Fill This Form To Receive Instant Help
Fill This Form To Receive Instant Help
Homework answers / question archive / MECH5465M Week 1, lecture 1-2, 2022/2023 Experimental Data A general overview MEHC5465M Lecture 1-2 • Week 2 Lecture 2-1: Basic statistics for analysis of experimental data Lecture 2-2: Inferential statistics • Week 3, Time dependent data • Week 4, Design of Experiments • Week 1 Lecture 1-1: Introduction to the module, basics of experimentation Lecture 1-2: Characteristics of experimental data, precision and accuracy MECH5465M 2022/23, Lecture 1-2 2 Experimental scientific approach in problem solving • Preparation • Design of experiments • Preliminary experiments • Repeatability Performing an experiment consists of all the steps included in the scientific approach
MECH5465M Week 1, lecture 1-2, 2022/2023 Experimental Data A general overview MEHC5465M Lecture 1-2 • Week 2 Lecture 2-1: Basic statistics for analysis of experimental data Lecture 2-2: Inferential statistics • Week 3, Time dependent data • Week 4, Design of Experiments • Week 1 Lecture 1-1: Introduction to the module, basics of experimentation Lecture 1-2: Characteristics of experimental data, precision and accuracy MECH5465M 2022/23, Lecture 1-2 2 Experimental scientific approach in problem solving • Preparation • Design of experiments • Preliminary experiments • Repeatability Performing an experiment consists of all the steps included in the scientific approach. Remember that recording data is only a step in a longer often iterative process. Experiments Science 1. Discovery/exploratory experiments Engineering 2. Experiments to test and validate a hypothesis/theory/model 3. Measurements in complex systems where available theory is sufficient 4. Experiments to validate powerful reliable computational solvers Types of Experiments: MECH5465M 2022/23, Lecture 1-1 4 Quantitative experiments Experimental data 5 • In engineering, we may perform some preliminary qualitative experiments to develop the initial hypotheses and identify the important parameters and variables. MECH5465M 2022/23, Lecture 1-1 - Distance - Mask type - Activity Independent variables Parameters - Temperature - Humidity - Ventilation Quantitative experiments Experimental data 1. 2. Abkarian, M. et al. (2020) PNAS 117 (41) 25237-25245. 2. Asadi, S. et al. (2020) scientific reports 10, 15665. 6 • After this preliminary tests, experimentalists are often interested in building a setup that allows quantification of variables (recording experimental data) and finding correlations between the critical parameters. • In engineering, we may perform some preliminary qualitative experiments to develop the initial hypotheses and identify the important parameters and variables. Quantitative experiments Experimental data 1. 2. Abkarian, M. et al. (2020) PNAS 117 (41) 25237-25245. 2. Asadi, S. et al. (2020) scientific reports 10, 15665. 7 • In order to be able to design informative quantitative experiments, a good knowledge of problem and previous studies on the topic is essential. • After this preliminary tests, experimentalists are often interested in building a setup that allows quantification of variables (recording experimental data) and finding correlations between the critical parameters. • In engineering, we may perform some preliminary qualitative experiments to develop the initial hypotheses and identify the important parameters and variables. Experimental data • Base quantities and units of measurements • Data variability • Organising the data • Estimation/anticipation of data before measurements MECH5465M 2022/23, Lecture 1 8 -2 Estimation 9 For most of the measurements of that you will need to perform in engineering, you can follow your engineering common sense and simple empirical and/or theoretical to estimate at least a range or an order of magnitude for the quantity before performing the measurements. Such rough estimates are essential before you start performing any experimental measurements and reports of measurements that include order of magnitude errors are by no means acceptable. Remember that the error in the measurement can acquire only values that are equal to a fraction of the quantity of interest and not multiples of that quantity. Additionally, if you are asked to measure the temperature of water in an open pot in your kitchen and you report the value 110 °C, you need to go back and work on your common sense as an engineerJ MECH5465M 2022/23, Lecture 1-2 Lab notebook 10 During the experiments, the settings on the instruments, environmental conditions , methods of data acquisition and even the experimentalist ay change. Therefore, an accurate record of “what has been done” during every experiment is essential. Curie’s lab notebook - Parameters - Observations - Thoughts - Schematics - Preliminary graphs Base quantities and units of measurements The first step in performing quantitative experimental measurements that can provide understanding and independent comparison for further development is an agreement on a set of measurement units. 11 The base quantities of a system is a group of quantities that cannot be expressed in terms of other quantities, while all the other quantities can be expressed in terms of base quantities. The ISQ (International System of Quantities) defines seven base quantities. Quantity Symbol for dimensions Mass M Length L Time T Temperature Θ Amount of substance N Electrical current I Luminous intensity J MECH5465M 2022/23, Lecture 1-2 Metric system, SI (Système international d'unités) Principles of metric system. SI system. • Each of the fundamental dimensions of nature is expressed by a single base unit of measure. https://en.wikipedia.org/wiki/Metric_system • For an unlimited number of quantities derived from the fundamental base units of the system, units derived from the base units are used. For example, the cubic metre is the unit for the volume and is derived for the base unit length. • These derived units are coherent, which means that they involve only products of powers of the base units, without empirical factors. • For any given quantity, whose unit has a special name and symbol, an extended set of smaller and larger units is defined that are related by factors of powers of ten, will be covered in the next slide. Quantity Symbol for dimensions Unit Mass M kilogram, kg Length L metre, m Time T second, s Temperature Θ Kelvin, K Amount of substance N mole, mol Electrical current I ampere, A Luminous intensity J candela, cd • Is the modern metric system. • Is internationally accepted. • Is the main unit of measurements used in modern scientific communications (books, conferences, lectures, journal papers) Matric system, SI (Système international d'unités) 13 Do NOT report any data in non-metric units in your reports!!! MECH5465M 2022/23, Lecture 1-2 Multiples and Subdivisions of Units Submultiples Prefix Power of 10 femto, f 10-15 pico, p 10-12 nano, n 10-9 micro, μ 10-6 milli, m 10-3 centi, c 10-2 deci, d 10-1 The derived metric units are coherent, meaning that they involve only products of powers of the base units, with no factors. For any given quantity with a special unit, an extended set of smaller and larger units is defined that are related by factors of powers of ten. Multiples Prefix Power of 10 peta, P 1015 tera, T 1012 giga, G 109 mega, M 106 kilo, k 103 hecto, h 102 deca, da 101 Be consistent throughout your report/scientific writing. It is often expected to use a single submultiple or multiple when reporting measurements of the same quantity. Reporting quantities and units in scientific texts Use of an italic, bold italic and roman fonts has a specific meaning when used for symbols in scientific text and equations: • Symbols for the fundamental physical constants are