Water/Wastewater Conversion Examples

Use Table 1.4 and Table 1.5 to make the conversions indicated in the following example problems.

Other conversions are presented in appropriate sections of the text.

Example 1.4

Convert cubic feet to gallons.

Sample problem:

How many gallons of biosolids can be pumped to a digester that has 3600 ft³ of volume available?

Example 1.5

Convert gallons to cubic feet.

Sample problem:

How many cubic feet of biosolids are removed when 18,200 gal are withdrawn?

Example 1.6

Convert gallons to pounds.

Sample problem:

If 1650 gal of solids are removed from the primary settling tank, how many pounds of solids are removed?

Gallons = Cubic Feet, ft³ × gal/ft³

Gallons = 3600 ft³ × 7.48 gal/ft³ = 26,928ggal

Cubic Feet gal 7.48 gal/ft³

=

Cubic Feet 18,200 gal

7.48 gal/ft₃ 2433 ft

= = ³³

Pounds, lb = gal × 8.34 lb/gal

Pounds = 1650 gal × 8.34/gal = 13,761 lb

L1681_book.fm Page 16 Tuesday, October 5, 2004 10:51 AM

CONVERSION FACTORS AND SI UNITS 17

Example 1.7

Convert pounds to gallons.

Sample problem:

How many gallons of water are required to fill a tank that holds 7540 lb of water?

Example 1.8

Convert milligrams per liter to pounds.

Key point: For plant operations, concentrations in milligrams per liter or parts per million deter-mined by laboratory testing must be converted to quantities of pounds, kilograms, pounds per day, or kilograms per day.

Sample problem:

The solids concentration in the aeration tank is 2580 mg/L. The aeration tank volume is 0.95 MG. How many pounds of solids are in the tank?

Example 1.9

Convert milligrams per liter to pounds per day.

Sample problem:

How many pounds of solids are discharged per day when the plant effluent flow rate is 4.75 MGD and the effluent solids concentration is 26 mg/L?

Example 1.10

Convert milligrams per liter to kilograms per day.

Gallons lb

8.34 lb/gal

=

Gallons 7540 lb

8.34 lb/gal 904 gal

= =

Pounds=Concentration, mg/L × Volume, MG × ..34 lb/mg/L/MG8

Pounds = 2580 mg/L × 0.95 MG × 8.34 lb/mg/L//MG = 20,441.3 lb

Pounds/Day = Concentration, mg/L × Flow, MGDD × 8.34 lb/mg/L/MG

Pounds/Day = 26 mg/L × 4.75 MGD × 8.34 lb/mgg/L/MG = 1030 lb/day

Kg/Day = Concentration, mg/L × Volume, MG × 3.785 kg/mg/L/MG

L1681_book.fm Page 17 Tuesday, October 5, 2004 10:51 AM

18 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

Sample problem:

The effluent contains 26 mg/L of BOD₅. How many kilograms per day of BOD₅ are discharged when the effluent flow rate is 9.5 MGD?

Example 1.11

Convert pounds to milligrams per liter.

Sample problem:

The aeration tank contains 89,990 lb of solids. The volume of the aeration tank is 4.45 MG.

What is the concentration of solids in the aeration tank in milligrams per liter?

Example 1.12

Convert pounds per day to milligrams per liter.

Sample problem:

The disinfecting process uses 4820 lb per day of chlorine to disinfect a flow of 25.2 MGD.

What is the concentration of chlorine applied to the effluent?

Example 1.13

Convert pounds to flow in million gallons per day.

Sample problem:

Per day, 9640 lb of solids must be removed from the activated biosolids process. The activated biosolids concentration is 7699 mg/L. How many million gallons per day of waste-activated biosolids must be removed?

Kg/Day = 26 mg/L× 9.5 MG × 3.785 kg/mg/L/MG = 934 kg/day

Concentration, mg/L Quantity, lb Volume, M

= GG × 8.34 lb/mg/L/MG

Concentration, mg/L 89,990 lb 4.45 MG 8.

= × 334 lb/mg/L/MG= 2425 mg/L

Concentration, mg/L Quantity, lb/day Volum

= ee, MG × 8.34 lb/mg/L/MG

Concentration, mg/L 4820

25.2 MGD 8.34 l

= × bb/mg/L/MG= 22.9 mg/L

Flow Quantity, lb/day

Concentration, mg/L

= ×× 8.34 lb/mg/L/MG

L1681_book.fm Page 18 Tuesday, October 5, 2004 10:51 AM

CONVERSION FACTORS AND SI UNITS 19

Example 1.14

Convert million gallons per day to gallons per minute (gpm).

Sample problem:

The current flow rate is 5.55 MGD. What is the flow rate in gallons per minute?

