ME 311 Mechanical Measurements Page 1 of 6 Wind Tunnel Laboratory. Name: Group: Campus Mail:

Similar documents
Measurement of Flow Rate, Velocity Profile and Friction Factor in Pipe Flows S. Ghosh, M. Muste, M. Wilson and F. Stern

5.2 Exponent Properties Involving Quotients

Goals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite

R. I. Badran Solid State Physics

Physics I Math Assessment with Answers

Math 2260 Written HW #8 Solutions

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives

Electricity and Magnetism Electric Dipole Continuous Distribution of Charge

The area under the graph of f and above the x-axis between a and b is denoted by. f(x) dx. π O

Name Date. In Exercises 1 6, tell whether x and y show direct variation, inverse variation, or neither.

Chapters 4 & 5 Integrals & Applications

Problem set 5: Solutions Math 207B, Winter r(x)u(x)v(x) dx.

Mathematics Number: Logarithms

Unit Six AP Calculus Unit 6 Review Definite Integrals. Name Period Date NON-CALCULATOR SECTION

Part I: Basic Concepts of Thermodynamics

Mathematics Extension 1

adjacent side sec 5 hypotenuse Evaluate the six trigonometric functions of the angle.

5.5 The Substitution Rule

y b y y sx 2 y 2 z CHANGE OF VARIABLES IN MULTIPLE INTEGRALS

DERIVATIVES NOTES HARRIS MATH CAMP Introduction

Calculus AB. For a function f(x), the derivative would be f '(

Math 8 Winter 2015 Applications of Integration

Unit 1 Exponentials and Logarithms

A Bi-Lateral Comparison of a 0.5 gram to gram Weight Set

5.1 How do we Measure Distance Traveled given Velocity? Student Notes

The Fundamental Theorem of Calculus Part 2, The Evaluation Part

( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that

UNIT 1 FUNCTIONS AND THEIR INVERSES Lesson 1.4: Logarithmic Functions as Inverses Instruction

Space Curves. Recall the parametric equations of a curve in xy-plane and compare them with parametric equations of a curve in space.

MATH 144: Business Calculus Final Review

Solution Set 2. y z. + j. u + j

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007

Improper Integrals. Introduction. Type 1: Improper Integrals on Infinite Intervals. When we defined the definite integral.

Lecture 7 notes Nodal Analysis

ES.182A Topic 30 Notes Jeremy Orloff

Review of Calculus, cont d

Solution for Assignment 1 : Intro to Probability and Statistics, PAC learning

1 The Riemann Integral

Unit #9 : Definite Integral Properties; Fundamental Theorem of Calculus

Loudoun Valley High School Calculus Summertime Fun Packet

The Velocity Factor of an Insulated Two-Wire Transmission Line

The Fundamental Theorem of Calculus, Particle Motion, and Average Value

Student Activity 3: Single Factor ANOVA

Chapter 19. Technology

AP Calculus AB Exam Review Sheet B - Session 1

Sections 1.3, 7.1, and 9.2: Properties of Exponents and Radical Notation

HQPD - ALGEBRA I TEST Record your answers on the answer sheet.

Chapter 3 Exponential and Logarithmic Functions Section 3.1

5.7 Improper Integrals

Objective: To simplify quotients using the Laws of Exponents. Laws of Exponents. Simplify. Write the answer without negative exponents. 1.

Continuous Random Variable X:

Integrals - Motivation

Advanced Algebra & Trigonometry Midterm Review Packet

Math 1431 Section M TH 4:00 PM 6:00 PM Susan Wheeler Office Hours: Wed 6:00 7:00 PM Online ***NOTE LABS ARE MON AND WED

The steps of the hypothesis test

Department of Mechanical Engineering ME 322 Mechanical Engineering Thermodynamics. Lecture 33. Psychrometric Properties of Moist Air

Math Calculus with Analytic Geometry II

Calculus - Activity 1 Rate of change of a function at a point.