always regarded as quantities and they must always be italic. • Vectors, tensors and matrices are denoted using bold italic fonts. • Symbols representing physical quantities (or variables) are italic, but symbols representing units, or labels, are roman. L = 2 m μ = 2 μm • When symbols are supplemented with subscripts or information in brackets to further specify the quantity, the additional symbols are either italic or roman depending on whether they represent physical quantities or labels. Lt = 2 m (t refers to time) Lp = 2 m (p refers to plate) Reporting quantities and units in scientific texts Use of an italic, bold italic and roman fonts has a specific meaning when used for symbols in scientific text and equations: A summary of the main rules is provided at https://iupac.org/wp-content/uploads/2016/01/ICTNS-Onthe-use-of-italic-and-roman-fonts-for-symbols-in-scientific-text.pdf. • Symbols for mathematical operators are always roman. This applies to the symbol ? for a difference, δ for a small difference, d for an infinitesimal difference (in calculus), and to capital Σ and Π for summation and product signs. • The symbols π, e (base of natural logarithms), i (square root of minus one), etc. are always roman. • The symbols for named functions such as log (lg, ln or lb), exp, sin, cos, tan, erf, div, grad, curl or rot are always in roman. Tabulation of Data Type 1 data. Repeated measurement of a quantity that remains unchanged in time. In this case, the table reports the measurement in every repeat: Type 2 data. Measurement of quantity A that is dependent on B at varying quantities of B. * Instead of curved brackets [g] and /g or , g are also often used. In this module, we use (g). Experiment 1 2 3 4 5 6 7 8 9 10 Mass (g)* 12.01 12.00 12.02 11.98 12.01 12.02 11.99 12.04 12.00 11.99 Table 1. Measurement of mass of a 1 cm3 of copper at temperature T = 20 °C. Temperature (°C) 0 5 10 15 20 25 30 35 40 45 Mass (kg) 999.84 999.97 999.70 999.10 998.20 997.05 995.65 993.92 992.20 990.2 Table 2. Measurement of the mass of 1 m3 of water at varying temperature. For type 2 measurements, we often want to perform several measurements at every temperature. This allows us to identify relationships between A and B as well estimating the variations in measurements using a given instrument. Significance of graphs Slutsky, D. J. The Effective Use of Graphs. J. Wrist Surg. 3 (2014) 67–68. 18 A graphs is the most common method to demonstrate relationships between variables tested in an experiments. The purpose of a graph is to present a larger number of data points in a manner that is easy to perceive. Although you all have access to a variety of software that provide support for scientific plotting of the data, you will need knowledge of the basic rule for plotting graphs to be able to present your findings effectively. Graphs should always have at minimum a caption, axes and scales, symbols, and a data field. Plotting graphs Basic rules 19 If possible, plotting graphs during the course of experiments is preferred to plotting graphs after finishing all experiments as this permits finding interesting or unexpected patterns and relationships. x-y graphs are the most common graphs in engineering. In such graphs, the y-axis normally represents the dependent variable while the x-axis presents the independent variable. Both axes should have titles and unit of measurements. The limits of x and y axes should be decided based on the range of measurements. Commonly used types of graphs are: • Scattergram • Line graph • Bar graph • Histogram • Pie chart MECH5465M 2022/23, Lecture 1-2 0.015 t L (µm) 0 20 40 60 t (s) 0 1000 2000 3000 X-Y graphs, Linear scale graphs If convinced from the measurements and/or theoretical predictions that the range of measurements in x and y covers one order of magnitude in units of measurement and the data is linearly distributed, you can choose to plot your data on linear (arithmetic) scales. On linear/arithmetic scales, equal distances represent equal amounts. Note that choosing linear scales does not imply that there is a linear relationship between the variables. 0.85 t 0.5 d (µm) 0 10 20 t (s) 0 200 400 L d MECH5465M 2022/23, Lecture 1-2 20 X-Y graphs, Logarithmic graphs η 0 (mPa.s) 0 20 40 60 80 Φ/T (1/K) 6×10−4 7×10−4 8×10−4 η 0 (mPa.s) 1 10 100 Φ/T (1/K) 5×10−4 6×10−4 7×10−4 8×10−4 9×10−4 The dependent variables presented on the y-axis expand at least two orders of magnitude, therefore, in order to accommodate the entire range of data on a linear scale, the data corresponding to the viscosities lower than 10 cannot be easily read from the graph. Instead, if a logarithmic scale is chosen for the y-axis, the entire range of the data is easily readable. This is often referred to as a semi-logarithmic of log-linear graph. Anton Paar MECH5465M 2022/23, Lecture 1-2 X-Y graphs, Power laws 22 2.5 × d-2 α (µm/s) 0.01 0.1 1 d (µm) 2 5 10 L 0.015 t L (µm) 0 20 40 60 t (s) 0 1000 2000 3000 d α 1 Log-log plots are useful when both x and y data have data that span over orders of magnitude and when we expect a power-law relationship between the two quantities. ? = ??! log"# ? = log"# ? + ? log"# ? Tabulation of Data Type 1 data. Repeated measurement of a quantity that remains unchanged in time. In this case, the table reports the measurement in every repeat: Type 2 data. Measurement of quantity A that is dependent on B at varying quantities of B. * Instead of curved brackets [g] and /g or , g are also often used. In this module, we use (g). Experiment 1 2 3 4 5 6 7 8 9 10 Mass (g)* 12.01 12.00 12.02 11.98 12.01 12.02 11.99 12.04 12.00 11.99 Table 1. Measurement of mass of a 1 cm3 of copper at temperature T = 20 °C. Temperature (°C) 0 5 10 15 20 25 30 35 40 45 Mass (kg) 999.84 999.97 999.70 999.10 998.20 997.05 995.65 993.92 992.20 990.2 Table 2. Measurement of the mass of 1 m3 of water at varying temperature. For type 2 measurements, we often want to perform several measurements at every temperature. This allows us to identify relationships between A and B as well estimating the variations in measurements using a given instrument. Uncertainty MECH5465M 2022/23, Lecture 1-2 True Value and Error True Value (TV) is the actual value of a quantity to be measured. Error is the difference between the measured value (x) and the True Value (TV). Δ? = ? − ?? TV is not known, naturally, the error is not definable either. To define the uncertainty is to define a range for the TV. We cannot define the error but can define the uncertainty band in which the TV will exist if we know the accuracy and precision of measurements. To define this range, we must perform repeated experiments (measurement variability/uncertainty) and/or quantify the limitations of experimental instruments (precision). 25 True value Precise Accurate Imprecise Accurate Imprecise Precise Inaccurate True value value frequency frequency value value value Precision defines how close a series of measurements are to one another. Accuracy defines how close a measurement is to the true value. Precision vs Accuracy Inaccurate Precision vs Accuracy Precision defines how close a series of measurements are to one another. Experiment 1 2 3 4 5 6 7 8 9 10 Mass (g) 12.01 12.00 12.02 11.98 12.01 12.02 11.99 12.04 12.00 11.99 Copper has density of 8.96 g/cm3 so the mass of the cube (the estimated true value) is 8.96 g. 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 0 2 4 6 8 10 12 Mass (g) Experiment No. Example 1. I used an uncalibrated balance with 0.01 g resolution to measure the mass of 1 cm3 of copper, and recorded the following 10 readings: The measurements are precise. The difference between the maximum and minimum of the measurements is 0.06 g, but they are far from the true value, so they are inaccurate. 