Example 1.15

Convert million gallons per day to gallons per day (gpd).

Sample problem:

The influent meter reads 28.8 MGD. What is the current flow rate in gallons per day?

Example 1.16

Convert million gallons per day to cubic feet per second (cfs).

Sample problem:

The flow rate entering the grit channel is 2.89 MGD. What is the flow rate in cubic feet per second?

Example 1.17

Convert gallons per minute to million gallons per day.

Flow 9640 lb

7699 mg/L 8.34 lb/MG/mg/L

= × = 00.15 MGD

Flow Flow, MGD 1,000,000 gal/MG 1440 min

= ×

//day

Flow 5.55 MGD 1,000,000 gal/MG 1440 min/

= ×

d

day = 3854 gpm

Flow = Flow, MGD × 1,000,000 gal/MG

Flow = 28.8 MGD × 1,000,000 gal/MG = 28,800,,000 gpd

Flow, cfs = Flow, MGD × 1.55 ft /sec/MGD³

Flow = 2.89 MGD × 1.55 ft /sec/MGD³ = 4.48 ftt /sec³

Flow MGD Flow, gpm 1440 min/day 1,000,000

, ×

gal/MG

L1681_book.fm Page 19 Tuesday, October 5, 2004 10:51 AM

20 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

Sample problem:

The flow meter indicates that the current flow rate is 1469 gpm. What is the flow rate in million gallons per day?

Example 1.18

Convert gallons per day to million gallons per day.

Sample problem:

The totalizing flow meter indicates that 33,444,950 gal of wastewater have entered the plant in the past 24 h. What is the flow rate in million gallons per day?

Example 1.19

Convert flow in cubic feet per second to million gallons per day.

Sample problem:

The flow in a channel is determined to be 3.89 ft³/sec. What is the flow rate in million gallons per day?

Example 1.20

Problem:

The water in a tank weighs 675 lb. How many gallons does the tank hold?

Solution:

Water weighs 8.34 lb/gal. Therefore:

Flow, MGD 1469 gpm 1440 min/day 1,000,000

× g

gal/MG = 2.12 MGD (rounded)

Flow, MGD Flow, gal/day 1,000,000 gal/MG

Flow, MGD 33,444,950 gal/day

1,000,000 gal/MGG = 33.44 MGD

Flow, MGD Flow, ft /sec 1.55 ft /sec/MG

3 3

Flow, MGD 3.89 ft /sec

1.55 ft /sec/MG 2.5

3

3 = MGD

675 lb

8.34 lb/gal= 80 9. gallons

L1681_book.fm Page 20 Tuesday, October 5, 2004 10:51 AM

CONVERSION FACTORS AND SI UNITS 21

Example 1.21

Problem:

A liquid chemical weighs 62 lb/ft³. How much does a 5-gal can of it weigh?

Solution:

Solve for specific gravity; get pounds per gallon; multiply by 5.

Example 1.22

Problem:

A wooden piling with a diameter of 16 in. and a length of 16 ft weighs 50 lb/ft³. If it is inserted vertically into a body of water, what vertical force is required to hold it below the water surface?

Solution:

If this piling had the same weight as water, it would rest just barely submerged. Find the difference between its weight and that of the same volume of water. This is the weight needed to keep it down.

Specific Gravity wt. channel wt. water

=

62 lb/ft

62.4 lb/ft .99

3

3 =

Specific Gravity = wt. channel wt. water

.99 wt. chemical 8.34 lb/gal

=

8.26 lb/gal = wt. chemical 8.26 lb/gal × 5 gal = 41.3 lb

62.4 lb/ft (water) 50.0 lb/ft (piling)

3

− 3

12.4 lb/ft difference³

Volume of piling = .785 × 1.33² × 16 ft = 22.21 ft2 ³

12.4 lb/ft³ × 22.21 ft³ = 275.4 lb (neededtto hold piling below water surface)

L1681_book.fm Page 21 Tuesday, October 5, 2004 10:51 AM

22 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

Example 1.23

Problem:

A liquid chemical with a specific gravity (SG) of 1.22 is pumped at a rate of 40 gpm. How many pounds per day is the pump delivering?

Solution:

Solve for pounds pumped per minute; change to pounds per day.

Example 1.24

Problem:

A cinder block weighs 70 lb in air. When immersed in water, it weighs 40 lb. What is the volume and specific gravity of the cinder block?

Solution:

The cinder block displaces 30 lb of water; solve for cubic feet of water displaced (equivalent to volume of cinder block).

Cinder block volume = 0.48 ft³; this weighs 70 lb.

In document ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK By Spellman (Page 32-38)