Time in Seconds Speed in ft/sec (a) Sketch a possible graph for this function.

Polynomial Approximations for the Natural Logarithm and Arctangent Functions. Math 230

Interpreting Integrals and the Fundamental Theorem

spring from 1 cm to 2 cm is given by

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1

Tests for the Ratio of Two Poisson Rates

ECE 327 Solution to Midterm 2016t1 (Winter)

APPROXIMATE INTEGRATION

ENGI 3424 Engineering Mathematics Five Tutorial Examples of Partial Fractions

Logarithmic Functions

V E L O C I T Y a n d V E L O C I T Y P R E S S U R E I n A I R S Y S T E M S

Chapter 9 Definite Integrals

fractions Let s Learn to

Numerical integration

MA123, Chapter 10: Formulas for integrals: integrals, antiderivatives, and the Fundamental Theorem of Calculus (pp.

Review of basic calculus

The Fundamental Theorem of Calculus. The Total Change Theorem and the Area Under a Curve.

BRIEF NOTES ADDITIONAL MATHEMATICS FORM

Lesson 1: Quadratic Equations

INTRODUCTION TO INTEGRATION

SESSION 2 Exponential and Logarithmic Functions. Math 30-1 R 3. (Revisit, Review and Revive)

Lesson 5.3 Graph General Rational Functions

Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011

u( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.

2.4 Linear Inequalities and Interval Notation

We are looking for ways to compute the integral of a function f(x), f(x)dx.

Algebra Readiness PLACEMENT 1 Fraction Basics 2 Percent Basics 3. Algebra Basics 9. CRS Algebra 1

f ) AVERAGE RATE OF CHANGE p. 87 DEFINITION OF DERIVATIVE p. 99

Equations and Inequalities

Before we can begin Ch. 3 on Radicals, we need to be familiar with perfect squares, cubes, etc. Try and do as many as you can without a calculator!!!

Math 1102: Calculus I (Math/Sci majors) MWF 3pm, Fulton Hall 230 Homework 2 solutions

Quasi Steady State Modelling of an Evaporator

List all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1.

Best Approximation in the 2-norm

Experiments, Outcomes, Events and Random Variables: A Revisit

Math 190 Chapter 5 Lecture Notes. Professor Miguel Ornelas

#6A&B Magnetic Field Mapping

. Double-angle formulas. Your answer should involve trig functions of θ, and not of 2θ. sin 2 (θ) =

332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006

MATH SS124 Sec 39 Concepts summary with examples

Total Score Maximum

Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom

Transcription:

ME Mechnicl Mesrements Pge o 6 Wind Tnnel Lbortory Nme: Grop: Cmps Mil: NOTE: I my be 0-5 mintes lte becse I will be working with the vibrtion nd reqency lb grop to get them strted. Plese go over this lb hndot while yo re witing. Overview Objectives: Find the velocity in wind tnnel by mesring the dierence between the totl pressre nd sttic pressre o the ; Estimte the ncertinty in this velocity mesrement or the entire rnge o velocities ond; Identiy the cses o ncertinty nd wys to redce them. Instrmenttion: Pitot-sttic tbe Dierentil pressre gges (ll-scle rnges o nd in H O) Brometer Thermocople Schemtic o Pitot-sttic tbe: low direction to mnometer to mnometer

ME Mechnicl Mesrements Pge o 6 Wind Tnnel Lbortory Smple Clcltion: Recll the Bernolli s eqtion yo lerned in ES 0, p totl p sttic V ind the velocity o the moving (in t/sec) i the totl pressre is 60 inches H O nd the sttic pressre is 59 inches H O, nd the density o is 0.0077 slg/t. Ction with nit conversion: Yo will need to mke etensive se o nit conversions nd mke sre the nits o every term in this eqtion re consistent with one nother. Feel ree to se the inormtion on the net pge.

