Problem Solving & Energy Balances 2: Using Units to Understand (and save your butt)

Transcription

1 Problem Solving & Energy Balances 2: Using Units to Understand (and save your butt) ABET Course Outcomes: 1. solve and document the solution of problems involving elements or configurations not previously encountered (e) 2. solve problems using multiple approaches including varied analytic approaches, diagrams, formal solution steps or simple computer programs (e) By the end of this today you should be able to: Explain and use units in problem solving for unit conversions identifying term type inferring likely equation Explain basic Electrical Units 14 th Annual Opportunity Banquet Career Fair Banquet Speaker: P.E., Director of MDOT Games & Prizes!!! Handout: none Class Plan Lecture Outline: 1. Review: Chain to Remember & Metric Unit conversions Intro: 2. Evaluating physical meaning of units 3. Inferring functional form 4. Electrical units: Power and energy Next Slide: Introduce Quick review of the Chain (Future: animate blanks in diagram for students to id) distance time a. Energy b. Impulse c. Force d. Horsepower e. Velocity Velocity 1 Momentum A Chain to Remember time acceleration x mass x mass Force 2 Area Pressure x distance Energy 3 time Power

2 Unit Conversions (Review): Complete these metric conversions: Simple: How many bar (10 5 Pa) is 130,000 Pa?, = 1.3 bar / Squared: What is the area of a 4 x 4 square in m 2? 4 x 4 = 16 in 2 x ( m/in) 2 = m Compound: Convert 10 mi/hr to m/s (note: m/mi) 10 mi m min. hr 4.47 m = hr mi 60 s 60 min s Conversion: Students should have tried go over review (next slide) Simple: How many bar (10 5 Pa) is 130,000 Pa? uses simple conversion factor multiplication can cancel units Squared: What is the area of a 4 x 4 square in m 2? again simple conversion factor multiplication critical to square conversion factor to convert squared unit Compound: Convert 10 mi/hr. to m/s uses a railroad style table to complete conversion Helpful for complex conversions Notice two different approaches used to keeping track of units Always consider whether units are getting larger or smaller if units are smaller the # must be larger if units are larger the # must be smaller Use Units/Dimensions for: Unit Conversion: Check an equation or calculation, Make units consistent Physical Nature: Determine the nature of a group or equation Possible Equations: Determine the likely relationship between variables Next Slides Introduction Making units work for you Unit Conversion basic but important, where we were last time This Class: Physical Nature using units to identify the nature of a term (is it a force, an energy, ) Possible Equations using units to infer functional form

3 Physical Nature: The group P*V (pressure times volume) comes up frequently in thermodynamics: What are the metric basic units for this group? The resulting units are equivalent to the units to In the group PV (pressure times volume) comes up frequently in thermodynamics: What are the MKS basic units of this group? The mks units for P are kg/(m s 2 ) The mks units for V are m 3 PV [=] (kg/(m s 2 ))(m3) = kg m 2 /s 2 The resulting units are equivalent to the units for (circle one): Physical Nature: For the group F*v (force times velocity) What are the metric basic units for this group? Physical Nature: For the group Fv (force times velocity) What are the SI (MKS) basic units for this group? The resulting units are equivalent to the units to The resulting units are equivalent to the units to

4 Determining Possible Equations: Consider a mass sitting on a frictionless surface attached to a horizontal spring. If the spring is stretched and then let go, it will oscillate with a period Ts (units of time). This period is related to the mass on the spring (m) and the spring constant (k) which has units of force per length. The basic equation is of the form: 2 g ( m, k ) T s (i.e., Ts = 2 times a function of m & k) Using the MKS basic units, propose the form of the function g(m, k) that has proper units. Previous slide: problem Using units to find functional form Need to explain the two variable functional nomenclature (i.e., unknown function of m and k) Give students/groups a little time to try solving Goal is that they see what the do an do not understand Next slide Walk through a simple formalism for these problems Step titles appear right away Solution pieces are animated to appear one at a time. Possible Steps (a formalism): 0. Setup: Determine the units of the system m [=] kg, k [=] (kg m/s 2 ) / (m) = kg/(s 2 ) T S [=] s 1. Goal: What are the units you need to end up with (the LHS) the function must end up with units of time LHS = T S [=] s 2. Easy Stuff: Find the unique sources of units in your goal k must be in the denominator of a fraction inside a square root.? s g ( m, k ) [ ] k kg 3. Clean up: Get rid of stuff you do not want the numerator must be mass to cancel out the kg m m g ( m, k ) T k s 2 k Pressure: P [=] kg / m s 2 Velocity: v [=] m / s Density: [=] kg / m 3 P = f( v, )? How would you relate pressure to velocity, for flow through a pipe that suddenly narrows? (use units and density) Steps 0. Setup: List units of all terms: 1. Goal: Look at units desired (equation s LHS) 2. Easy Stuff: Consider needed units that are unique in remaining terms 3. Clean up: Use remaining groups to add or get rid of additional factors

5 How would you relate, pressure to velocity? (Ask students to try, similar to oscillation problem) 0. Setup: List units of all terms: Pressure: P [=] kg / m s 2 Velocity: V [=] m / s Density: [=] kg / m 3 P =? Units can help you by: Determining correct/consistent units (Unit Conversion): Check an equation or calculation, Make units consistent 1. Goal: Look at units desired (equation s LHS) Question asks for P [=] kg / m s 2 2. Easy Stuff: Consider needed units that are unique in remaining terms to get kg, need density [=] kg / m 3 3. Clean up: Use remaining groups to add or get rid of additional factors cancel out m 2 in denominator, need s 2 in denom. v 2 accomplishes this P v 2 Finding what a term means (Physical Nature): Determine the nature of a group or equation Inferring what the correct equation might be (Possible Equations): Determine the likely relationship between variables Quantity Charge Current Voltage Resistance Electrical Variables & Units A fluid analogy Unit Coulombs Ampere Volts Ohms Watt s law: Power = Current x Voltage (Potential Energy per Mass) Main point of these two slides 1. previous: review basic electrical concepts current as a flow of electrons (electrons per time) voltage is energy per electron (work per electron) (and the logic of power term) voltage x current = (energy/time) = power! 2. next: note electrical and mechanical power are the same 3. next: Also note the introduction of a new basic unit current 4. Basic units rarely used in ECE, what are used: Voltage (V), Current (I), Resistance ( ) and Power (W) 5. How would you get an energy unit (what is on your electric bill) power is energy/time so power x time = energy (e.g. kw hr.)

6 Electrical Energy Units Quantity Definition Unit What is it Current Ampere (A) A flow of electrons Voltage Volt (V) Energy carried by electrons Power Watt (W) Rate of Energy (just like mechanical power) Energy E =?