Chemical processes I LECTURER Dr. Riham Hazzaa TEXTBOOK R.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 Dr.Riham Hazzaa

Fundamental Quantities Length Mass Time Temperature Amount of substance Electric current Dr.Riham Hazzaa

• Area [Length × length or (length)2] • Volume [(Length) 3] 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] Dr.Riham Hazzaa

Value Unit Dimension 110 mg mass 24 hand length 5 gal volume (length3) 110 mg of sodium 24 hands high 5 gal of gasoline Value Unit Dimension 110 mg mass 24 hand length 5 gal volume (length3) Dr.Riham Hazzaa

Dimension :A property that can be measured directly (e. g 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. Dr.Riham Hazzaa

SYSTEMS OF UNITS Dr.Riham Hazzaa

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: Dr.Riham Hazzaa

Derived SI Units The unit for Force can be expressed in terms of the derived unit (newton) or in base units (kg.m/s2) Dr.Riham Hazzaa

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. Dr.Riham Hazzaa

Acceleration (a) V/t = L/t2 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 Dr.Riham Hazzaa

What is the dimension of P? Pressure (P ) is defined as “the amount of force (F ) exerted onto the area (A) Dr.Riham Hazzaa

Unit of pressure (P), in SI system, kg/m.s2 N/m2 “Pascal (Pa)”, which is defined as Dr.Riham Hazzaa

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 Dr.Riham Hazzaa

This is defined as follow: 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: Dr.Riham Hazzaa

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

EXAMPLE 2 Convert 10 m2/s to ft2/s. The conversion factor is Dr.Riham Hazzaa

EXAMPLE 3 Convert 10 kg m/s2 to lb ft/min2 1 kg = 2.2 lb 1m = 3.28 ft 60 s = 1 min Dr.Riham Hazzaa

EXAMPLE 5 Convert the mass flux of 0. 04g/m 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 Dr.Riham Hazzaa

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

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? Dr.Riham Hazzaa

Force & Weight force (F) is the product of mass (m) and its acceleration (m) F=ma its corresponding units: "Pound-force" (lbf), Dr.Riham Hazzaa

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 Dr.Riham Hazzaa

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/lbm Dr.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 N g/ gc =9.8066 N/kg Dr.Riham Hazzaa

W(lbf) = 124.8 lbm g/gc (lbf/lbm) 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/lbm W= 124.8 1bf In Denver, g = 32.139, g/gc=32.139/32.174 lbf/lbm W= 124.7 1bf Dr.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? Dr.Riham Hazzaa

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. Dr.Riham Hazzaa

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? Dr.Riham Hazzaa

Dr.Riham Hazzaa