8.00 8.50 9.00 9.50 10.00 10.50 11.00 11.50 12.00 12.50 0 2 4 6 8 10 12 Mass (g) Experiment No. MECH5465M 2022/23, Lecture 1-2 MECH5465M 2022/23, Lecture 1-2 Precision vs Accuracy Accuracy defines how close a measurement is to the true value. Example 2. I used a less expensive calibrated balance with 0.1 g resolution to measure the mass of 1 cm3 of copper, and recorded the following 10 readings: The measurements are not as precise those performed in Example 1 (the difference between the maximum and minimum value is 0.4 g), but they are accurate. Experiment 1 2 3 4 5 6 7 8 9 10 Mass (g) 8.8 9.0 9.1 9.0 8.9 9.2 8.9 9.0 8.9 8.9 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 0 2 4 6 8 10 12 Mass (g) Experiment No. 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 0 2 4 6 8 10 12 Mass (g) Experiment No. Measurements Expected value Copper has density of 8.96 g/cm3 so the mass of the cube (the estimated true value) is 8.96 g. Precision vs Accuracy MECH5465M 2022/23, Lecture 1-2 30 Ideally, we seek for precise AND accurate experimental measurements. Precise measurement with low accuracy are USELESS unless a calibration curve is provided for the instrument. Accurate measurements performed with lower precision instruments provide informative reliable estimation of the true value if measurement uncertainty is documented. Data variation 31 Uncertainties Despite the effort of the experimentalist to perform accurate measurements and the quality of the instrument, there will naturally be variations in experimental data. Your job will be to reduce this variation as if possible but certainly to report it accurately. Do take notes of any variations that you note when performing the measurements in a laboratory. Any time a set of experimental data is reported the associated uncertainties should be included. (this will be the topic of Week 2 lectures) MECH5465M 2022/23, Lecture 1-2 MECH5465M 2022/23, Lecture 1-2 Uncertainty Experimentation relies on measurements with various devices. Even if we repeat multiple measurements of the same quantity with the same instrument, we will record varying values confirming that there is certain level of uncertainty in the measurements. The uncertainty and variability is an inherent feature of the measurements, it is the duty of the experimentalist to identify and quantify this variation. So, a big task in experimentation is to quantify the measurement uncertainty and if possible, identify the main source that causes the variability and try to reduce it effects when redesigning the experiments. 32 MECH5465M 2022/23, Lecture 1-2 Errors and uncertainty in experimental measurements 33 Systematic error • Offset error Random error/uncertainty in repeated measurements Measurement uncertainty/accuracy in a single measurement • Instrument uncertainty/accuracy • Reading uncertainty We will use statistical analysis to estimate the uncertainty due to the random error in more detail in the next lecture. • Calibration uncertainty • Gain error MECH5465M 2022/23, Lecture 1-2 • Resolution uncertainty • Reading uncertainty • Calibration uncertainty 34 Uncertainty of a single measurement MECH5465M 2022/23, Lecture 1-2 35 Calibration uncertainty Calibration of the measurement instruments is crucially important wherever accuracy of the measurements is intended. Most laboratory equipment that you use are calibrated using another instrument that has been calibrated and references to a known set of parameters. The equipment used as a reference should itself be directly traceable to equipment that is calibrated according to ISO/IEC 17025. If using uncalibrated equipment, or an equipment with an expired calibration license, try to compare your initial measurements with those recorded on a calibrated tool. 36 Resolution uncertainty All measurements are limited (in terms of accuracy) by the instrument that is used, even if all necessary care is taken by the experimentalist. On a scale measuring device, the uncertainty is ± half of the resolvable division on the the instrument. The resolution limit of the instrument you are using is the smallest uncertainty that you can report for a single measurement. ± 0.5 mm ± 0.01 mm ± 0.01 g ± 0.0001 g On a digital measuring device, the uncertainty is ± the resolvable division on the the instrument. MECH5465M 2022/23, Lecture 1-2 37 Instrument uncertainty Resolution/calibration uncertainty of an instrument represents the minimum resolvable unit when using performing measurements using that specific device. Example 3. The stopwatch on my phone has a resolution/uncertainty of 0.01 s, but if I use this stopwatch to measure the duration of any event, I need to tap on the screen to record the start and the stop time. My tapping action introduces a ‘reaction error’ into the measurement that is somewhere between 0.4 to 1.5 s in my measurements. Try the stopwatch on your phone. Tap to start and immediately tap again to stop. Repeat this exercise 10 times. Larger uncertainties are often introduced into the measurements due to human interactions and environmental effects. MECH5465M 2022/23, Lecture 1-2 38 Reading uncertainty In practice, some environmental effects may cause difficulty in reading a measurement. Reading uncertainty can often be eliminated or at least minimized: Example 4. When holding a graduated measuring beaker in the hand, there is a large reading uncertainty in measurement of the volume of the liquid inside. You can place the beaker on a table to stabilize the top interface of the liquid and perform a better reading. You can further improve your reading uncertainty by levelling the table before the measurement to ensure a flat interface at the top. 39 Reading uncertainty Not all quantities will remain constant throughout the measurement or across the field where the measurement is performed. If it is not possible to eliminate the source of reading uncertainty, you must report the larger uncertainty (comparing the measurement uncertainty and the instrument uncertainty in such cases) Example 5. You are reporting the room temperature at the time of a measurement with a thermometer which has ± 1 °C uncertainty. However, the room temperature varies between 24 ± 1 °C and 28 ± 1 °C, during the course of the measurement. In such a condition, the uncertainty in the reported room temperature during a single measurement is not ± 1 °C, but it is more reasonable to report the room temperature as 26 ± 3 °C. Example 6. You are reporting the room temperature at the time of a measurement with thermometers which have ± 1 °C uncertainty. However, the three thermometers that are installed around the room show 23 °C, 25 °C, and 27 °C. In such a condition the uncertainty in the reported room temperature during a single measurement is not ± 1 °C and it is more reasonable to report the room temperature as 25 ± 3 °C. Systematic Errors Offset error Consider example 1-1 again: Experiment 1 2 3 4 5 6 7 8 9 10 Mass (g) 12.01 12.00 12.02 11.98 12.01 12.02 11.99 12.04 12.00 11.99 Calculating the mean (?( = 12.006 g) and the uncertainty based on the range (!.!# $! = 0.006), we can estimate the mass of the cooper cube: m = 12.01 ± 0.01 g Although precise, measurement of m is far from the expected value of 8.96 g and there is systematic offset error of around + 3.05 g in these measurements. WATCH OUT!!! If no accurate benchmark or measurements from another instrument is available, identification and quantification of the systematic error may not be simple. MECH5465M 2022/23, Lecture 1-2 Gain error Unlike the offset error, the magnitude of the gain error is not constant. V (cm3) 0.010 0.125 1 mc (g) 0.090 1.120 8.960 mm (g) 0.098 1.232 9.856 mm – mc (g) 0.008 0.112 0.896 Example 7. Let’s get back to the example of measuring the mass of a cube of copper. This time we measure the mass of 3 different cubes of different dimensions/volumes which we call the measured mass mm. The cubes are calibrated beforehand, so we know their accurate mass which we call the calibrated mass mc . 