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"Aprende qué es la incertidumbre en metrología, su importancia en las mediciones y cómo se calcula para asegurar la precisión y confiabilidad de los resultados. Descubre cómo la incertidumbre afecta la interpretación de los datos en diversas aplicaciones científicas e industriales." What is Uncertainty in Measurements? In simple words! Go to home Uncertainty is a parameter that must always accompany any measurement of any magnitude, since no measurement is complete without its associated uncertainty. As always, there are many definitions, and they are all facets of the same reality. So let's start with the first. There is a document called GUM (Guide to the Expression of Uncertainty in Measurement) that has become a standard in many countries. For example, in Mexico, it is standard NMX-CH-140-IMNC. This document sets forth the rules and definitions for how uncertainty should be calculated and expressed. The formal explanation given in this guide (GUM) defines measurement uncertainty as a "parameter associated with the result of a measurement, which characterizes the dispersion of the values that could reasonably be attributed to the measurand." In other words, uncertainty represents the range of values within which the true value of what is being measured is likely to lie. This definition includes another term that is sometimes little known: "measurand." The measurand is the technical name we use in metrology to refer to the specific quantity we want to measure. It is the objective of our measurement, the "what" we are trying to quantify. For example, if we want to calibrate a scale, then the magnitude is Mass, but the measurand is the Error of Indication of said scale. In the case of a liquid-in-glass thermometer, the magnitude is temperature, but the measurand is the reduced correction (RC). And finally, if we have a flowmeter, the magnitude is flow, but the measurand is the meter factor (MF). So, returning to uncertainty, this parameter does not indicate error, but rather expresses reasonable doubt about the measured value, taking into account the possible factors of variation in the measurement process. These factors can be intrinsic to the equipment, environmental factors, and factors related to the personnel performing the calibration. In simpler terms: Every time we make a measurement, no matter how precise the equipment or how careful we are, there is always a margin of doubt. That is uncertainty. It doesn't mean we've done something wrong or that the equipment is simply damaged; in the real world, conditions are never 100% perfect. Uncertainty helps us quantify this reality. It tells us that our result is close to the true value, but within a possible range, and it can also be interpreted as a quantitative measure of measurement quality: the lower the uncertainty, the higher the quality. Now, it's important to know that there are several types of uncertainty, and they can be divided into: Type A Uncertainty Type A uncertainty is assessed using statistical methods. Imagine we take the same measurement many times, with the same instrument, under the same conditions. Each time, the results may vary slightly, and those small changes are due to natural random variations in the measurement process. To quantify this uncertainty, we analyze that data using statistics (for example, by calculating the mean and standard deviation). When we talk about Type A uncertainty, you're basing your analysis on repeatedly observed data. By analyzing the results, you can see how much they vary and use that information to estimate a margin of uncertainty. The more times you repeat the measurement, the more accurate the data you have about those variations will be. This assessment is reliable because it's based directly on practical observations. In short, Type A uncertainty reflects the variability that can be observed and quantified with statistical methods using repeated data. Type B Uncertainty Type B uncertainty is different because it's not assessed through repeated measurements, but rather through other types of information. Here, factors such as previous experience, information provided by the instrument manufacturer, or historical data must be considered. For example, if you have a scale and the manufacturer specifies a margin of error of ±0.1 grams, you use that data as a source of Type B uncertainty. You can also consider the influence of external factors that you can't directly observe at the time of the measurement, such as estimated environmental conditions or known limitations of the equipment. Type B uncertainty is a combination of expert judgment, specifications, and references, and although it is not based on directly observed data, it is still a valid and well-founded estimate. In short, Type B uncertainty is uncertainty we estimate based on external information and experience, without the need for repeated measurements. Now, the above is how uncertainty is classified, but it can also be divided according to which part of the uncertainty process it involves. Let's explain each type of uncertainty in a little detail: Associated Uncertainty Associated uncertainty is the uncertainty of each component or magnitude of influence that can influence the result of a measurement. When we measure something, several factors can introduce small variations, such as the precision of the equipment or the conditions of the environment. These small variations are represented by probability distributions that reflect the "way" in which these variations occur in each component. Each distribution has its own "profile" that describes how the measured values are likely to behave, and this affects the