 100% pure chlorine (active) and what you need is a certain percentage (available) then you divide (its not pure so you will need more of it!)

Chlorine in lbs DOSE in a tank!

Conversion Volume

)/34.8)()(/(

Conc

lbsgallbsMGLmg

lbs

lbsgallbsMGLmg

2.29 x

)/34.8)(07.0)(/50(

1. Wells are disinfected2. Tanks and reservoirs get chlorinated3. Pipelines get chlorinated after repair or installation

1. Wells are disinfected2. Tanks and reservoirs get chlorinated3. Pipelines get chlorinated after repair or installationExample 5: A storage tank needs to be disinfected with a 50 mg/L chlorine solution. If the tank holds 70,000 gallons, how many lbs of chlorine gas will be needed?

Example 5: A storage tank needs to be disinfected with a 50 mg/L chlorine solution. If the tank holds 70,000 gallons, how many lbs of chlorine gas will be needed?

Step 1 Chlorine mg/L to lbs/day formula

Hypochlorite DOSAGE

/177)/34.8)(85.0)(/25( chlorinedaylbsgallbsMGDLmg

1. Calculate lbs/day chlorine2. Calculate lbs/day hypochlorite needed by dividing the

lbs/day chlorine by the percent available chlorine

1. Calculate lbs/day chlorine2. Calculate lbs/day hypochlorite needed by dividing the

lbs/day chlorine by the percent available chlorineExample 6: A wastewater flow of 85,000 gpd requires a chlorine dose of 25 mg/L. If sodium hypochlorite (15% available chlorine) is used, how many lbs/day of sodium hypochlorite are required? How many gal/day is this?

Example 6: A wastewater flow of 85,000 gpd requires a chlorine dose of 25 mg/L. If sodium hypochlorite (15% available chlorine) is used, how many lbs/day of sodium hypochlorite are required? How many gal/day is this?

Conversion Flow

/)/34.8)()(/(

Conc

daylbsgallbsMGDLmg

Step 2 Calculate lbs/day sodium hypochlorite

/1180 .100

15 /177(

2

2 tehypochloridaylbsClAvail

Cldaylbs

(1180 lbs/d)/(8.34 lbs/gal)=141 gal/day

sodium hypochlorite

Determining Cl Concentrations from Hypochlorite dosage

1. Disinfection requires 280 lb/day chlorine. If CaOCl (65% available Cl) is used how many lbs day are required1. Disinfection requires 280 lb/day chlorine. If CaOCl (65% available Cl) is used how many lbs day are required

(%concentration)(X lb/day)= total lbs/day required

Rearrange:(X lb /day) = Total lbs/d = (280 lbs) = 430.77 lb/d CaOCL

% concentration (.65)

(%concentration)(X lb/day)= total lbs/day required

Rearrange:(X lb /day) = Total lbs/d = (280 lbs) = 430.77 lb/d CaOCL

% concentration (.65)

Solutions with Specific Gravity

1. How many pounds of available chlorine are in 5 gallons of 12% hypochlorite solution if its specific gravity is 1.19?

1. How many pounds of available chlorine are in 5 gallons of 12% hypochlorite solution if its specific gravity is 1.19?

Lb=(% concentration) X (Specific gravity) X (lb/gal) X (gal)Lb= (.12) X (1.19) X (8.34 lb/gal) X (5 gal)

Lb=5.95 lb

Lb=(% concentration) X (Specific gravity) X (lb/gal) X (gal)Lb= (.12) X (1.19) X (8.34 lb/gal) X (5 gal)

Lb=5.95 lb

Calcium hypochlorite, gal= (lb CaOCl2 @ 100%)/(8.34 lb/gal)(CaOCl2 %)Calcium hypochlorite, gal= (lb CaOCl2 @ 100%)/(8.34 lb/gal)(CaOCl2 %)

Calcium hypochlorite, lbs= (gal CaOCl2)(8.34 lb/gal)(62.5%)/(100%)Calcium hypochlorite, lbs= (gal CaOCl2)(8.34 lb/gal)(62.5%)/(100%)

Hypochlorite Solutionsis disinfected with 62.5% calcium hypochlorite solution,

If 3.03 gal of CaOCl2 were used, what must have been the dosage of the calcium hypochlorite? Assume the calcium hypochlorite weighs 8.34 lb/gal. Get answer in (lbs) to solve for dosage in lbs formula!

is disinfected with 62.5% calcium hypochlorite solution, If 3.03 gal of CaOCl2 were used, what must have been the dosage of the calcium hypochlorite? Assume the calcium hypochlorite weighs 8.34 lb/gal. Get answer in (lbs) to solve for dosage in lbs formula!