0 0.2 0.4 0.6 0.8 1 0.000 5.000 10.000 m m - mc (g) mc (g) The gain error increases as the quantity increases. The fractional error in this example remains constant at 10%, however, the absolute error is increasing. You may see such constant fractional errors stated in manuals of different experimental devices. Gain error Example 8. Pay attention to the gain error when designing your experiment and choosing your measurement device. 0.35 mbar 6.8 mbar 2 mbar 4 mbar If you are trying to perform a pressure measurement in the system that is lower than 2 mbar, you can only use MPS 0. Elveflow pressure sensor data sheet Errors and uncertainty in experimental measurements 44 Systematic error • Offset error Random error/uncertainty Measurement uncertainty/accuracy in a single measurement • Instrument uncertainty/accuracy • Reading uncertainty We will use statistical analysis to estimate the uncertainty due to the random error in the next lecture. • Calibration uncertainty • Gain error Question? Random Error and uncertainty in multiple measurements This lecture covers the concept of uncertainty analysis for multiple measurements. Statistical analysis of multiple measurements and larger data sets will be discussed in Week2. Uncertainty of multiple measurements The best estimate of a quantity that has been repeatedly measured is the average of all measurements. The average of a sample group of measurements is referred to as the mean and is labelled as ??: ??= ∑$ % ?& ? Experiment 1 2 3 4 5 6 7 8 9 10 Mass (g) 8.96 8.98 8.95 8.92 8.95 8.97 8.94 8.98 8.96 8.94 ?! = !.#$%!.#!%!.#&%!.#'%!.#&%!.#(%!.#)%!.#!%!.#$%!.#) *+ = 8.955 g Before we move on, the important question is: what is the significant figure in the mean value of a quantity measured with a certain uncertainty. Significant figures • All non-zero figures are significant. Place holders which bring 0.00524 m the measurement into the right place holder 3 significant figures • If reported numbers are greater than 10, any 0 at right end of the number is not counted as a significant figure unless explicitly stated: 1020 m 3 significant figures • Zeros within a number are significant. • Place holder zeros are not significant. • Zeros that are not place holders are significant. 0.002456 4 significant figures 1234 1.002767 7 significant figures 2.8880 5 significant figures MECH5465M 2022/23, Lecture 1-2 Reporting measurements and uncertainties 524 mm 3 significant figures 3 significant figures A simple and general method to eliminate all ambiguities related to significant figures is to use the scientific notations: 0.00524 m = 5.24 x 10-3 m 1020 m = 1.020 x 103 m 4 significant figures 1020 m = 1.02 x 103 m 3 significant figures MECH5465M 2022/23, Lecture 1-2 50 Rules in reporting the measurement uncertainty Rule 1. Experimental uncertainties are just an estimation and cannot have more significant figures than the measurement. It is generally accepted that the uncertainty should be stated to one significant figure. Rule 2. When stating the measurement, the last significant figure of the measurement (counting from the left) should be in the same place as the significant figure of the uncertainty. Example. Do not report an uncertainty of ± 0.052 m Example. Do not report 122.45 ± 0.5 m Example. Do not report 1035.2 ± 10.2 m but report ± 0.05 m instead. but report 122.5 ± 0.5 m instead. but report 1040 ± 10 m instead. 51 Significant figures and rounding Example 9. Estimate the length of one chocolate cube L in the bar using the ruler below: L Length of the chocolate bar 7 = 107 mm 7 = 15.2857 mm 15.2857 mm 15.3 ± 0.5 mm 52 When adding or subtracting experimental measurements, the number of decimal places in the final quantity must be equal to the smallest number of decimal places in all measurements: Handling significant figures in calculations m = 2.4564 m + 7.69 m + 3.0 m = 13.1464 m m = 13.1 m When multiplying or dividing experimental measurements, the number of significant figures in the final quantity should be equal to the lowest number of the significant figures in all measurements: A = 10.30 m x 0.7 m = 7.21 m2 A = 7 m2 Outlier data 53 Deciding which data is reliable and which one is not, is not an easy task. General advice is to keep all the recorded data. If a data point is suspicious, try to repeat the experiment at identical conditions if possible. For large enough data sets acquired to identify trends and correlations, statistical analysis can assist in removing the impact the outliers if there is only a limited number of outlier data. It is your task to make the decision when to discard/repeat a data point and what statistical analysis to report the general behavior of the system. MECH5465M 2022/23, Lecture 1-2 Propagation of error and uncertainty MECH5465M 2022/23, Lecture 1-2 Propagation of uncertainty Simple arithmetic method Example 10 (in class): Estimate the mass of a cube of tin. The density of the block is: ρ = 7.265 g/cm3 Using a ruler with uncertainty of 0.05 cm, the length of each square side is L = 2.00 cm Mass of the cube must be: m = ρ x L3 = 58.12 g What does the balance show? If L acquires its largest quantity according to the uncertainty: mmax = 7.265 x 2.053 = 62.6 g If L acquires its smallest quantity according to the uncertainty: mmin = 7.265 x 1.953 = 53.9 g 56 Propagation of uncertainty Simple arithmetic method Example 11: Estimate the front area of the block. ? = 10 ± 0.05 cm A ? = 1 ± 0.005 cm Using a ruler with 0.1 cm accuracy to measure the height: ? = 10.00 ± 0.05 cm Using a caliper with 0.01 cm accuracy to measure the width: ? = 1.000 ± 0.005 cm ? = ?. ? = 1.000 . 10.00 = 10.00 ± ? ? ? ?!"#= 1.005 . 10.05 = 10.10 cm2 ?!$% = 0.995 . 9.95 = 9.90 cm2 ?? = &!"#'&!$% ( = 0.10 cm2 ? = 10.0 ± 0.1 cm2 is there a way to achieve a general formulation for the final uncertainty if the relationship between the variables is known. 57 Combining uncertainty ? = ? ? ? = ?0 ± ?? ?? = ?? ?? B ?? ?0 f(x) x0 x 0 + ? x x 0 - ? x f(x0) + ?f f(x0) - ?f f(x0) ? = ? ?, ? ?? = ?? ?? B ?? + ?? ?? B ?? ?0, ?0 ?0, ?0 There are cases where the error in multiple variables are uncorrelated and in such cases the formulation above often overestimate the uncertainty in the measurements. In such cases, use: ?? = ( ?? ??)(??( + ( ?? ?? )(??( 58 Propagation of uncertainty Using the derivative of the function Example 12: Estimate the front area of the block. ? = 10 ± 0.05 cm A ? = 1 ± 0.005 cm Using a ruler with 0.1 cm accuracy to measure the height: ? = 10.00 ± 0.05 cm Using a caliper with 0.01 cm accuracy to measure the width: ? = 1.000 ± 0.005 cm ? = ? ? = 1.000 x 10.00 = 10.00 ± ? ? ? cm2 ?? = ?. ?? + ?. ?? = 0.050 + 0.05 = 0.10 cm2 ? = 10.0 ± 0.1 cm2 ?? = ?(. ??( + ?(. ??(= 0. 07cm2 ? = 10.0 ± 0.1 cm2 Propagation of uncertainty Combination of variables, Exercise 2-1 Pressure drop, ?? d L Flow of liquid known flow rate Q unknown viscosity μ ?? ? = ?" ? 2 ?0# ? ?" = 64 ?? Exercise. Consider uncertainties of δ(ΔP), δ(Q), δ(d), δ(L) in pressure drop, flow rate, tube diameter and tube length, respectively. Derive the equation for calculation of the fluid viscosity and estimate the uncertainty in viscosity calculations using this method. ?? = ??0? ? MEHC5465M Lecture 1-2 • Week 2 Lecture 2-1: Basic statistics for analysis of experimental data Lecture 2-2: Inferential statistics • Week 3, Time dependent data • Week 4, Design of Experiments • Week 1 Lecture 1-1: Introduction to the module, basics of experimentation Lecture 1-2: Characteristics of experimental data, precision and accuracy MECH5465M 2022/23, Lecture 1-2 60 Question?