associated uncertainty value differently. Why does distribution matter? Each distribution has a particular method for calculating uncertainty that suits the nature of the data and best reflects the reality of the measurement process. Choosing the right distribution helps to obtain an accurate and reliable estimate of uncertainty, tailored to how the data behave in practice. Selecting the correct distribution is key to an accurate and reliable estimation of the associated uncertainty. As an example, we can say that if we have a scale with a resolution of 0.01 g, the uncertainty associated with that resolution will be uniform, so we have the following: Combined Uncertainty Combined uncertainty is the result of grouping or combining associated uncertainties to obtain a total measure of uncertainty of the measurement process. This is done by applying statistical methods, such as "adding" the uncertainties, which is appropriate for independent uncertainties. Here all the associated uncertainties of each component or influence quantity are taken and a total uncertainty is calculated. The combination is done according to statistical principles to reflect how the uncertainties interact together. Example: If in a temperature measurement, in addition to the thermometer, other factors intervene such as humidity or the stability of the ambient temperature, the combined uncertainty will be the result of "adding" the associated uncertainties of each of these factors. The sum is not done algebraically, it is done through the law of propagation of uncertainties that is declared by the BIPM (Bureau international des poids et mesures) in the GUM. Here we enter into another definition that brings with it the same law of propagation, The sensitivity coefficients . To understand what a sensitivity coefficient is (the partial derivative in the law of propagation) you must first understand that in order to make a good measurement or good calibration, you must have the mathematical model that describes the behavior of that magnitude or measurand. This mathematical model has some variables that are magnitudes of influence, which we already talked about, for example, the resolution, but not all of these variables affect the measurand in the same way, some have more weight than others, so they cannot simply be added together, so it is necessary to know mathematically how much they are affected, normally it is measured as a percentage in an uncertainty budget and it is known as the impact percentage. The sensitivity coefficient is calculated by deriving the effect of an input variable on the measurement result. In general, the sensitivity coefficient (ci) for a specific variable is defined as the partial derivative of the measurement function with respect to that variable: Where: And it is the result of the measurement (measurand). Xi is the input variable that influences Y. This value of ci shows us how much the result (Y) changes with a small variation in Xi. Step by step to calculate the sensitivity coefficient: Identify the Measurement Function: First, you need a formula or model that relates the measurement result to the input variables. For example, if you are measuring electrical resistance and you know that it depends on temperature, then your model will include that relationship. Differentiate with respect to each input variable: Calculate the partial derivative of the measurement function with respect to each variable of interest. This is done by taking the mathematical model and differentiating it with respect to the variable you want to analyze. This gives the sensitivity coefficient ci for that variable. Evaluate at Measurement Point: If the function includes specific constants or conditions, such as the current ambient temperature or the accuracy of the instrument, use these values to evaluate the sensitivity coefficient under those conditions. Practical example: Let's imagine that we are measuring the length (L) of an object which depends on the temperature (T). The relationship between length and temperature is expressed by the following function: Where: L0 is the initial length at a reference temperature (e.g. 20 °C). α is the coefficient of thermal expansion of the material. β is the coefficient of expansion due to moisture (how moisture affects the length of the material). To find the coefficient of sensitivity with respect to temperature (cT), we differentiate L with respect to T: This result shows us that the sensitivity coefficient is equal to the initial length multiplied by the coefficient of thermal expansion. This means that for every degree of change in temperature, the length will vary by this value. This sensitivity coefficient is then used to adjust for uncertainty. If the temperature uncertainty is, for example, ±0.5 °C (obtained from a calibration certificate), then the effect of this uncertainty on length is calculated by multiplying the sensitivity coefficient cT by the temperature uncertainty. This helps to determine how variation in T influences the measurement result (L). Also multiplying the temperature uncertainty which is in terms of °C by the sensitivity coefficient helps to convert units into terms of the measurand (m). The other sensitivity coefficient of the mathematical model would be the following: So, having the two coefficients of the model and applying the Law of Propagation of Uncertainties, the combined uncertainty can be calculated as follows: It should be noted that u(T) and u(H) can propagate independently and may include uncertainties due to certification, resolution, repeatability, drift, etc. Expanded Uncertainty Expanded uncertainty is a value that provides an interval within which the true value of a