1. Engineering Calculations

2. Engineering Dimensions and Units Density D = M/V M = mass V = volume Water: 1 x 10 3 kg/m 3 or 1 g/cm 3 or 62.4 lb m /ft 3

3. Concentration C A = concentration of A M A = mass of material A V A = volume of material A V B = volume of material B

4. Concentration Parts per million is a common measure of Concentration (ppm). It is equivalent to mg/L in water since one milliliter of water weighs one gram.

5. Mass Concentration

6. Concentration 10,000 mg/L = 10,000 ppm (if D = 1) 10,000 ppm = 1% (by weight)

7. Flow Rate Volumetric flow rate Mass (gravimetric) flow rate m 3 /s, ft 3 /s, gpm, mgd kg/s, lb m /s Realted since mass = density x volume (Q M = Q V D )

8. Mass flow of a component Q ma = C A x Q V(A+B) Example: A wastewater treatment plant discharges a flow of 1.5 m 3 /s at a solids concentration of 20 mg/L. How much solids is the plant discharging each day? Q ma = 20 mg/L X (1 x 10 -6 kg/mg) x (1.5 m 3 /s x 10 3 L/m 3 x 86,400 s/day) = 2592 kg/day

9. A useful conversion Mass flow rate in pound per day = Volumetric flow rate in million gallons per day, mgd x Concentration in mg/L x8.34

10. Residence Time Also referred to as detention time or retention time The average amount of time it takes a particle of fluid spends in a container it is flowing through or you can think of it as the amount of time it takes to fill the container. t = V/Q - Example: A lagoon has a volume of 1500 m 3 amd the flow into the lagoon is 3 m 3 /hour. What is the residence time in this lagoon? t = 1500/3 = 500 hours -

11. Approximations in Calculations 1. Define the problem 2.Introduce simplifying assumptions 3.Calculate answer 4. Check the answer

12. Significant Figures Significant figures are those that transfer information based on the value of the digit