Introduction to practical 2
Week 6, lecture 6-1, 2022/2023
MECH5465M
Microcapillary viscometer
A detailed list of experiments to be performed for practical 2 in week 7
will be uploaded on Minerva and provided in the lab.
1
• Week 6
Lecture 6-1: Introduction to practical 2
Seminar 1 (Methods and analysis in mechanical testing of biological tissue)
• Week 7
Practical 2: Micro-capillary viscometer
• Week 8
Seminar 2 (Experimental measurements of fluid flows at microscales )
• Week 9
Seminar 3 (Tribology – the science of surfaces in contact)
• Week 11
Seminar 5 (Imaging for bioengineering)
2
• Week 10
Seminar 4 (Experimental measurement of temperature)
Practical 2
3
In this practical, you will set up and use an unconventional
microcapillary platform to measure the viscosity of fluids, based on
pressure drop measurements at different flow rates in laminar flow
conditions. This will allow you to measure the dynamic viscosity without
access to the fluid density.
On the day of the practical, you will be working in teams of 3 on an
experimental setup. Remember that every person needs to submit their
own report for this practical so ONE REPORT PER PERSON.
Marked report
4
IMPORTANT NOTICE:
If available, bring your laptop (Windows operating system) with you for practical 2.
Download and install software ESI V 3.06.00
from https://www.elveflow.com/microfluidic-products/microfluidics-software/elveflowsoftware-sdk before you arrive to your practical 2 lab sessions
You must review and understand the guidelines for setting up the experiments
for practical 2 before coming to your timetabled session in week 7.
Space and number of experimental rigs are limited in the laboratory
designated for practical 2. You must attend the session that appears in your
timetable. Upon arrival in the lab, please sign the attendance form.
References (experiments)
5• https://www.elveflow.com
• https://darwin-microfluidics.com/blogs/reviews/microfluidic-chips-a-quick-overview
• F. M. white, Fluid Mechanics, Fifth edition (2003), McGraw-Hill
• H. Bruus, Theoretical microfluidics (2008)
References (report)
6
• Youtube channel of Karen L. McKee: https://www.youtube.com/watch?v=WBdg2OLU1UY
• Wordvice Editing services: https://www.youtube.com/c/Wordvice/playlists
• How to write a first-class paper, https://www.nature.com/articles/d41586-018-02404-4
• 11 steps to structuring a science paper editors will take seriously, Elsevier Connect
https://www.elsevier.com/connect/11-steps-to-structuring-a-science-paper-editors-will-take-seriously
• How to Prepare a Manuscript for International Journals
https://www.elsevier.com/connect/six-things-to-do-before-writing-your-manuscript
• Literature Review Guide: How to organise the review, https://ait.libguides.com/literaturereview/organise
• Marco Pautasso, Ten Simple Rules for Writing a Literature Review (2013) PLOS Computational Biology
https://doi.org/10.1371/journal.pcbi.1003149
Fluid viscosity
7
• The viscosity is the measure of fluid’s resistance to gradual deformation by shear or tensile
stress.
• There are two related measures of fluid viscosity
- dynamic ? (or absolute), is a measure of internal resistance. Dynamic (absolute)
viscosity is the tangential force per unit area required to move one horizontal plane with
respect to another plane at unit velocity, considering that planes are located at unit
distance. Dynamic viscosity is measurable, and its SI unit is Pa.s.
- kinematic ?, measures how fast a given volume of fluid travels a known downward
distance when subjected to gravitational force.
Kinematic viscosity can be measured by a traditional capillary viscometer or by dividing
the dynamic viscosity by the fluid density. The SI unit of kinematic viscosity is m2/s.
• The shear resistance in a fluid is caused by molecular friction exerted when layers of fluid
attempt to slide by one another.
Fluid viscosity
Newtonian and non-Newtonian fluids
8
!
?
Δ?
Δ?
= ?
Shear stress (N/m
2
)
Shear rate (s-1)
Newtonian fluids (water)
Non-Newtonian shear thickening fluid (corn starch solution)
Non-Newtonian shear thinning fluid (ice cream, ketchup, paint)
Fluids with zero yield stress
Fluids with yield stress (toothpaste)
Measurement of fluid viscosity
Viscometer
9
1. U-tube/Otswald/capillary viscometers
4. Falling ball viscometers
2. Falling piston viscometers
3. Rotational viscometers
5. Vibrational viscometers
Measurement of fluid viscosity
Viscometer
10
1. U-tube/Otswald/capillary
Wilhelm Ostwald, Grundriss der
allgemeinen Chemie, 2. Aufl. 1891
Measures the time
for a known
volume of fluid to
travel the known
distance between
points c and d.
Typically measures
kinematic viscosity
and requires the
density to estimate
the dynamic
viscosity.
3. Rotational
HAAKE™ Viscotester™ Rotational Viscometer
Rotational viscometers estimate the
Newtonian/non-Newtonian viscosity by
analysing the torque required to rotate a
spindle submerged in a fluid at a
constant speed. The continuous rotation
of the spindle ensures calculations are
made over time, allowing timedependent viscosity measurement.
4. Falling ball
Höppler falling ball viscometer
Measures the viscosity of
transparent Newtonian fluids
by measuring the elapsed
time required for the ball to
fall under gravity through a
tube filled with a sample of
known density.
Microfluidic viscometer (commercial unit)
11
https://www.rheosense.com/what-is-viscosity
Practical 2. Microfluidic viscometer
12
Flow rate, Q
Over length, L
Pressure drop, Δ?
Practical 2:
Extra verification is done for different tube diameters.
At temperature, T
diameter, d
You measure Δ? at different flows rates and report the fluid viscosity μ assuming a
homogeneous solution.
?? = ?(?, ?, ?, ?, ?, ?, Re)
13
Practical 2. Microfluidic viscometer
Measurement of tap water viscosity
Data acquisition for practical 2
Please refer to the document provided in the lab and on Minerva.
14
15
Flow rate, Q
At temperature, T
Pressure drop, Δ? (? − ?atm)
Darcy-Weisbach equation:
??
?
= ?!
?
2
?,"
?#
For a tube of circular cross-section, ?$ = ?
diameter, d
Practical 2. Microfluidic viscometer
Over length, L
?! =
64
?? For laminar flow, , where ?? =
??,?
?
?, =
?
? , with
P Patm
Practical 2. Experiments
1. Syringe pump
controls the flow rate
Inlet
2.1. Micro capillaries
Tube 1
Tube 2
Tube 3
2.2. Microfluidic connectors
3.1. In-line gauge pressure sensor
4. Atmospheric pressure 3.2. Measurement software
outlet
5. Thermometer
16
Practical 2.
1. Microfluidic syringe pump (SyringeONE)
https://darwin-microfluidics.com/collections/syringe-pump-systems/products/syringeone-programmable-syringepump?variant=29727482282029 17
You will have access to plastic syringes for practical 2. In order to operate the syringe pump, you
will need to input the correct syringe diameter into the syringe pump at the start.
Practical 2.
1. Microfluidic syringe pump (Syringe ONE)
Set the syringe diameter
18
Practical 2.
1. Microfluidic syringe pump (SyringeONE)
Set the infusion rate
19
Practical 2.
2.1. Microcapillaries
• You have 3 pieces of microcapillaries for experiments in practical 2. These are referred to
as test tubes and are labelled. Do not remove any of the labels.
- Tube 1: FEP 1/32 inch industrial tubing natural, , 1.58 mm OD
The diameter of this tube is 0.8 mm.