ME Mechnicl Mesrements Pge o 6 Wind Tnnel Lbortory Conversion o pressre rom inches o wter or inches o mercry to lb/t Hydrosttic eqtion: reltes the height o lid colmn to pressre dierence p lid g h lb t slg t t s Units conversion: ( t) wter slg.94 t nd Hg wter sg Hg.6 Compting density rom pressre nd tempertre nder tmospheric conditions Idel gs eqtion: reltes pressre, tempertre, nd density o n idel gs (when is the idel gs model pproprite?) R 8. 4 kj kmol K M 8. 97 kg kmol R R kj t lb 0.87 or 76 M kg K o slg R pv nr T R ( nm ) T m R T p R T M lb slg t lb o Units conversion: ( R) Compting Velocity t t slg o R p V t recll lb slg s Unit conversion: lb t t s slg t slg t s t slg t

ME Mechnicl Mesrements Pge 4 o 6 Wind Tnnel Lbortory Dt Sheet P tm in Hg T o F Reding Uncertinty o gge in H O Reding Uncertinty o gge in H O Trget Fn Speed (RPM) Actl Fn Speed (RPM) P (in H O) [sing gge nless noted] 000 000 ( gge) 00 Above XXXXXXXXX XXXXXXXXX 00 000 000 ( gge) Below XXXXXXXXX XXXXXXXXX 000 000 ( gge) 00 Above XXXXXXXXX XXXXXXXXX 00 000 000 ( gge)

ME Mechnicl Mesrements Pge 5 o 6 Wind Tnnel Lbortory Dt Redction Averge mesrements or the ctl n speed nd corresponding pressre dierences or ech nominl n speed sing only the dt rom the " gge. Do the sme or the " gge t 000 RPM. Compte the velocities or these verge pressre dierences. Uncertinty Anlysis Compte the ncertinty in pressre dierence by root-sm-sqring the two sorces o ncertinty in pressre: instrment ccrcy nd redbility. The instrment ccrcy is qoted s 0.5% o the ll-scle reding. The redbility is p to yor decision, typiclly / or /4 o scle division on n nlog gge. Note tht the ncertinty will be dierent or the two gges (why?) Compte the corresponding ncertinty in velocity (U v ) or this ncertinty in pressre dierence. This will involve tking prtil derivtive to get the sensitivity coeicient (the ctor tht determines how mch the velocity chnges de to chnge in pressre.) Plot V, VU v, nd V-U v ginst RPM on the sme grph or the dt rom the " gge only. Use mrkers nd solid line or the V verss RPM dt, bt only dshed line (i.e., no mrkers) or the ncertinty lines. Trn In This lb hndot with qestions nswered below nd dt sheet illed ot. Ech person mst trn in his/her own lb, bt I epect yo to work together. Plot o V verss RPM with ncertinty bnds Spredsheet with rw dt nd clcltions Smple clcltion o ncertinties Qestions To Answer. Compre the velocities nd ncertinties ond with the " gge nd the " gge t 000 RPM. Do their ncertinty intervls overlp? Wht does this imply?. Wht does the instrment ccrcy (0.5% o ll scle) imply bot the selection o gge or pressre mesrement?. Wht hppens to the ncertinty in velocity s velocity increses? Why?

ME Mechnicl Mesrements Pge 6 o 6 Wind Tnnel Lbortory Notes on the Uncertinty Anlysis When yo hve clclted qntity (,,..., n ) where clclted reslt bsed pon nmber o independent prmeters. i mesred vles o the independent prmeters (i.e. the nominl vles o the prmeters) i ncertinty in i net ncertinty in the clclted reslt de to the combined eects o i To determine how the vritions in i inlence the ncertinty o, we se n n L I the clcltion is prodct o terms, the clcltion cn be simpliied considerbly. For emple: then the percent ncertinty in is where i the eponent o i in the eqtion i i i vrible % ncertinty o