Engineering Calculations

Engineering Dimensions and Units

Density

= M/V

M = massV = volume

Water: 1 x 103 kg/m3 or 1 g/cm3 or 62.4 lbm/ft3

Concentration

BA

A

A

VV

MC

CA = concentration of AMA = mass of material AVA = volume of material AVB = 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.

g

g

g

g

cm

g

ml

g

L

mg

000,000,1

1

1000

001.0

1000

001.0

1000

001.01

3

Mass Concentration

100

BA

A

A

MM

M

Concentration

10,000 mg/L = 10,000 ppm (if = 1)

10,000 ppm = 1% (by weight)

Flow Rate

Volumetric flow rate

Mass (gravimetric) flow rate

m3/s , ft3/s, gpm, mgd

kg/s, lbm/s

Realted since mass = density x volume (QM = QV )

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

Mass flow rate in pound per day

=Volumetric flow rate

in million gallons per day, mgd

x Concentration in mg/L

x 8.34

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 problem2. Introduce simplifying assumptions3. Calculate answer4. Check the answer

Significant Figures

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