Replacing Figures and Tables for Engineering Design with Simple In-House Developed Computer Software

YoonKook Park, Kyung C. Kwon, Nader Vahdat, and Tamara M. Floyd

kwonk@tuskegee.edu, Tel: (334) 727-8976, Fax: (334) 724-4188 Chemical Engineering Department, Tuskegee University

Tuskegee, Alabama 36088

Prepared for Presentation at AIChE 2004 Annual Meeting, November 8-12, Austin, TX at the Session of Incorporating New Technologies into Chemical Engineering Education

(529g).

Copyright YoonKook Park, K. C. Kwon, Nader Vahdat, and Tamara M. Floyd Tuskegee University, Alabama, USA

Unpublished

AIChE Shall Not Be Responsible for Statements or Opinions Contained in Papers or Printed in its Publications.

Introduction

Numerous tables and figures are used to solve engineering design problems in Chemical Engineering courses such as fluid mechanics, thermodynamics and heat transfer. Tables and figures are often misread, and significant times/efforts are consumed to understand them, because their complex formats make them difficult to be comprehended. Such problems can be alleviated by developing simple computer programs with readily available software such as FORTRAN, C++, and Microsoft EXCEL, to replace conventional figures and tables with computer-generated engineering design data.

Fluid Mechanics Course

Objectives of fluid mechanics course are for chemical engineering students to apply knowledge of mathematics, computer science, material balances and thermodynamics to fluid mechanics, to determine friction factor using appropriate formulas and physical property tables, to identify appropriate equations for fluid statics and fluid flows to solve steady-state fluid flow problems with physical property tables, and to design pipes, pumps, compressors, fluid-measuring devices, and fluid-handling equipment with various design equations.

The friction factor chart is utilized to determine skin friction loss of pipes. The chart (shown in Fig. 1) is replaced with a simple computer program, which can be easily developed with the Colebrook equation as shown in Equation 1, using EXCEL software. Figure 2 shows pressure drop for the flow of oil in a schedule-40 3-inch pipe, while Figure 3 shows friction loss for the flow of air in straight ducts. These figures are substituted with computer software, which is developed by incorporating the Colebrook’s equation into the Bernoulli’s equation.

+−=

fRD

f

255.17.3

log41ε (1)

where f: friction factor ε: absolute roughness of pipe D: inside diameter of pipe or duct R: Reynolds number

Table 1 shows flow of water through schedule-40 steel pipes. Table 2 shows properties of water at various temperatures, whereas Table 3 shows properties of air at various temperatures. Relationships between properties of water and air, and temperatures are developed with EXCEL software or hand calculators. These simple relationships can be substituted with Tables 1 and 2. Table 1 can be replaced with simple computer software developed with the Colebrook’s equation, Bernoulli’s equation, and relationships between properties of water and temperatures.

Heat Transfer Course

Objectives of heat transfer courses are for chemical engineering undergraduate students to apply knowledge of mathematics, computer science, material balances, energy balances and fluid mechanics to heat transfer, to determine heat transfer coefficients for forced/free convection heat transfer, condensation heat transfer, and overall heat transfer coefficient, using appropriate design equations and physical properties, to identify appropriate equations for conduction heat transfer, convection heat transfer, and condensation and boiling heat transfer to solve steady-state/unsteady-state heat-transfer design problems with physical property tables and Heisler charts, and to design heat exchangers with design equations, design-data tables, and design figures.

The Gauss error function values as shown in Table 4 are used to solve unsteady-state convection heat transfer problems of semi-infinite solids. If the desired error function values are not available, approximate error function values may be obtained with the interpolation method. A simple computer software is developed to obtain easily more accurate error function values than those of the Gauss error function table. The Gauss error function equation (see Equation 2) is applied to Taylor series expansion, and the first 25 terms of Taylor series expansion are selected to be integrated with the help of EXCEL.

( ) ∫ −=U U dUeUerf0

2 2

π (2)

Water, steam and air are frequently utilized as heat transfer media for heat exchangers and

condensers. Convection heat transfer coefficients in the presence of water and air, and condensation heat transfer coefficients in the presence of steam are obtained with properties of water and air, using their property tables (see Tables 2 and 3). Desired properties may be obtained with the aid of the interpolation method, which is tedious and time-consuming. Relationships between properties of water and air, and temperatures are developed with EXCEL software or hand calculators. These simple relationships can be substituted with Tables 1 and 2.

Thermodynamics Course

The Depriester charts (see Figures 4 and 5) are used to compute dew-point pressures, bubble point pressures, vapor-phase compositions, and liquid-phase compositions for hydrocarbons in the design of a flash drum. These charts are very difficult to be read for the computation of these desired values, which are frequently obtained with the trial-and-error method. The McWilliams equations (see Equation 3) replace these charts, and are incorporated into vapor-liquid equilibrium equations for the programming of simple computer software with FORTRAN.

PF

PE

TB

TA PDCK +++++= 22 lnln (3)

where K: equilibrium constant of hydrocarbon T: oR P: psia A, B, C, D, E, and F: unique parameters of individual hydrocarbon

Table 1. Flow of Water through Schedule 40 steel Pipe

Table 2. Properties of water.

Table 3. Properties of 1-atmosphere air.

Table 4. Error function.

Figure 1. Friction factors for circular pipes

Figure 2. Pressure drop for flow of 62.3-lbm/ft3 and 50-cP oil in 3-inch schedule-40 pipe.

Figure 3. Friction of air in straight ducts.

Figure 4. Equilibrium constants of light hydrocarbons in the low-temperature range.

It’s

Figure 5. Equilibrium constants of light hydrocarbons in the high-temperature range.

References 1. Bird, R.B., Stewart, W.E., and Lightfoot, E.N., “Transport Phenomena”, 2nd Edition,

2002. 2. Noel D. Nevers, Fluid Mechanics for Chemical Engineers, Second Edition, McGraw-

Hill, 1991. 3. J.P. Holman, “Heat Transfer”, 9th Edition, McGraw-Hill, 2002 4. Smith and Van Ness, Introduction to Chemical Engineering Thermodynamics 4th

Edition, McGraw-Hill, 1987

Acknowledgments

The authors thank to the Tuskegee University Title III program - faculty development program for support of travel expenses for presentation of this paper at AIChE 2004 Annual Meeting