Calcium hypochlorite, lbs= (gal CaOCl2)(8.34 lb/gal)( % Available) (100%)

Calcium hypochlorite, lbs= (gal CaOCl2)(8.34 lb/gal)( % Available) (100%)

Calcium hypochlorite, lbs= 15.79 lbs Calcium hypochlorite, lbs= 15.79 lbs

Calcium hypochlorite, lbs= (3.03 gal CaOCl2)(8.34 lb/gal)(.625)

Calcium hypochlorite, lbs= (3.03 gal CaOCl2)(8.34 lb/gal)(.625)

Solve lbs formula  Number of lb=(MG)(Dosage)(8.34 lb/gal) 

Solve lbs formula  Number of lb=(MG)(Dosage)(8.34 lb/gal) 

Dosage mg/L CaOCl2=15.79 lbs CaOCl2/(0.038MG)(8.34 lb/gal)Dosage mg/L CaOCl2=15.79 lbs CaOCl2/(0.038MG)(8.34 lb/gal)

Calcium Hypochlorite Solutions

Midterm 3. storage tank requires disinfection with a 65% calcium hypochlorite solution.  How many gallons of hypochlorite solution are required if the desired dose is 50.0 mg/L.  Assume the calcium hypochlorite solution weighs 10.21 lb/gal.?  

Midterm 3. storage tank requires disinfection with a 65% calcium hypochlorite solution.  How many gallons of hypochlorite solution are required if the desired dose is 50.0 mg/L.  Assume the calcium hypochlorite solution weighs 10.21 lb/gal.?  

Calcium hypochlorite, gal= (lb CaOCl2 @ 100%) (10.21 lb/gal)(CaOCl2 % available)

Calcium hypochlorite, gal= (51.7 lb CaOCl2) = 7.79 gal (10.21 lb/gal)(.65)

Calcium hypochlorite, gal= (lb CaOCl2 @ 100%) (10.21 lb/gal)(CaOCl2 % available)

Calcium hypochlorite, gal= (51.7 lb CaOCl2) = 7.79 gal (10.21 lb/gal)(.65)

Specific Gravity, LBS, Gallons, Solution Strength

))(/34.8( chlorine)strength )( . chlorine (%

)(

))( )( )(/34.8(

)( . chlorine %

) )(/34.8(chlorine)strenght (full) . chlorine (%

)(

))(g )(/34.8)( )( . chlorine (%

gallonsgallbfullstrengthsol

lbsGravitySpecific

gallonsGravitySpecificchlorinestrengthfullgallb

lbsStrengthSol

GravitySpecificgallbstrengthsol

lbsGallons

galravityspecificgallbschlorinestrengthfullstrengthsolLbs

Problem #1

1. Determine the chlorinator setting (lbs/day) needed to treat a flow of 3.2 MGD with a chlorine dose of 1.7 mg/L (5 pts).

1. Determine the chlorinator setting (lbs/day) needed to treat a flow of 3.2 MGD with a chlorine dose of 1.7 mg/L (5 pts).

Cllbs/day 45lbs/day

lbs/gal) MGD)(8.34 mg/L)(3.2 (1.7lbs/day

)/34.8)()(/(/

gallbsMGDLmgdaylbs

Problem #2

2. The chorine demand was calculated to be 11 lb/day, and the residual was measured at 0.5 mg/L. What was the chlorine dose (lbs) that day, if the flow was 1.2 MGD?

