Chapter 1 - Introduction to Engineering Calculations

 

OVERVIEW

Chapter 1 provides motivation for a quantitative engineering approach and exposure to different bioengineering technologies and research topics.  First, units, dimensions, and unit conversion are reviewed.  Intensive and extensive physical variables and their relevance to the conservation laws are explained.  Thirty physical variables are introduced in the context of five bioengineering technologies and research topics plus one environmental system.  The topics and a subset of the elaborated physical variables are listed below:

 

·       Drug delivery for Parkinson’s disease (mass, moles, mass fraction, concentration)

·       Mars surface conditions (temperature, density, saturation)

·       Gene transfer technology (momentum, kinetic energy, current, charge)

·       Getting to and life on Mars (force, weight, pressure, heat, work)

·       Microsurgical assistant (flow rates, pressure)

·       Victoria Falls (rate of momentum, rate of potential energy)

 

A methodology or process for solving engineering problems is introduced in Chapter 1.  This method is similar to those found in other leading engineering textbooks.  The four main steps in the problem-solving methodology are as follows:

 

1.  Assemble (diagram, problem statement, selection of units)

2.  Analyze (make appropriate assumptions, collect extra data, set a basis if needed)

3.  Calculate (apply and simplify governing equations, calculate unknown quantities)

4.  Finalize (check if answers are reasonable, state answer clearly)

 

This methodology for solving problems is used throughout the textbook for about 70% of the worked example problems.

 

 

EXAMPLE PROBLEMS

 

1.     Calculate the force and pressure acting across the pelvis and at the feet of a 150 lb_m person.  Model the body using cylinders.  Neglect external pressures (such as air pressure).  Assume that the individual distributes his/her weight equally between two legs.  Assume that the cross-sectional area of the foot is approximately that of the leg.  Assume that the cross-sectional area of the pelvis is approximately that of the trunk of the body.  Several additional assumptions will be needed; state them clearly.  In your model, is the pressure higher on the pelvis or the feet?  Is this consistent with what you expected?

 

2.     What is the force (N and lb_f) on a 20.0 kg mass under normal gravity?  What is the force (N and lb_f) on a 20.0 lb_m mass under normal gravity?

 

3.     Ti-6Al-4V is a metal alloy used to make biomaterials.  Its composition is 90% Ti, 6% Al, and 4% V (mass percents).  What are the mass fractions of Ti, Al, and V?  What are the mole fractions of Ti, Al, and V?  Calculate the MWav of the alloy.

 

4.     Approximate the linear gas velocity in the trachea during normal exhalation. Do this by timing exhalations, measuring volumes of exhaled gas, and looking up or estimating the inner diameter of the trachea.  A balloon or paper or plastic bag may be helpful to measure the volume of exhaled gas.  Do more than one measurement and compute an average and standard deviation.  Repeat the estimate for forced exhalation.  Describe the process that you used to make the calculations and estimates.  List three potential sources of error in your measurements.  Compare your experimental gas velocity in the trachea during normal exhalation with the linear velocity given in Homework Problem #13.