Problem Solving Using Common Engineering Concepts Introduction to Mechanical Engineering The University of Texas-Pan American College of Science and Engineering

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.

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.

Rate Problems  The relation between rate, quantity, and time is

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 °R = °F K = °C K = °C °R = 1.8 K

Temperature

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

The Ideal Gas Law  PV = nRT (R is the Universal Gas Constant)

Density and Specific Gravity  ρ = M / V – Density is the ratio of the mass of a substance to its volume.  SG = ρ S / ρ 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 4°C which has a density of 1,000 kg/m 3.

Mass and Volumetric Flow  MF = M / t  VF = V / t  If the fluid is incompressible, then MF = ρ (VF)  Incompressible implies that the density of the fluid is constant.

Material Balance 0 = I - O + G - C  Steady State: 0 = I - O + G - C I = O  No Chemical Reactions: I = O A = G - C  Batch Process:A = G - C

Heat, Work, and Energy  Kinetic Energy: E K = (mv 2 ) / 2 – Energy due to velocity  Potential Energy: E P = mgh – Energy due to height

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

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.

Open Forum  Assignment: Handout or visit website.

Analytic Method 1.Define the problem and summarize the problem statement. 2.Diagram and describe. 3.State your assumptions. 4.Apply theory and equations. 5.Perform the necessary calculations. 6.Verify your solution and comment.

Problem #1 – Statement  Robert lives 65 miles from you. You both leave home at 3:00 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?

Problem #1 – Summary  At what time will you pass Robert?

Problem #1 – Solution  Initial time = 3:00 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 3:43 pm.

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?

Problem #2 – Summary a)Time to transfer in (hrs) ? b)% of the spherical tank filled?

Problem #2 – Solution

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?

Problem #3 – Summary  Who will win the bet? – (who has less area since they paint at the same rate?)

Problem #3 – Solution

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.

Problem #4 – Summary  Determine the mass flow rate for the vapor and residual mixture. x y 100 kg/hr 50 % benzene 50 % toluene  60 % benzene 40 % toluene  37.5 % benzene 62.5 % toluene

Problem #4 – Solution

Problem #4 – Solution cont.

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.

Problem #5 – Summary  Total amount of coolant wasted in six months (in gallons)?

Problem #5 – Solution