measurement is expected to lie with a specified level of confidence (usually 95%). It is an extension of the combined uncertainty uc, which represents only the standard uncertainty in the measurement, multiplied by a coverage factor k, which widens the range of uncertainty. The general formula for expanded uncertainty U (capital U) is: U= uc(y)*k where k =2. For a confidence level of approximately 95%, the coverage factor k is typically 2, although this value may vary depending on the effective degrees of freedom. But what are the effective degrees of freedom? The effective degrees of freedom ( ν eff) help us to determine the coverage factor k when the standard uncertainties of the input components have different degrees of freedom, for example in measurements with different sources of uncertainty or in small samples (sample). These degrees of freedom are calculated using the Welch-Satterthwaite method: where: uc(y) is the combined uncertainty. ci is the sensitivity coefficient of the variable xi. u(xi) is the standard uncertainty of xi. νi are the degrees of freedom of each uncertainty component. Once ν eff is calculated, a Student t table is used to determine the coverage factor k corresponding to the desired confidence level and effective degrees of freedom. The degrees of freedom (Vi, differentiated from effective degrees of freedom) are assigned for each uncertainty component based on the way in which that uncertainty has been estimated. For statistically evaluated uncertainties (Type A), degrees of freedom are assigned based on sample size. In this case: If you have n observations of a measurement, the degrees of freedom are Vi=n−1 This is because when we calculate a standard deviation from a sample, we lose a degree of freedom (because calculating the sample mean uses one of the data). Example: If you have 10 measurements of a length and you calculate the standard uncertainty of the mean u(x) of these measurements, the associated degrees of freedom will be Vi=10−1=9. For uncertainties assessed by non-statistical methods (Type B), the assignment of degrees of freedom is less straightforward. In this case, the value is estimated based on your confidence and knowledge about the source of uncertainty. Rectangular (Uniform) Distribution: If the uncertainty comes from a source with known limits (e.g. an instrument with a stated accuracy of ±MPE), a high value of degrees of freedom is usually assigned, since there is greater confidence in the accuracy of the estimate (e.g. between 50 and 100 degrees of freedom). This depends on the experience of the metrologist and the knowledge of the equipment. Normal or Gaussian Distribution: When there is enough information to assume that the value is normally distributed, a high value for degrees of freedom can be assigned. If you do not have precise data, a common value is between 20 and 30 degrees of freedom. Triangular Distribution: If the value is more concentrated around a point (with less defined limits), an intermediate number of degrees of freedom is usually used, generally between 10 and 20. Once the degrees of freedom have been assigned and the effective degrees of freedom calculated using the Welch-Satterthwaite equation, we will apply the T-Student table, example: If in the Welch-Satterthwaite calculation we obtained Veff= 21, that is, 21 effective degrees of freedom, then we will go to the T-student Table and look for the value that corresponds to 21 effective degrees of freedom and a confidence of 95% or what is the same α/2= 0.025, then it gives us a value k=2.080, to be able to multiply it by the combined uncertainty and thus be able to expand it. So: U= uc(y)*k where k =2.08. In most cases, the t-distribution tables are for 95% probabilities; however, in metrology, a confidence level of 95.45% is used, which completely changes the coverage factor (k). Therefore, it is more advisable to calculate the inverse of the t-distribution using software or Excel (=INV.T.2C(1-0.9545,21)), which gives us k = 2.13. Care must be taken when choosing the probability to be used. The following table is a representation of the t-distribution table for a 95.45% coverage factor: However, the GUM not only mentions how to calculate uncertainty, but also how to express it. Uncertainty must be expressed in a clear and standardized way to ensure that the results are understandable and useful. It establishes several guidelines for expressing uncertainty so that other users can interpret the results in a consistent manner. Example of a length measurement with these details: Result: y=10.0 mm Combined standard uncertainty: uc(y)=0.15 mm Coverage Factor k=2 (for 95% confidence) Expanded uncertainty: U= 0.30 mm It is also valid to use the symbol ± , example: 10.0 mm ± 0.30 mm The use of the ± symbol is not recommended when using standard or combined uncertainty since the symbol is usually associated with intervals corresponding to high confidence levels. Uncertainty should be expressed to two significant figures, where possible. What Are Significant Figures? Significant figures are the digits in a number that contribute to its precision. In the context of uncertainty, using two significant figures ensures that the reported value is sufficient to understand the variability in the measurement without being excessive. Example of expression in two significant figures: ±0.013578mm -> ±0.014mm ± 0.123456 mm -> ± 0.12 mm ± 123.7 mm -> ± 12 cm And this is how, in a few words and summarizing the topic, the uncertainty in a measurement is calculated, so now you can understand that the action of just measuring, by itself, is not enough if it is not accompanied by the most important parameter within metrology, and if you want to know more about metrology, visit our article: Metrology If you have any questions about a topic, ask us. Mail