2. The chorine demand was calculated to be 11 lb/day, and the residual was measured at 0.5 mg/L. What was the chlorine dose (lbs) that day, if the flow was 1.2 MGD?

Cllbs/day 5lbs/day

lbs/gal) MGD)(8.34 mg/L)(1.2 (0.5lbs/day

)/34.8)()(/(/

gallbsMGDLmgdaylbs

daylbsdaylbsDoseCl

daylbsdaylbsdaylbsDoseCl

daylbssidualCldaylbsDemandCldaylbsDoseCl

/16)/(

/11/5)/(

)/(Re)/()/( .1

2

2

222

Problem #3

3. How many gallons of 15% liquid chorine (s.g. = 1.2) would be required to dose a circular tank to a 50 mg/L concentration? The tank diameter is 25 ft. and the water depth in the tank is 5 ft.

3. How many gallons of 15% liquid chorine (s.g. = 1.2) would be required to dose a circular tank to a 50 mg/L concentration? The tank diameter is 25 ft. and the water depth in the tank is 5 ft.

lbsweightchlorine

gallbsweightchlorine

gallbsweightchlorine

6.7lbs) (

)/34.8( MG) (.018349 mg/L) 50(lbs) (

)/34.8( (MG))container of (volume L)dosage(mg/lbs) (

? Gallons? Gallons

1.2 SG15% OCl1.2 SG15% OCl

25 ft

5 ft

•Volume= 0.785(diameter2)(depth)

•Volume= 0.785(25ft)2(5 ft)

•Volume=2453ft3

•Conversion= 2453 ft3 (7.48 gal/1ft3)

•Conversion=18349 gallons

•Conversion=.018349 MG

•Volume= 0.785(diameter2)(depth)

•Volume= 0.785(25ft)2(5 ft)

•Volume=2453ft3

•Conversion= 2453 ft3 (7.48 gal/1ft3)

•Conversion=18349 gallons

•Conversion=.018349 MG

gallonsgallb

chlorinelbsGallons

GravitySpecificgallbstrengthsol

lbsGallons

06.5)2.1)(/34.8)(15(.

6.7

) )(/34.8)( . chlorine (%

)(

Problem #4

4. A barrel contains 30 gallons of 12% liquid hypochlorite at a specific gravity of 1.19. How many pounds of dry HTH (65% active hypochlorite) would be needed to replace the chlorine in the barrel?

4. A barrel contains 30 gallons of 12% liquid hypochlorite at a specific gravity of 1.19. How many pounds of dry HTH (65% active hypochlorite) would be needed to replace the chlorine in the barrel?

1.19 SG12% OCl= 35 lbs pure Cl2

1.19 SG12% OCl= 35 lbs pure Cl2

solution tehypochlori theofportion 12% in the Cl pure of 72.35lbs) (

(30gal))19.1)(/34.(8 )12(.lbs) (

))(g )(/34.8)( . chlorine (%

2lbsweightchlorine

gallbsweightchlorine

galravityspecificgallbsstrengthsolLbs

(%concentration)(X lb)= total lbs requiredX lb= 35.72 lbs/.65X=54.96 lbs of 65% HTH

The lbs/day formula calculates the pure concentration of chlorine within a % solution of chlorine. Thus in the 12% hypochlorite solution there are 35 lbs of pure Cl (A). Imagine the same size barrel of a higher concentration of OCl- as 65% HTH (B). Which solution has more lbs of pure Cl2? Well, the 65% it’s a more concentrated solution so there will be more pure chlorine in it.

(%concentration)(X lb)= total lbs requiredX lb= 35.72 lbs/.65X=54.96 lbs of 65% HTH

The lbs/day formula calculates the pure concentration of chlorine within a % solution of chlorine. Thus in the 12% hypochlorite solution there are 35 lbs of pure Cl (A). Imagine the same size barrel of a higher concentration of OCl- as 65% HTH (B). Which solution has more lbs of pure Cl2? Well, the 65% it’s a more concentrated solution so there will be more pure chlorine in it.

65% OCl as HTH 55 lbs pure Cl265% OCl as HTH 55 lbs pure Cl2

A B