# Working Math Formulas, Units, Conversions

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1 Working Math Formulas, Units, Conversions This presentation has been adapted from Math for Subsurface Operators given at the North Carolina Subsurface Operator School Math will be used to Determine a flow rate for a facility Determine the minimum length of line needed for a drainfield Calculate the minimum dose volume required 1

2 Basic Equations Area of a circle π x r 2 Area of a rectangle L x w Volume of a cylinder L xπ x r 2 Volume of rectangle L x w x h Equations Area of a circle = π r 2 or 3.14 x radius x radius The area of a circle with Area a 3 diameter is 3.14 x (1.5 in x 1.5 in) = 7.07 in 2 R Equations Area of a rectangle or square = Length x width = square units L Area W 2

3 Converting Units A drainfield is 4 ft wide and 102 in long What is the area of the drainfield? 102 in 12 in/ft = 8.5 ft 4 ft x 8.5 ft = 34 ft 2 OR 48 in x 102 in = 4896 in in in 2 /ft 2 = 34 ft 2 Equations Volume of a rectangular tank: length x width x depth = units 3 8 ft x 4 ft x 5 ft = 160 ft 3 Inside width Inside depth Inside length Conversion factor To convert cubic feet to gallons 1 cubic foot = 7.48 gallons 3

4 Equations Volume of a rectangular tank: 8 ft x 4 ft x 5 ft = 160 ft ft 3 x 7.48 gal/ft 3 = 1197 gallons Inside width Inside depth Inside length Determining Gallons per Inch L (ft) x W (ft) x 1 ft x 7.48 gal = gal 12 in. ft 3 in. 1 ft. Example: A tank is 10 feet long and 4.5 feet wide How many gallons are there per inch of liquid depth? 10 ft. x 4.5 ft. x 1 ft. = 45 ft 3 45 ft 3 x 7.48 gal = gal. ft

5 Example: A tank is 10 feet long and 4.5 feet wide How many gallons are there per inch of liquid depth? gal. = gal. 12 in. in Equations Volume of a cylinder (e.g., a tank or pipe): π r 2 x length L π r 2 L Operating volume (ft 3 ) of a cylindrical pump tank: π r 2 x length (or depth) (3.14 x 1.5 ft x 1.5 ft) x 5 ft = 35.3 ft 3 Flow 5 (Inside Liquid Depth) 3 Inside width 5.5 (Inside depth) 5

6 Operating volume (gal) of a cylindrical pump tank: Volume (ft 3 ) x 7.48 gal = gallons ft ft 3 x 7.48 gal = gal ft Volume of a pipe can be calculated the same way: Length π r 2 π r 2 x length x 7.48 gal/cu ft Pipeline Volume (Gallons per 100 feet) Nominal Size (inches) ¾ PVC Rigid Pipe Schedule 40 Schedule PVC Flexible Pressure Pipe SDR 26 (160 psi) SDR 21 (200 psi) Corrugated tubing ¼ ½

7 Units of Measure and Calculations Calculating percent First, divide one number into another: A B = quotient The quotient expresses how many times a quantity is contained in another. A = 20 ; B = = 0.67 So, A is: 0.67 the size of B Calculating percent When we multiply the quotient by 100 we obtain how many times a number is contained in 100 of another (percent). Using the same example: 0.67 x 100 = 67 So, A is: 67% the size of B 7

8 Calculating percent There are 50 dots shown above and 20 of them are black. What percent of the dots are black? Divide # black by total = 0.4 Convert to percent 0.4 x 100 = 40% Calculating percent solids in a septic tank Liquid depth = 60 Scum depth = 6 Sludge depth = 18 Add amount of scum and sludge = 24 Divide by tank liquid depth = 0.4 Convert to percent 0.4 x 100 = 40 % Units Pressure: Force applied to a unit area. Expressed in: pounds per square foot (psf) A tank lid designed to support 150 psf. pounds per square inch (psi) 60 psi pressure of water in a force main Feet of head An alternative expression of water pressure psi x 2.31 = Head (ft) 8

9 Units Concentration Milligrams per liter (mg/l) Parts per Million (ppm) A system may have a requirement for the effluent not to exceed 10 mg/l (or ppm) of nitrate nitrogen. % Reduction in concentration is a reflection of the treatment efficiency of a system component. % reduction = influent effluent x 100 influent % Reduction in Concentration The influent concentration to a sand filter is 300 ppm BOD. The effluent concentration is 30 ppm BOD. What is the % reduction in concentration? % reduction = influent effluent x 100 influent % reduction = x 100 = 90% 300 9

10 Units Flow rate is volume per unit time Gallons per minute (gpm) Gallons per day (gpd) Cubic feet per sec (cfs) Flow Velocity Flow velocity is distance per unit time Feet per sec (fps) The minimum flow rate should be at least 2 fps for good scour The equation to calculate the minimum flow rate in a pipe of known diameter is: x [pipe diameter (in)] 2 = gpm required Flow rate in gallons per minute to achieve a flow velocity of 2 feet per second in rigid PVC pipe Schedule 40 PVC Schedule 80 PVC Nominal Dia. (inches) 1 1 ¼ 1 ½ 2 2 1/ Flow Rate (gpm) Nominal Dia. (inches) 1 1 ¼ 1 ½ 2 2 1/ Flow Rate (gpm)

11 Pump Delivery Rate (PDR): the rate at which wastewater is pumped to the drainfield or treatment unit in gallons per minute (gpm) PDR = gallons of water pumped (gal) pump run time (min) 40 gallons = 8 gal/min 5 minutes Hydraulic loading rate: the amount of wastewater applied per day to a given area of trench bottom or sand filter surface expressed as: gallons per day per square foot or gpd / ft 2 Calculate the Hydraulic Loading Rate to a sand filter surface, given: 3 Bedroom home: 360 gpd Sand Filter is 18 x 10 HLR = gal. applied per day (gpd) area (ft 2 ) = 360 gpd = 2.0 gpd 180 ft 2 ft 2 11

12 Example An LPP Drainfield is 20 x 90 or 1800 ft 2. How many gallons per day can be dosed to the drainfield without exceeding the permit limit of 0.2 gpd / ft 2? Design flow in gpd HLR = (gpd) area (ft 2 ) area (ft 2 ) x HLR = (gpd) x area (ft 2 ) area (ft 2 ) area (ft 2 ) x HLR = gpd An LPP Drainfield is 30 x 90 or 2700 ft 2. How many gallons per day can be dosed to the drainfield without exceeding the permit limit of 0.2 gpd / ft 2? area (ft 2 ) x HLR = gpd 2700 ft 2 x = 540 gpd 0.2 gpd ft 2 12

13 Slope Slope correction is the process of determining, based on soil depth, amount of slope, system type, and trench width requirements if there is enough suitable soil to install a system Slope Slope is the ratio of the rise to the run (or the change in height over the length of the area) The rise is 4 units and the run is 6 units from our graph, so the slope is 67%. Slope Correction Minimum soil depth = trench depth needed + (trench width x slope) MSD = TD + (TW x S) MSD minimum soil depth TD trench depth TW trench width S percent slope 13

14 Slope Correction To install a conventional gravel trench on a 30% slope, what is the minimum soil depth needed? MSD = TD + (TW x S) TD 30 inches minimum TW 36 inches S 0.3 MSD = 30 in + (36 in x 0.3) = 41 in 14

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