Axotek te ayuda en ingeniería y metrología, Generador de QR gratuito, Calculadoras, Hojas de calculo, documentos, conversores de unidades realizados por expertos en metrología, About Us and the World This world is full of problems, and one day we hope to solve them, but for now, we can do our part by solving problems that involve calculations. Let us help you speed up those everyday processes that involve calculations with information, data, and tools. "Calculus is the most powerful tool the human intellect has devised for exploring reality." — Bertrand Russell Learn more... Technological Synergy... Welcome! Discover and browse in-depth articles, how-to guides, tools, calculators, trend analysis, and tech product reviews, all created with the goal of keeping you up-to-date in the digital world. At Axotek, we're passionate about the world of technology and its power to transform the way we live, work, and connect. We're dedicated to providing high-quality content, tools and calculators, in-depth analysis, and how-to guides for science and technology enthusiasts. What sets us apart? We listen to our users, bringing relevant content that genuinely helps someone stay up-to-date, informed, or simplify their daily calculations. Nombre* Apellido* Email* Teléfono Explicanos tus solicitud para recibir una cotización: Respuesta larga* Enviar Secciones Contamos con una gran variedad de artículos, y herramientas necesarias en el día a día completamente gratis. Herramientas Calculadoras Temas Informativos Discover Most visited: Local Gravity Calculator: Local gravity Local Gravity Calculator: Measure the Force of Attraction in Your LocationGravity, one of the fundamental forces of the universe, varies slightly depending on where you are on Earth. For those interested in understanding these variations and how they affect our environment, a local gravity calculator becomes an invaluable tool. Local gravity, measured in meters per second squared (m/s²), can be influenced by several factors, such as altitude, latitude. Water density calculator Water Density Water Density Calculator: Accuracy as a Function of Temperature The density of water, a fundamental property in both science and various practical applications, changes with temperature. For those who need to accurately measure this value based on specific conditions, a water density calculator based on temperature is an essential tool. Free QR Code Generator: Generate QR

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Calcula el valor de (4 a 20) mA y calcula el rango de tu equipo con dos puntos. Process Calculator (4 to 20) mA The analog (4 to 20) mA communication standard is used to communicate process transmitters with a PLC, computer, indicator, recorder, etc., located in a control room or remote location. How to enter the values: -Maximum and Minimum Range: This is the range in which the equipment operates (for example, 0 to 100) °C). Enter the lowest operating range and then the highest. - Unit: the unit in engineering units; example " °C " -Current: Enter the measured value in mA with a minimum range of 3 mA and a maximum of 22 mA. The range (4-20) mA can also be calculated if two points are known, and for each point the value in units and the value in mA are known, example: Knowing that 19.634 °C is equivalent to 5.789 mA and that 128.265 °C is equivalent to 15.687 mA, the range can be calculated as 4 mA = 0.20 mA = 175.6 Why is the 4 to 20 mA range used? 1. Diagnostics: Using 4 mA as the starting point, rather than 0 mA, allows for the differentiation of a device's idle state from a fault due to a power failure, a short in the wiring, a turned-off device, or a damaged device. 2. Robustness: Current signals are much less susceptible to electromagnetic interference than voltage signals, ensuring more accurate transmission in industrial environments and allowing the signal to be transmitted over long distances. The current maintains its value with almost no loss along the circuit, regardless of the wiring resistance, allowing for reliable transmissions even over considerable distances. 3. Reliability and installed equipment: Most industrial sensors are designed to operate with 4-20 mA signals. Although this technology began to be used in the 1950s, it remains in use today due to its reliability. It has also evolved with integrations such as the HART digital communication protocol, which offers advanced diagnostics and the ability to integrate the equipment into a distributed control system, allowing it to visualize and control different variables at the same time. At Axotek, we listen to our users. If you need a calculator to make your work and/or projects easier, you can contact us, and as soon as possible, we'll have it online at no cost to you. Request calculator

