Problem Solving Using Common Engineering Concepts

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Problem Solving Using Common Engineering Concepts

• UTPA
• College of Science and Engineering

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Objective

• Practice how to set up engineering calculations
  and how to deal with common physical quantities
  and concepts.
• Practice how to analyze and solve problems
  involving processes which change with time.
• Practice how to analyze and solve problems in the
  absence of exact and complete information.

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Problem Solving Ability

• Problem solving ability only develops with
  experience gained through repetitive practice.
• For a student, practice comes in the form of
  solving class and homework problems.
• This presentation introduces simple concepts
  fundamental to engineering problem solving.

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Rate Problems

• The relation between rate, quantity, and time is

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Temperature

• Temperature is commonly measured using the
  Fahrenheit or Celsius scale.
• When temperature appears as a term in a
  scientific or engineering equation, it is
  absolute temperature (measured in Kelvin or
  Rankine).

F 1.8 C 32 R F 460 K C
273 R 1.8 K
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Temperature
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Pressure

• Pressure is the force per unit area exerted on a
  surface by a fluid (gas or liquid).
• P F / A
• Units Pascals, psi

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The Ideal Gas Law

• PV nRT (R is the Universal Gas Constant)

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Density and Specific Gravity

• ? M / V
• Density is the ratio of the mass of a substance
  to its volume.
• SG ?S / ?R
• Specific gravity is the ratio of the density of a
  substance to the density of a reference
  substance.
• Reference substance is liquid water at 4C which
  has a density of 1,000 kg/m3.

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Mass and Volumetric Flow

• MF M / t
• VF V / t
• If the fluid is incompressible, then
• MF ? (VF)
• Incompressible implies that the density of the
  fluid is constant.

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Material Balance

• Steady State 0 I - O G - C
• No Chemical Reactions I O
• Batch Process A G - C

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Heat, Work, and Energy

• Kinetic Energy EK (mv2) / 2
• Energy due to velocity
• Potential Energy EP mgh
• Energy due to height

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Power

• Power (P) is the rate of energy production or
  consumption.
• P E / t
• Power can also be defined as the amount of work
  done per unit time.
• Power Work / time

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Estimation and Approximation

• It is often necessary to make a reasonable
  estimate that gives an answer within 10 to 20 of
  what might be calculated with complete
  information.
• In absence of complete information, you must make
  assumptions to simplify the problems and/or make
  intelligent guesses.

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Open Forum

• Assignment Handout or visit website.

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Analytic Method

• Define the problem and summarize the problem
  statement.
• Diagram and describe.
• State your assumptions.
• Apply theory and equations.
• Perform the necessary calculations.
• Verify your solution and comment.

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Problem 1 Statement

• Robert lives 65 miles from you. You both leave
  home at 300 pm and drive toward each other on
  the same road. Robert travels at 40 mph, and you
  travel at 50 mph. At what time will you pass
  Robert on the road?

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Problem 1 Summary

• At what time will you pass Robert?

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Problem 1 Solution

• Initial time 300 pm
• Distance Average Velocity time
• 65 miles 40 mph (t) 50 mph (t)
• t 65 miles/(40 mph 50 mph) .72 hrs
• 0.72 hrs (60 minutes/hr) 43.3 minutes
• Hence, you should pass Robert at 343 pm.

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Problem 2 Statement

• A rectangular tank 10 feet wide, 30 feet long,
  and 12 feet high is completely filled with
  gasoline. The gasoline is to be pumped into a
  spherical tank that is 6.0 meters in diameter.
  The pump moves gasoline at a rate of 30.0
  gallons/minute. (a) How long, in hours, will it
  take to transfer the gasoline? and (b) what
  percentage of the spherical tank will be filled
  with gasoline?

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Problem 2 Summary

• Time to transfer in (hrs) ?
• of the spherical tank filled?

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Problem 2 Solution
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Problem 3 Statement

• Juan and Charles are commercial painters. Juan
  has a job to paint a water storage tank that is a
  sphere supported above the ground by three legs.
  The sphere is 15.5 meters in diameter. Charles
  has a job to paint a gasoline storage tank that
  is a cylinder 48.0 feet in diameter and 39.0 feet
  high. The bottom of the tank sits on a concrete
  pad, and therefore, will not be painted. Juan has
  bet Charles that he will complete his job first.
  Assuming that Juan and Charles both paint at a
  rate of 150 feet square / hour, who will win the
  bet?

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Problem 3 Summary

• Who will win the bet?
• (who has less area since they paint at the same
  rate?)

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Problem 3 Solution
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Problem 4 Statement

• A liquid mixture of benzene and toluene contains
  50 benzene by mass. The mixture is fed
  continuously to a distillation apparatus that
  produces vapor containing 60 benzene and a
  residual mixture containing 37.5 benzene, each
  by mass. The still operates at a steady state. If
  the mixture feed rate is 100 kg/hr, determine the
  mass flow rates for each stream.

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Problem 4 Summary
x
?60 benzene 40 toluene
100 kg/hr 50 benzene 50 toluene
y
?37.5 benzene 62.5 toluene

• Determine the mass flow rate for the vapor and
  residual mixture.

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Problem 4 Solution
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Problem 4 Solution cont.
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Problem 5 Statement

• Estimate the total amount of coolant in gallons
  wasted by a radiator that drips continually at
  the rate of one drop every two minutes for six
  months. State all your assumptions clearly.

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Problem 5 Summary

• Total amount of coolant wasted in six months (in
  gallons)?

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Problem 5 Solution