- Tube 2: TFE Teflon tubing 0.5 mm ID, 1.58 mm OD
The diameter of this tube is 0.5 mm.
- Tube 3: TFE Teflon tubing 0.3 mm ID, 1.58 mm OD
The diameter of this tube is 0.3 mm.
• Measure the length of tubes that you receive, using the flexible measuring tape
mounted on the laboratory bench.
20
Practical 2.
2.2. Microfluidic connectors
• Connect the inlet tubing to the syringe using the blunt dispenser needle provided.
Make sure that the luer lock is safely in place. This tube is labelled inlet.
• Connect the end of the inlet tubing to the inlet of the pressure sensor using the red
microfluidic connector.
• Connect your test tube (labelled tube 1, 2, 3) to the other side of the pressure sensor.
• Insert the end of the test tube into outlet tank through the opening on the top.
21
Practical 2.
3.1. Microfluidic pressure sensors, Elveflow
The MPS 2 pressure sensor used in practical 2 is a gauge pressure sensor, measuring positive and negative
pressure relative to the atmospheric pressure.
You can find more details of the pressure sensor at
https://www.elveflow.com/microfluidic-products/microfluidics-flow-measurement-sensors/pressure-sensor/
22
Practical 2.
3.2. Setting up the pressure sensor on the day of practical 2
1. Install ESI – 3.06.00 before coming to your session
2. Open the software
3. Click on ADD INSTRUMENT
4. Choose instrument type as MSR and name it appropriately. Click OK to add the reader.
5. Click on ADD SENSOR
6. Choose sensor type as Pressure sensor and name it appropriately.
3
4
5
6
23
Practical 2.
3.2. Setting up the pressure sensor on the day of practical 2
6. Choose sensor type as Pressure sensor.
7. Choose MPS2-1 bar as the sensor model.
8. Make sure that the sensor is connected to the MSR reader and the channel correctly
indicates the number associated to the sensor at the back of the MSR reader.
9. When the sensor and the reader are added, click on the play sign to start the
instrument.
6 7
9
8
24
Practical 2.
3.2. Setting up the pressure sensor on the day of practical 2
10. Upon starting the instrument, a new window will appear showing the reading from your sensor.
11. Click on the previous window with graph sign to open the ESI Graph window.
12. Click on the top left corner of the window on the setting button
and set the graph configuration as illustrated.
13. Remember to reset the graph at the beginning and save your data at the end
of every test.
10 11
12
13
25
Data analysis for practical 2
26
Practical 2 data analysis and report writing
- This session covers the main data analysis steps that you need to follow and the results that
you need to produce for the report of practical 2.
- Details of the template and the sections to be included in the report will be provided in an
MS Word file on Minerva. This will be uploaded on 19th of November.
- The session on Friday 26th of November will cover the essential knowledge to write the
introduction and prepare the reference section for the report of practical 2.
27
28
Flow rate, Q
At temperature, T
Pressure drop, Δ? (? − ?atm)
Darcy-Weisbach equation:
??
?
= ?!
?
2
?,"
?#
For a tube of circular cross-section, ?$ = ?
diameter, d
Over length, L
?! =
64
?? For laminar flow, , where ?? =
??,?
?
?, =
?
? , with
P Patm
Overview of practical 2
Overview of practical 2
29
Measurement uncertainties
Pressure sensor: Refer to the website of the sensor supplier
https://www.elveflow.com/microfluidic-products/microfluidics-flow-measurement-sensors/pressure-sensor/
Flow rate of syringe pump: ± 1%
Micro capillary tube diameter: ± 0.1 mm
You will need to calculate the propagated error to viscosity values calculated in this practical using
the following relationship. Please refer to week1-lecture1-2 for more details.
30
Duration of sampling
• Sampling rate • Duration of sampling
30
32
34
36
38
40
42
44
46
48
50
0
2
4
6
8 10
Displacement (mm)
Time (s)
Here, we focus on examples of
constant frequency signals and
discuss the minimum number of
data points that must be recorded in
each cycle
.
For signals with non
-stationary means
reporting unsteady phenomena, we
discuss the concept of steady
-state the
minimum duration of data recording.
xxxx
1000
1200
1400
1600
1800
2000
2200
0 10 20 30 40
Pressure drop (mbar)
Time (s) 31
Time to steady-state (SS)
- In experimental measurements of a
variable, that is believed to be constant in
time, the steady-state state is reached
when the fluctuations in the recorded
quantities is equal to the uncertainty of the
measurement approach.
SS1 SS3
SS2
- To estimate the time that the system
requires after changing the parameters
(here the flow rate), you will need to
measure the mean and the range of
oscillations in the SS regime. The SS is
reached once your measurements fall
within the range of the mean value.
32
Hysteresis (comparison of SS at given flow rates)
- In the context of experiments that you performed in practical 2, hysteresis refers to the
dependence of pressure drop measurements on the history of variation of flow rate in the
experiments.
- Hysteresis refers to the dependence of a state of a physical/chemical/biological system on the
history of events/conditions that the system has been exposed to.
- In physical systems, hysteresis often arises from irreversible phenomena and energy losses due
to irreversible thermodynamic phase change and internal frictional loss.
- For a physical system with no hysteresis, knowledge of the input variable (factor) at any instant
of time allows us to predict the response variable at that moment and no dependence on the
pathways taken to reach that specific point of time is expected.
33
Data analysis for practical 2
• Test 1 (Figure 2). Identification of steady-state behaviours
• Test 2 (Figure 3). Fluid viscosity measurements
• Test 3 (Figure 4). Impact of randomisation
• Test 4 (Figure 5). Hysteresis in viscosity measurements during increasing and
decreasing flow rate cycles
• Test 5 & 6 (Figure 6). Impact of tube diameter
• Description of the problem and experimental setup (Figure 1)
34
Overview of practical 2
Test 1 (Figure 2). Identification of steady-state behaviours
1.1. mean and standard deviation of the signal
1.2. time to steady state
1.3. hysteresis in the measurements
Test 2 (Figure 3). Fluid viscosity measurements
2.1. Error propagation and estimation of uncertainty in measurement of the viscosity
2.2. Multiple measurements of pressure drop at increasing flow rates, mean and standard
deviation
2.3. Linear regression analysis
2.4. Comparison between 2.2 and 2.3
Test 3 (Figure 4). Impact of randomisation
3.1. Linear regression analysis of randomly selected flow rates data
3.2. Comparison of 3.1 and 2.3
Test 4 (Figure 5). Hysteresis in viscosity measurements during increasing and decreasing flow rate cycles
Test 5 & 6 (Figure 6). Impact of tube diameter
1.1. Pressure drop measurements at different flow rates for various tube diameters
1.2. Impact of tube diameter on the viscosity measurements 35
Test 1 (data analysis)
Test 1 (Figure 2). Identification of steady-state behaviours
SS1 SS3
SS2
1.1. Identify the steady-states at each condition
(SS1, SS2, SS3) and the corresponding mean and
standard deviation of the signal
1.2. Time to steady state. Measure the time that it
takes the system to go from SS1 to SS2 and from SS2
to SS3. Compare these two measurements and
provide a discussion on any differences observed.
1.3. hysteresis in the measurements. Compare SS1
with SS2 at no flow condition and provide a
discussion on the results. If the mean values of the
two states do not match
36
Test 1 (Figure 2)
Test 1 (Figure 2). Identification of steady-state behaviours
SS1 SS3
SS2
Figure 2 must include measurements of pressure
drop vs time captured in test 1.