Conversor de unidades de Flujo, Caudal, Gasto en varias unidades. Flow Unit Converter The concept of flow is fundamental to disciplines ranging from physics and engineering to biology and economics. It represents the transfer or movement of a physical quantity (such as mass, energy, particles, or information) through a medium or system in a given time. Its study has led to technological advances, improvements in industrial processes, and a deeper understanding of natural phenomena. Volumetric flow (or rate) is a fundamental quantity in engineering and applied sciences. It quantifies the volume of a fluid (liquid or gas) that passes through a cross-section (usually a pipe or channel section) per unit of time. Understanding it is critical for designing pumping systems, distribution networks, industrial equipment, and even for modeling natural phenomena such as blood flow or ocean currents. Volumetric flow (Q) is defined as: Where: Q: Flow rate (m³/s). V: Volume of fluid (m³). t: Time (s). v: Average fluid velocity (m/s). A: Cross-sectional area of the pipe or conduit (m²). The second equality, also known as the continuity equation or Castelli equation, establishes a direct relationship between fluid velocity and conduit cross-sectional area. However, this apparent simplicity hides an underlying complexity when we consider factors such as viscosity, density, turbulence, profile, and compressibility of fluids. For gases or liquid hydrocarbons and petroleum products, the situation is more complex due to their compressible nature, requiring the use of thermodynamic equations that consider changes in density and temperature. Accurate volumetric flow measurement has evolved significantly since the early rudimentary methods. Currently, we have technologies such as: Electromagnetic flowmeters, ideal for conductive fluids such as drinking water. These flowmeters are very cost-effective and their accuracy is suitable for most non-fiscal industrial processes, with an accuracy of 0.5% to 1% of the reading. Ultrasonic transit-time or Doppler systems are very efficient due to their portability and, above all, the ability to measure flow non-intrusively. However, if they are poorly configured or not properly installed, their accuracy can drop significantly, with an accuracy of 1% to 2% of the reading. Coriolis mass flowmeters for high-precision applications, widely used in custody transfer (fiscal measurement), can achieve an accuracy of up to 0.025% of the reading. Their biggest disadvantage is their price. However, these are not the only technologies, as there are some older ones and others that have emerged that have very specific applications, either due to design or industrial culture. For example, for steam measurement, the vortex meter is the most widely used; for natural gas measurement, orifice plate flow measurement is used (differential pressure principle); for liquid petroleum measurement, it is still common to see measurements with positive displacement equipment. This does not mean that there is no other better measurement technology, but rather that the industry seeks the best cost-benefit ratio in measurement. These principles apply not only to flow measurement in pressurized pipes, but also to free surface or open channel flow measurement. Flow measurement in rivers, canals, weirs, and drainage systems presents unique challenges for measurement and control. Unlike flow in pressurized pipes, where flow rate can be calculated directly, in these systems, the irregular behavior of the fluid (affected by slopes, bed roughness, and atmospheric conditions) makes the energetic approach more practical than the volumetric approach. In free surface systems, the fluid (usually water) is in contact with the atmosphere, and its movement depends on: Gravity: The main driving force. Channel geometry: Slope, cross-section, and roughness. External conditions: Precipitation, evaporation, and lateral inflows. These factors generate non-uniform or unsteady behavior, also called transient behavior: If the flow depth (y) does not change along the channel (with respect to distance x): it is uniform. If the flow depth (y) does change along the channel: If the flow depth (y) does not change with time (t): If the flow depth (y) does change over time: However, these changes in depth are not the only associated phenomena. The analysis of these behaviors involves a combination of velocities, which are the Lagrangian velocity (dynamics), the Seddon velocity (kinematics), and the average axial velocity. Normally, the single velocity measured is the average axial velocity. However, both velocities also affect behavior. Celerities are the speeds at which disturbances (waves) travel in water. Imagine throwing a stone into a river: the waves that form move at a specific velocity, which depends on how the water flows. 1. Lagrangian velocity (dynamics) → Fast waves (like those of a stone). When you throw a stone into a calm river, circular waves form and expand. The speed of these waves is the Lagrangian velocity. 2. Seddon's Velocity (kinematics) → Slow waves (like those of a flood). Now imagine there is a flood in the river. The water rises slowly (it is not an instantaneous wave like that of a stone). This flood wave travels at Seddon's Velocity. Because it is easier to analyze the flow of a river or channel as a form of energy, it is possible to calculate the flow rate without having to measure the average axial velocity or use the continuity formula (Castelli). This can be done through Manning's formula. However, this is usually used as an approximation because it assumes a uniform flow (which is not always the case) and because it requires knowing very specific parameters such as the roughness of the material and the slope of the channel. Donde: v = Velocidad media del agua (m/s). n = Coeficiente de rugosidad de Manning (adimensional). R = Radio hidráulico (m), calculado como: S = Pendiente longitudinal del canal (adimensional) para calcular el radio hidráulico (R) se utiliza esta fórmula: A = Wetted cross-sectional area (m²). P = Wetted perimeter (m). Flow is a magnitude present, from the veins in your body to the large reservoirs that carry water to cities. Its study and behavior are complex but important for all aspects of life. Making the correct conversions is crucial to understanding the world around us. If you're interested in learning more about this topic, visit our articles where we explain this and many other topics in more detail. GO TO CONVERTERS...

