Chemical processes I 

 LECTURERDr. Riham Hazzaa 

  

TEXTBOOKR.M. Felder and R.W. Rousseau “ Elementary Principles of Chemical Processes”, John Wiley & Sons, 3rd Edition 2005.

 Dimensions, Units, and Unit Conversion

• “Every physical quantity can be expressed as a product of a pure number and a unit, where the unit is a selected reference quantity in terms of which all quantities of the same kind can be expressed”

• Physical Quantities   • Fundamental quantities   • Derived quantities

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Fundamental Quantities• Length•  Mass• Time• Temperature• Amount of substance• Electric current

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Derived Quantities• Area   [Length × length or (length)2]• Volume  [(Length) 3]• Density [Mass/volume or mass/ (length) 3]• Velocity  [Length/time]• Acceleration [Velocity/time or length/ (time) 2]• Force [Mass × acceleration or (mass × length)/ (time) 2]

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ValueUnitDimension

110mgmass

24handlength

5galvolume (length3)

•110 mg of sodium •24 hands high 

•5 gal of gasoline 

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• Dimension :A property that can be measured directly (e.g., length (L), mass (M), time (t), temperature (T)) or calculated, by multiplying or dividing with  other dimensions (e.g., volume, velocity, force)

• Unit: A specific numerical value of dimension. "Units" can be counted or measured. Many different units can be used for a single dimension, as inches, miles, centimeters  are all units used to measure the dimension length.

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SYSTEMS OF UNITS

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Every system of units has: • A set of "basic  units" for the dimensions of

mass, length, time, absolute temperature, electric current, and amount of substance.

• Derived units, which are special combinations of units or units used to describe combination dimensions (energy,  force,  volume,  etc.)  For example:

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The unit for Force can be expressed in terms of the derived unit (newton) or in base units (kg.m/s2)

Derived SI Units

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• Multiple units, which are multiples or fractions of the basic units used for convenience (years instead of seconds, kilometers instead of meters, etc.).

• the base unit is second, the multiple units of time: • Minutes = 60 seconds • Hour = 3600 seconds • Day = 86400 second.

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• Examples of the Dimensions of Derived Quantities

• Area (A)                    A = L×L=L2

• Volume (V)  V = L×L×L=L3

• Density (ρ)                ρ =   M/V=M/L3

• Velocity (V)    V =   L/t• Acceleration (a)      V/t = L/t2

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• What is the dimension of P? • Pressure (P ) is defined as “the amount of

force (F ) exerted onto the area (A)

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• Unit of pressure (P), in SI system, • kg/m.s2 • N/m2

• “Pascal (Pa)”, which is defined as

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• Example: Determine the units of density, in c• gs, SI, and AE systems?

• cgs unit system is  g/cm3

• SI unit system is Kg/m3

• AE unit system is 1bm/ft3

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CONVERSION OF UNITS • To convert units from one system to another,

we simply multiply the old unit with a conversion factor.

• This is defined as follow:

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EXAMPLE 1 Convert 10 m/s to ft/s. • 1 m is equal to 3.28 ft.• The conversion factor is 3.281ft/m

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• EXAMPLE 2 Convert 10 m2/s to ft2/s. •  The conversion factor is

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• EXAMPLE 3 Convert 10 kg m/s2 to lb ft/min2

• 1 kg = 2.2 lb • 1m = 3.28 ft • 60 s = 1 min

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• EXAMPLE  5  Convert the mass flux of 0.04g/m.min2 to that in the unit of lbm/h ft2

•

= 4.92 × 10-4 lbm/h ft2

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• EXAMPLE 6 Convert 23 1bm ft/ min2 to its equivalent in kg.cm/s2

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• EXAMPLE 7 • At 4 oC, water has a density of 1 g/cm3. Liquid A has a

density at the same temperature of 60 lbm/ft3. When water is mixed with liquid A, which one is on the upper layer?

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Force & Weight• force (F) is the product of mass (m) and its

acceleration (m)F=ma

• its corresponding units:

• "Pound-force" (lbf),

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• The force in newtons required to accelerate a mass of 4 kg at a rate of 9 m/s2 is

• The force in lbf required to accelerate a mass of 4 lbm at a rate of 9 ft/s2 is

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• The conversion between the defined unit of force (N, dyne, lbf) and natural units is so commonly used that we give it a special name and symbol, gc.

g/ gc =9.8066 N/kg

g/ gc =980.66 dyne/g

g/ gc = 1 lbf/lbm24Dr.Riham Hazzaa

Weight• Weight is defined to be the force exerted on

an object by gravity, so an object of mass m subjected to the gravitational acceleration g, will have weight

W = mg/gc• For example, the mass of a steel ball is 10 kg. 

The weight of this ball on the earth’s surface is:

W = 10 Kg x 9.81 N/kg = 98.1 Ng/ gc =9.8066 N/kg

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• Example: Water has a density of 62.4 1bm/ft3. How much does 2 ft3 of water weigh

• (1) at sea level and 45◦ latitude • (2) in Denever, Colorado, where the altitude is 574 ft and the

gravitational acceleration is 32.139 ft/s2 • The mass of the water is

• The weight of water is W(lbf) = 124.8 lbm g/gc (lbf/lbm)

• At sea level, g= 32.174ft/s2, g/gc=1  lbf/lbmW= 124.8 1bf

• In Denver, g = 32.139, g/gc=32.139/32.174 lbf/lbm

W= 124.7 1bf26Dr.Riham Hazzaa

DIMENSIONAL HOMOGENEITY 

• When adding or subtracting values, the units of each value must be similar to be valid.

• EXAMPLE • A (m) =2 B(s)+5 • What should the units for constants 2 and 5

have to be for the equation to be valid?

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DIMENSIONLESS QUANTITIES • An example of a dimensionless quantity is Reynold’s number NRe.

• This describes the ratio of inertial forces to viscous forces (or convective momentum transport to molecular momentum transport) in a flowing fluid. It thus serves to indicate the degree of  turbulence. Low Reynolds numbers mean the fluid flows in "lamina" (layers), while high values mean the flow has many turbulent eddies.

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• A quantity k depends on the temperature in the following manner:

• The units of the quantity 20,000 are cal/mol, and T is in K (kelvin). What are the units of 1.2 105 and 1.987?

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