The values of SS1, SS2 and SS3 must be included by
flat lines on the graph.
The transition zones covering the time to SS must be
demonstrated on the graph.
Use the figure on the right as a model and produce
your own figure.
37
Test 2 (data analysis)
Test 2 (Figure 3). Fluid viscosity measurements
2.1. Error propagation and estimation of uncertainty in measurement of the viscosity. Based on
the knowledge of the uncertainty of different measurements involved and the error propagation
algorithm discussed in lecture week1_lecture1-2 and slide 30 in this lecture, estimate the
uncertainty in viscosity calculations.
2.2. Multiple individual viscosity measurements using measurements of pressure drop at
increasing flow rates. Define the mean and standard deviation of the viscosity calculation.
Remember to subtract the offset value (at no pumping condition) in the pressure drop
measurements.
2.3. Linear regression analysis. Calculate the viscosity of the fluid by fitting a least-square linear
fit to the pressure drop-flow rate data and deriving the viscosity from the slope of the fit.
2.4. Comparison between 2.2 and 2.3 and viscosity of tap water at the ambient temperature.
Provide a discussion on the accuracy of the measurements using the two methods (2.2 and 2.3)
in comparison to the measurements of water viscosity at similar temperature reported in the
literature.
38
Test 2 (Figure 3)
Test 2 (Figure 3). Fluid viscosity measurements
Figure 3 (a)
Provide measurements of viscosity vs flow rate. From measurements in test 2, you will be able to
calculate 5 values at 5 flow rates.
Present these in a graph using the uncertainty in calculation of viscosity for the error bars.
Figure 3 (b)
Present pressure drop measurements vs flow rate and the fitted linear regression trendline.
Provide the slope of the line and R2 on the graph.
39
Test 3 (data analysis)
Test 3 (Figure 4). Fluid viscosity measurements
Repeat 2.2, 2.3 and 2.4 for measurements performed in test 3.
Provide a discussion on any effect of randomisation in the measurements and its link with
hysteresis.
40
Test 3 (Figure 4)
Test 3 (Figure 4). Fluid viscosity measurements.
Figure 4 (a)
Provide measurements of viscosity vs flow rate. From measurements in test 3, you will be able to
calculate 5 values at 5 flow rates.
Present these in a graph using the uncertainty in calculation of viscosity for the error bars.
Figure 4 (b)
Present pressure drop measurements vs flow rate and the fitted linear regression trendline.
Provide the slope of the line and R2 on the graph.
41
Test 4 (data analysis)
Test 4 (Figure 5). Fluid viscosity measurements
4.1. Linear regression analysis for inceasing flow rate. Calculate the viscosity of the fluid by
fitting a least-square linear fit to the pressure drop-flow rate data and deriving the viscosity from
the slope of the fit.
4.3. Comparison between 4.1 and 4.2 and viscosity of tap water at the ambient temperature.
Provide a discussion on the accuracy of the measurements using the two methods (4.1 and 4.2)
in comparison to the measurements of water viscosity at similar temperature reported in the
literature.
4.2. Linear regression analysis for decreasing flow rate. Calculate the viscosity of the fluid by
fitting a least-square linear fit to the pressure drop-flow rate data and deriving the viscosity from
the slope of the fit.
4.4. Linear regression analysis for full set of data (increasing and decreasing flow rates). Calculate
the viscosity of the fluid by fitting a least-square linear fit to the pressure drop-flow rate data and
deriving the viscosity from the slope of the fit.
42
Test 4 (Figure 5)
Test 4 (Figure 5). Fluid viscosity measurements.
Figure 5 (a)
Provide measurements of viscosity vs flow rate for the two data sets (increasing and decreasing
flow rates). From measurements in test 4, you will be able to calculate 5 values at 5 flow rates
for each data set. Note that data ta flow rate 5 ml/min will be shared between the two sets of
data.
Present these in a graph using the uncertainty in calculation of viscosity for the error bars.
Figure 5 (b)
Present pressure drop measurements vs flow rate and the fitted linear regression trendline for the
full data set, including both increasing and decreasing flow rate data.
Provide the slope of the line and R2 on the graph.
43
Test 5 & 6 (data analysis, Figure 6)
5-6.1. Linear regression analysis. Calculate the viscosity of the fluid by fitting a least-square
linear fit to the pressure drop-flow rate data and deriving the viscosity from the slope of the fit.
Test 5 & 6 (Figure 6). Impact of tube diameter
Figure 6
Present pressure drop measurements vs flow rate and the fitted linear regression trendline for
the 3 test diameters in one graph.
Provide the slope of the line and R2 in the caption of the graph.
Table
Provide a table with length and diameter of the three test tubes and the corresponding
viscosity calculation.
Discuss the accuracy of the results in comparison with the reported measurements of water
viscosity at similar temperature.
44
Report/manuscript writing
Practical 2 report
45
Practical 2 – template
Research paper style
46
• Treat the experiments, data analysis and report writing of this practical as it is a research
project/paper.
• You will be marked not only for the correctness of your data and results, but also for the
readability of the text, quality of the figures and discussions.
• There is no single CORRECT way of writing and styling your research paper, however, there
are certain main questions that should be answered in every section for the research
manuscript to be acceptable.
• Follow the formatting/styling guidelines provided in the templates and refer to the lecture
notes for more details.
47
• The quality and readability of your writing will be assessed in this assignment, so please
consider spelling/grammar check before submitting your work. MS Word spelling check
and free online applications, such as https://www.grammarly.com might be helpful for a
quick assessment of your writing.
Practical 2 – assessment
• You will be assessed for:
- Formatting and style.
- Formulating the problem, findings and the discussions.
- Correctness of the data acquisition, analysis and representation of the results.
-Quality and readability of the figures.
- Style and relevance of the references.
Practical 2 – report template
MECH5465M_P2 report_MS Word template
48
Practical 2 – report template
49
0. Abstract
A brief FULL SUMMARY of the problem/hypothesis, methods, findings, conclusions.
1. Introduction
What is the PROBLEM of interest? Why is it IMPORTANT?
What has been one BEFORE and what is MISSING?
What have YOU done and why is it SIGNIFICANT?
2. Materials and methods
HOW did you do your research?
3. Results and discussions
WHAT have you found?
4. Conclusion
A BRIEF SUMMARY of rationale behind the work, findings, main conclusions and the perspective.
References
Title
Title
• The title is the first piece of information that your reader or marker will see.
• It should be short, informative and contain the right keywords to provide accessibility
through search engines and data bases.
1. Ask the following questions:
• To make a title for your research/report:
1.1. What is the work about?
1.2. Which techniques your used?
1.3. On what did you you perform the research/study?
1.4. What did you find?
2. Answer the questions and generate a list keywords from your answers.
3. Create a sentence from your keywords.
4. Remove any repeated words or non-essential information from the sentence to create a title.
50
51
1. Purpose/hypothesis
2. Method/approach
3. Results/findings
4. Conclusions
These elements appear in the order above to form a concise informative summary of the work.
A well-written abstract helps the reader to capture a summary of the work in a very short time.
A scientific abstract includes the following four elements:
0. Abstract
1. Introduction
52
1. Larger picture (mandatory)
What is the topic of the research and why it is important. Convince the reader that the topic is
interesting and explain how it is connected to bigger problems.