Use the law of propagation of uncertainty with a calculator to understand how the calculation works and how it should be performed. Law of Propagation of Uncertainty Law of Propagation of Uncertainty The Law of Propagation of Uncertainty is the cornerstone of modern metrology, based on the Guide to the Expression of Uncertainty in Measurement (GUM). It is used to determine how doubts (uncertainties) in input measurements affect the final result of a calculated quantity. Let's start by understanding what "uncertainty" is. In real life, nothing is measured with absolute precision. If you measure a table with a ruler, you might say it measures 1 meter, but in reality, it measures 1 meter ± 1 millimeter. That "± 1 millimeter" is uncertainty: it's the reasonable margin of doubt we have about our measurement. Although the GUM (Guide to the Expression of Uncertainty in Measurement) defines it more technically as: "A non-negative parameter that characterizes the dispersion of the values attributed to a measurand, based on the information used," colloquially we can say that it's the doubt we have about the measurement taken, or a measure of the quality of the measurement. The smaller the uncertainty, the higher the quality of the measurement (better method, better conditions, and better measuring equipment). If you want to learn more about uncertainty, visit our other article with a practical example here. What is the measurand? According to the VIM (International Vocabulary of Metrology), a measurand is: "The quantity to be measured." It seems like a simple definition, but the key word is "to be measured." The measurand is the ideal concept, the specific quantity we want to know under perfect conditions. In a calibration, we usually want to measure the indication error or the correction factor, but in a normal measurement without comparison, what we usually want to measure is a quantity like length, area, density, etc. And here a problem arises: We almost never measure something directly and that's it; we usually use that data to calculate something else. Example: You want to know the area of a plot of land, so you measure the length and the width. Your measuring tape has an uncertainty in the length and an uncertainty in the width because you took two measurements. What is the uncertainty of the total area? You can't simply add the uncertainties of the sides, because area is a product of two measurements. This is where the Law of Propagation comes in. To understand how uncertainty propagates, we need to know three key concepts: 1. The Mathematical Model This is the formula that describes the behavior of your measurement. For example: Speed = Distance / Time. If the formula changes, the way uncertainty propagates also changes. 2. Sensitivity Coefficients This is a tool that measures the "cause and effect" relationship between the parts of a system and its final result. In short, it tells us how much the result (measurand) is affected by each influencing variable in the mathematical model. The sensitivity coefficient indicates how much the output changes if one of the inputs varies slightly, while keeping the others constant. Mathematically, it is the partial derivative of the function with respect to that variable: 3. Combination In the world of uncertainty, doubts don't simply add up algebraically (1+1=2). They are added using the Pythagorean Theorem (the square root of the sum of the squares). Why? Because doubts can be upward (+) or downward (-), and squaring them ensures that they always add to the total uncertainty, never subtract from it. Each of these uncertainties is known as an associated uncertainty, and there must be one for each variable in your mathematical model. Steps for Uncertainty Assessment For an uncertainty budget to be technically valid, it must follow this sequence: Analysis of Sources: Identify what affects each input variable (systematic effects, random effects, resolution, drift, etc.). Quantification (Type A and Type B): Type A: Based on statistics (standard deviation of repeatability). Type B: Based on external information (calibration certificates, manuals, technical judgment, etc.). Calculation of Standard Uncertainties (u): Bring all sources to a common standard deviation or according to their distribution. For example, for a uniform distribution, divide the resolution by 2√3 or √12. Combination: Apply the law of propagation of uncertainties (the first formula). Expanded (U): Multiply by the coverage factor k (usually k=2 for a 95.45% confidence level). If you need more information on this, click here. Practical Example: Imagine you measure the length (L) and width (W) of a plate to obtain the area (S = L * W). Model: S = L * W Sensitivity Coefficients: Applying the law of propagation of uncertainty, it becomes as follows: Where uc(S) is the combined uncertainty of the area. A and L are the sensitivity coefficients, which in this case are Length and Width (resulting from the partial derivatives). uL and uA are the uncertainties associated with each measurement (resolution, repeatability, calibration, etc.). If you need to apply the calculation, we have provided a calculator for the law of propagation of uncertainty, considering the following:

