Process Calculations

Describing Physical Quantities

Units

the metric and America engineering systems are the most widely used unit systems in the industrial world. However, a single worldwide unit system was introduced in order to solve any problems that may arise when products are traded internationally from one unit system to another. Hence the Systeme Internatinale d’Units or SI system was formed.

Some widely used systems are summarized below

System	Mass	Length	Time	Temperature
SI	kg	m	s	Kelvin
American	lbm	ft	s	Fahrenheit
cgs	g	cm	s	Celcius

 

Conversion Factors

This is a relationship expressed by an equation where the entries on each side of the equation are the same quantity but expressed in a different form of units.

for example: Convert 3 meters to inches.

Moles

This is the number of molecules in a compound whose mass in grams is numerically equal to its molecular weight. can be in the form of gram-mol (gmol), kilogram-mol (kgmol) or pound-mole (lbmol) depending one your preferred unit system.

Mixture Composition

it is important to find the amount of a particular substance in a mixture using concentration (c) of the substance. The following relationships can help find the concentration, mass and mole fractions of a substance, A.

The above equations ca be manipulated to suit the problem being solved. Depending on what variables are provided, it is easy to solve for unknowns as follows (where MW stands for molecular weight of a species):

Dimensional Consistency

1.    Terms that are added or subtracted together MUST have the same units. For example, in the equation y = mx + b, the units of mx and b must be the same.

2.    Exponents MUST be unitless, therefore an exponent with multiple terms must have those terms cancel out.

Equations that correctly describe a physical phenomenon MUST obey the above rules of dimensional consistency

 

Exercise

1.    Convert the following

a)    an acceleration of 1 cm/s² to km/yr² (Ans: 9.95 * 10⁹ km/yr²)

b)    1 bar into g/cm-s² (Ans: 10⁶ g/cm-s²)

c)    10,000 g/cm²-s² into J (Ans: 0.001 J)

2.    Calculate the Pressure at the bottom of a swimming pool with a depth of 2 meters.

 

3.    When a fluid flows from one location to another under certain circumstances, the changes in fluid properties can be described by Bernoulli equations:

where α: dimensionless correction factor, ρ: fluid density, P: fluid pressure, v: fluid velocity, z: fluid elevation

Show that this equation is dimensionally consistent in the SI system.

4.    A gas mixture has the following mass percentage: 70% N₂, 14% O₂, 4% CO and 12% CO₂. What are the mole percentages of the gases in the mixture? what is the average molecular weight of the mixture? (MW for N₂ = 28g/mol, O₂ = 32 g/mol, CO = 28 g/mol and CO₂ = 44 g/mol).

Assume a mass basis of 100 g for the total mixture

components	mass fraction	mass (g)	MW (g/mol)	Moles	Mole fraction	Mole Percent
N2	0.70	70	28	2.500	0.745	74.5
O2	0.14	14	32	0.432	0.131	13.1
CO	0.04	4	28	0.143	0.043	4.3
CO2	0.12	12	44	0.273	0.081	8.1
Total	1.00	100		3.354	1.00	100

 

Average molecular weight