This is typically one paragraph.
2. Literature survey (mandatory)
Describe what is currently known (in terms of science) or what technologies are currently
available (state-of-the-art technologies).
Explain current gaps in the knowledge or the technical challenges.
This might be presented in multiple paragraphs.
3. Introduction to your research/approach (mandatory)
Explain your research question or the unique approach that you addressed/followed in your work.
Explain how your approach helps filling the existing gaps.
This might be presented in multiple paragraphs.
4. Outline of the paper (Optional)
Some authors provide a detailed point by point outline of the paper in the introduction.
1. Introduction, Examples
53
• S. K. Walsh et al., Maturation- and degeneration-dependent articular cartilage metabolism via optical redox ratio
imaging. Journal of Orthopaedic Research, 2021, 1-9.
• R. D. McArthur et al., Wake flows of highly detailed heavy vehicles. International Journal of Automotive Technology,
2021, 22(5), 1227-1243.
See the articles below for examples of comprehensive introductions:
• J. Winslow et al., Basic understanding of airfoil characteristics at low Reynolds numbers (104–105). Journal of Aircraft,
2018, 55(3), 1050-1061.
• R. L. Price et al., Nanometer surface roughness increases select osteoblast adhesion on carbon nanofiber
compacts. Journal of Biomedial Materials Research, 2004, 70A, 129-138.
1. Introduction, literature survey
Citing textbooks
54
In comparison with research papers, textbooks often better explain the basics/fundamentals of
the physics of the problem and are typically better organized.
Research papers are more specific and focused. When conducting research on advanced
specific topics, research papers provide great source of knowledge and are often the primary
references available to the researchers.
Textbooks are more comprehensive than research papers. However, finding textbooks on new
topics may be challenging.
1. Introduction, literature survey
Citing research papers
55
1. Start by searching for the main keywords of your research topic on an online search engine,
such as google scholar, Web of Knowledge, Scopus.
2. Choose a few articles to understand the topic and the stat-of-the-art research in the field.
Two types of articles are the best to start your literature survey with:
2.1. Very recent review articles on the topic: if written well, these will provide a good introduction
to the topic, as well as providing a long comprehensive list of relevant references.
2.2. Seminal articles on the topic: these are articles that first presented an important
idea/methodology/model in the field, thus can provide good understanding of the topic.
Furthermore, because these articles are repeatedly cited in field, you can follow their citing
articles to find more references.
3. When reading articles of primary interest, you may come across new concepts and terms that
you are not familiar with. In such conditions, try to read about the new concept/term briefly to
develop a basic understanding before continuing with the rest of your primary reference.
2.1. Recent review papers
56
2.2. Seminal articles in the field (technical and topical)
57
1. Introduction,
Organising the literature survey
58
How to organise the paragraphs/section summarizing the literature survey is a personal
choice. After introducing the bigger picture and citing the relevant references, you can follow
one the following ways to organize your literature survey paragraphs/section:
• Chronological order: starting from the earliest to the latest works.
• Seminal to most recent/advanced order: starting from the papers that initially defined the
field and move to more advanced new articles.
• General to specific order: starting from the broad topic and moving to more specific topics.
Depending on the field, this may be ordered from more general models to minor theories,
or for example, from conventional to novel techniques.
In all methods, you should try to group the references whenever possible instead of writing about
individual articles, unless citing a work that is the basis of your research.
For this assignment, you are required to write only a short literature review section that covers all
the essential sections.
2. Materials and methods
59
You should provide all the information that is needed to replicate your experiments and reproduce
your results in this section.
This section provides information on HOW you performed your work.
This should include information about materials that your use, the environmental conditions
at which you performed the experiments, the protocols that were followed, the
equipment/tools (with uncertainties) and any data processing algorithms that you used.
For examples of Materials and methods sections, please see:
• S. Khodaparast et al., A micro particle shadow velocimetry (μPSV) technique to measure flows in microchannels.
Experiments in Fluids, 2013, 54, 1474. (Very long methods section for a technique development paper.)
• S. Khodaparast et al., Pure and mixed aqueous micellar solutions of Sodium Dodecyl Sulfate (SDS) and
Dimethyldodecyl Amine Oxide (DDAO): Role of temperature and composition. Journal of Colloid and Interface Science,
2021, 582, 1116-1127. (An experimental paper where different techniques were used.)
You can use different formats of subheadings to group information related to materials,
experimental techniques, data processing schemes, etc.
• Y. E. Yu et al., Armoring confined bubbles in the flow of colloidal suspensions. Soft Matter, 2017, 13, 2857-2865.
• (An experimental paper where data processing is discussed.)
3. Results and discussion
60
When organising the sub-headings in this section, follow the order provided in the
instructions for the results and figures as shown in the next slide. This is very similar to the
order of the experiments that you performed in the practical session.
3. Results and discussion
Test 1 (Figure 2). Identification of steady-state behaviours
1.1. mean and standard deviation of the signal
1.2. time to steady state
1.3. hysteresis in the measurements
Test 2 (Figure 3). Fluid viscosity measurements
2.1. Error propagation and estimation of uncertainty in measurement of the viscosity
2.2. Multiple measurements of pressure drop at increasing flow rates, mean and standard
deviation
2.3. Linear regression analysis
2.4. Comparison between 2.2 and 2.3
Test 3 (Figure 4). Impact of randomisation
3.1. Linear regression analysis of randomly selected flow rates data
3.2. Comparison of 3.1 and 2.3
Test 4 (Figure 5). Hysteresis in viscosity measurements during increasing and decreasing flow rate cycles
Test 5 & 6 (Figure 6). Impact of tube diameter
1.1. Pressure drop measurements at different flow rates for various tube diameters
1.2. Impact of tube diameter on the viscosity measurements 61
3. Results and discussion
Figures’ captions
62
Follow all the details of the guideline in the file uploaded on Minerva/Assessment called
MECH5465M_Practical 2 report_MS Word template when preparing your figures and the captions.
63
Basic rules to follow when preparing figure captions:
Each figure must have a single caption that provides information about all the panels included.
Follow the guidelines of the template for styling your caption.
The caption of the figure must be centred under the figure. The caption of the table is centered
above the table. When the caption extends to more than one line of the text, make it justified.
A Figure and its caption must always appear on the same page.
Figures and their captions must appear as close as possible to the location in the text where they
are cited.
Captions must start with a capital letter and end with a period.
All figure captions must be informative, meaning that they should provide enough information
about the figure that allows the reader to understand the figure without referring to the text.
3. Results and discussion
Figures’ captions
64
• Do not simply summarise the results pointed out in the discussion section.
• Take the findings of your work and put into perspective, keeping in mind the broader context.
• Explain the importance of your findings.
• Describe the contribution of your findings to the specific and the broader field.
4. Conclusion
65
1. Start with describing the context
2. Provide a summary of your findings
3. Interpret your results with the broader context in mind
5. Point out the limitations if there exists any
6. Discuss major contributions and possibilities for improvements and future work
4. Discuss applications in other relevant systems and fields
4. Conclusion
References
66
References
67
https://images.webofknowledge.com/images/help/WOS/A_abrvjt.html
1. Author 1, A.B.; Author 2, C.D. Title of the article. Abbreviated Journal Name Year, Volume, page range.
Questions?
68
Already member? Sign In