Interactive interpolation and extrapolation calculator. Allows you to enter custom values, choose the number of decimal places, and define units. Visualize the results with dynamic graphs for better understanding. Calculadora interactiva de interpolación y extrapolación. Permite ingresar valores personalizados, elegir el número de decimales y definir unidades. Visualiza los resultados con gráficos dinámicos para una mejor comprensión. Interpolation and Extrapolation Calculator Visit our menu for more articles and information... Our online interpolation and extrapolation calculator is an accurate and easy-to-use tool designed for engineers, scientists, mathematicians, and anyone who needs to estimate values based on known data. It uses formulas based on classical linear and polynomial interpolation methods as well as extrapolation techniques to predict values outside the range of existing data. These methodologies have been widely used in a variety of disciplines, from physics and engineering to economics and data analysis. The calculator allows you to enter custom values, select the number of decimal places, and define units of measurement. It also offers an intuitive interface with dynamic graphics to visualize the results clearly and effectively. It is a versatile tool for professionals and students around the world. Optimize your calculations and improve your analysis with our online interpolation and extrapolation calculator! In almost every field of science and engineering, we work with data. However, we rarely have all the data we need. We measure the temperature at 8 AM and 10 AM, but what was the temperature at 9:15 AM? We obtain the efficiency of an engine at 2000 and 3000 RPM, but what will its efficiency be at 2450 RPM? This is where interpolation and extrapolation come into play: they are the mathematical tools that allow us to make intelligent estimates to predict unknown values from those we already know. The need to estimate values is not new. Its roots go back to antiquity, long before computers. Ancient Astronomy: Greek astronomers, such as Hipparchus (2nd century BC), and later Ptolemy, pioneered the use of interpolation. To predict the position of the planets and stars, they created trigonometric tables (such as tables of sines and cosines). These tables did not contain all possible angles, so they developed methods to estimate intermediate values, laying the foundation for interpolation. The Calculus Revolution: In the 17th century, with the development of calculus, interpolation took a giant leap forward. Isaac Newton developed his famous "divided difference interpolation formula," a very powerful method for fitting a polynomial (a smooth curve) that passed exactly through a set of known points. Almost at the same time, Joseph-Louis Lagrange developed an alternative polynomial method that is conceptually simpler. The Digital Age: With the advent of computers in the 20th century, interpolation became a cornerstone of numerical analysis. Methods that were previously tedious to calculate by hand could now be performed in seconds, allowing their use in fields as diverse as aircraft design, digital image processing, and financial modeling. How Does Linear Interpolation Work? (The Simplest Method) The most basic and common form of interpolation is linear. The idea is incredibly intuitive: if you have two known data points, you assume the relationship between them is a straight line and find your unknown value somewhere on that line. Let's imagine we have two known points: Point 1: (X1, Y1) Point 2: (X2, Y2) And we want to find the value of Y for a new point X that lies between X1 and X2. 1. Calculate the Slope (the steepness of the line): First, we calculate the slope (m) of the straight line joining our two points. The slope tells us how much Y changes for every unit that X changes. Once we have the slope, we can use the equation of the line to find our unknown Y. The formula is derived from the idea that the slope between the first point and our new point must be the same as the total slope. Substituting the slope formula, we obtain the complete equation for linear interpolation:

Calculadora velocidad del sonido en agua, velocidad sonido agua, velocidad del sonido en agua temperatura, velocidad del sonido en agua por temperatura, temperatura. Speed of sound in water The speed of sound in water changes depending on the temperature and type of water. Neither calculation takes into account contributions from changes in water pressure or depth. In the case of brackish water, the salinity of the water influences its density and therefore the speed of sound. Saline water is denser than fresh water due to the presence of dissolved salts in it. The speed of sound in a medium is influenced by the density and compressibility of the medium, and since salinity affects the density of water, it also affects the speed of sound in that medium. Therefore, to calculate the speed of sound in saline water, its salinity needs to be taken into account. A typical salinity range is 35 ppt or g/L. When velocity accuracy is required, as in the case of ultrasonic flow measurement, a fixed value for velocity cannot be assumed. It critically depends on environmental variables such as temperature, salinity, and pressure (depth). One of the most widely used formulas in scientific and industrial contexts is the one proposed by K.V. Mackenzie in 1981, which offers good accuracy for saltwater within a wide operational range. This equation allows the speed of sound c (in m/s) to be estimated as a function of: Temperature (°C): T Salinity (ppt): S Depth (m): D Its importance lies in the fact that depending on the measurement technology used, from sonars to ultrasonic flow meters, it can provide a difference in meters or L/min. This is because these devices depend entirely on sound propagation, especially when their operating principle is Time in Transit or Time of Flight. In scientific contexts, this can mean inaccurate oceanographic data; in the naval industry, it can lead to navigation errors; and in defense, it can compromise threat detection. In metrology, it can lead to errors during the calibration of critical equipment for different types of industries. Furthermore, the study of sound propagation in water also has an environmental impact. Underwater noise caused by vessels and industrial activities propagates differently depending on these physical conditions, directly affecting marine wildlife that navigate and communicate through sound. At Axotek, we listen to our users. If you need a calculator to make your work and/or projects easier, you can contact us, and as soon as possible, we'll have it online at no cost to you. Request calculator

