Engineering Calculations
Engineering Dimensions and Units
Density
D
= M/V
M = mass
V = volume
Water: 1 x 103 kg/m3 or 1 g/cm3 or 62.4 lbm/ft3
Concentration
CA 
MA
VA  VB
CA = concentration of A
MA = mass of material A
VA = volume of material A
VB = volume of material B
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.
1 mg
0.001 g

L
0.001 g
0.001 g

1000 ml

1000 cm
3
1g

1000 g
1 , 000 , 000 g
Mass Concentration
MA
A
 100

MA  MB
Concentration
10,000 mg/L = 10,000 ppm (if D = 1)
10,000 ppm = 1% (by weight)
Flow Rate
Volumetric flow rate
m3/s , ft3/s, gpm, mgd
Mass (gravimetric) flow rate
kg/s, lbm/s
Realted since mass = density x volume (QM = QV D)
Mass flow of a component
Qma = CA x QV(A+B)
Example:
A wastewater treatment plant discharges a flow of 1.5 m3/s at a solids
concentration of 20 mg/L. How much solids is the plant discharging each day?
Qma= 20 mg/L X (1 x 10-6 kg/mg) x (1.5 m3/s x 103 L/m3 x 86,400 s/day)
= 2592 kg/day
A useful conversion
Volumetric flow rate Concentration
Mass flow rate
= in million gallons x
x 8.34
in pound per day
in mg/L
per day, mgd
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 m3 amd the flow into the lagoon is 3 m3/hour.
What is the residence time in this lagoon?
t- = 1500/3 = 500 hours
Approximations in Calculations
1. Define the problem
2. Introduce simplifying assumptions
3. Calculate answer
4. Check the answer
Significant Figures
Significant figures are those that transfer
information based on the value of the digit