 Levinson Productivity
Systems, P.C.William A. Levinson, P.E. Principal 570-824-1986  |
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MGI (SmartPros LTD) offers correspondence study courses for all four major branches of the P.E. exam. MGI carries the P.E. Readiness (R) series for Chemical, Civil, Electrical, and Mechanical Engineering. We provided the Chemical Engineering review materials (Levinson, 1995, P.E. Readiness (R): Chemical Engineering Exam Preparation). The notes below should be helpful to everyone who is preparing for this examination.
- Mass and Energy Balances
- Three vital concepts: dimensional analysis, systems or control volumes, the steady state
- Fluid Mechanics
- The Bernoulli Equation: friction, and friction factors, Fanning equation, Colebrook equation, Darcy, Blasius, and Moody friction factors, Reynolds number
- Net positive suction head (NPSH)
- Compressible flow (gases): gas handling equipment, power equations for compression
- Centrifugal pumps
- Metering of fluids: venturi and orifice meters, pitot tubes
- Thermodynamics
- Basic thermodynamic properties and concepts
- Energy
- Laws of thermodynamics
- The phase rule
- Equilibrium
- Heat capacity
- Isobaric, isentropic, isothermal, and adiabatic processes, Carnot cycle
- Thermodynamic properties of gases: ideal gases, compressibility, critical properties
- Reaction, formation, and combustion: standard heats of reaction, formation, combustion
- Heat of mixing
- Power cycles and refrigeration: working fluids, nonideal power cycles, refrigeration
- Chemical equilibrium: stoichiometric numbers, extent of reaction, equilibrium, Gibbs free energy, Gibbs-Helmholtz equation
- Phase equilibrium
- Heat Transfer
- Conduction in solids: resistences in series, conduction in cylinders
- The series resistance model is an excellent way to analyze heat transfer problems
- Unsteady-state conduction
- Heat flow in fluids
- Double-pipe heat exchangers
- Temperature profiles in heat exchangers
- Individual heat transfer coefficients
- Shell and tube heat exchangers
- Prandtl number, Nusselt number, Sieder-Tate equation
- Condensers
- Evaporators: boiling point elevation
- Kinetics and Reactor Design
- Chemical reactions and reaction rates
- Steady state assumption
- Arrhenius equation
- Catalysts
- Rate equations from laboratory data
- Reactors: batch, continuous stirred tank reactor (CSTR), plug flow reactor (PFR)
- Separations and Mass Transfer
- Distillation: equilibrium curves, minimum plates, minimum reflux ratio, phase diagrams, azeotropes, and plate efficiencies, Murphree efficiency, Fenske-Underwood equation, McCabe-Thiele method
- Flash calculations: multicomponent phase equilibria, bubble and dew points, Chao-Seader k values
- Extraction: mass balances, phase diagrams, number of stages, Kremser equation
- Leaching
- Absorption: mass balances, transfer units
- Dimensional Analysis
- Thermodynamics: Carnot Cycle Efficiency
- Heat Transfer: Pipes and Tubes
- Reactor Design: CSTRs in Series
Dimensional Analysis: EXTREMELY IMPORTANT
The best "success secret" for passing the Engineering Licensure exam (or any other engineering exam) is, use dimensional analysis, or the factor-label method. It makes it difficult (although not impossible) to omit a factor from the calculation.
Engineers once HAD to use the factor-label method to set up problems for their slide rules. Slide rules do not keep track of powers of ten, so one had to write the equation in factor form (with the powers of ten in place). Calculators take care of this automatically, so many people no longer use the factor-label method.
However, diligent use of the factor-label method prevents many mistakes, such as forgetting a factor. If you've included everything, the answer will have the correct units of measurement. If the answer should be in kilograms, you will get kilograms. If you've left something out, you probably won't.
The following figure shows a Reynolds number calculation. The Reynolds number is dimensionless (has no units of measurement). If you go through the equation and multiply and divide the units of measurement, they'll all cancel out. In this example, 58 cubic feet of water per minute flow through a pipe whose inside diameter is 6.065 inches. The water's viscosity is 1.129 centipoise. Its density is 62.37 pounds per cubic foot. Note the presence of conversion factors in the equation. Their units (e.g. 1 centipoise = 2.42 pounds per foot hour) cancel against the others to yield the correct result. If, for example, you got an answer with the units "lb/ft-h-cP," it would tell you that a factor was missing. The Reynolds number has no units.
Dimensional analysis will not, of course, flag a mistake like a missing dimensionless number (the 4/pi factor for example) or inversion of a dimensionless group, but it will catch the omission of any factor that has units of measurement (or a necessary conversion factor).
Thermodynamics: Carnot Cycle Efficiency
Calculation of the Carnot Cycle efficiency uses ABSOLUTE temperature (Rankine or Kelvin). Results of 60 to 80 percent are not realistic--if they were, energy from coal-fired power plants and automobile engines would be dirt cheap--and usually occur when the denominator of (T_hot minus T_cold)/(T_hot) is in Fahrenheit or Centigrade.
- Also remember that the Arrhenius equation, and most other
calculations in kinetics and reactor design, use the absolute
temperature.
Heat Transfer: Pipes and Tubes
When computing the overall radius, only the pipe or tube diameter is divided by two. As an example, if a 1" OD tube is surrounded by an inch of insulation, the radius of the tube is 0.5 inch but the radius of the
insulated surface is 1.5 inch (0.5" plus 1" thickness).
- Many people divide the insulation thickness by 2 as well (e.g. radius = 1 inch), or else forget to divide the inner pipe/tube diameter by 2 (e.g. area per unit length becomes 2*pi*D instead of 2*pi*r).
- Remember that the pipe or tube has a diameter while the insulation has a thickness, and it is very easy to mix them up. It's best to draw a diagram if one is not sure.
For a series of N CSTR's of equal size, and first order kinetics, the conversion at the end of the series is 1-(1+kt)^-N where t = residence time tau