Clasificacion de IPFNA (Intrumentos para pesar de funcionamiento no automatico) y seleccion de patrones IPFNA Pattern Selection Professional Tool for Calculating Maximum Permissible Error (MPE) in Calibration. Welcome to our specialized tool for metrology, quality, and engineering professionals. This MPE calculator is an essential solution for determining whether a set of standard weights is suitable for the calibration of a non-automatic weighing instrument (NAWI), such as a scale or balance. Instructions: 1.- In the calculator, enter the range of the scale or balance. 2.- Select the units of the scale or balance. 3.- Select the resolution of the scale (d or e) . 4.- Press the "Calculate MPE" button In the world of precision measurement, ensuring that an instrument operates within its specified tolerances is an essential requirement for complying with quality standards, industry standards, and regulations such as those established by the OIML (International Organization of Legal Metrology). Our calculator simplifies one of the most critical steps in this process, using OIML R-111. What is the Maximum Permissible Error (MPE) and why is it so important? The Maximum Permissible Error (MPE) is the maximum difference allowed, by regulation or specification, between the nominal value of a standard weight and its actual conventional mass value. In simple terms, it is the small error that a high-precision weight can be "tolerated" to have. The key to good calibration lies in the following fundamental principle: the instrument you use to calibrate must be significantly more precise than the instrument being calibrated. The Golden Rule in Calibration: The One-Third Condition (PTH/3) To ensure the validity of a calibration, metrology establishes a crucial rule: the combined uncertainty of your standards (in this case, the sum of the PTHs of the weights you will use) must be at least three times better than the resolution (or minimum division) of the instrument to be calibrated. Condition to be met: Resolution ≥ (Sum of PTHs / 3) Our calculator automates this verification for you. Determine the optimal combination of weights to reach the maximum range of your scale and then check if this indispensable condition is met. Interpreting the Results Can be calibrated: Excellent! The result indicates that the uncertainty of your standard weights is low enough to perform a reliable calibration of your instrument, complying with the one-third rule. Cannot be calibrated: This result means that the sum of the errors of your weights is too large compared to the resolution of your scale. To proceed, you would need to use a set of weights of a higher accuracy class (for example, going from F1 to E2). Our tool gives you the confidence to perform accurate calibrations that meet the highest quality standards. Start calculating now and ensure the reliability of your measurements!

Conversor de unidades de Presion, °C, °F, K, °R, etc. Temperature Unit Converter Temperature, that intangible quality that determines everything from the weather to chemical reactions in our bodies, has been an object of scientific fascination for millennia. Its study represents one of humanity's most significant intellectual endeavors, one that intertwines physics, philosophy, and technological ingenuity. Temperature, in its purest form, is a measure of the average kinetic energy of the particles that make up a substance. This microscopic definition is expressed mathematically as: Where: ⟨Ek⟩ = average kinetic energy per particle kB = Boltzmann constant (1.380649 × 10⁻²³ J/K) T = absolute temperature in Kelvin This fundamental relationship connects the observable world with the quantum realm, revealing that what we perceive as "heat" is actually the frantic dance of atoms and molecules. In temperature, everything starts from absolute zero: The concept of absolute zero (-273.15°C or 0 K) is not merely a mathematical convention, but a physical limit imposed by the laws of thermodynamics. The third law formally states: Where S represents the entropy of the system and S₀ its value in the ground state, in practice, this principle implies that reaching absolute zero is impossible, although modern laser cooling techniques have achieved nanokelvin temperatures, approaching this cosmic limit. The path to precise temperature measurement began with qualitative devices such as Galileo's thermoscope (1592), which lacked a numerical scale. The major innovation came with liquid-in-glass thermometers, whose operation is based on the thermal expansion equation Where: ΔV = volume change V₀ = initial volume β = coefficient of thermal expansion ΔT = temperature change Later, more robust and specialized sensors were developed for each specific situation, for example: Thermocouples: These work through the Seebeck effect, which is the union of two different metals. The most common are type K (chromel-alumel) and type J (iron-constantan). When subjected to temperature changes, they generate an electrical potential difference. These sensors are very robust, have a long measuring range, are inexpensive, and have a very fast response time. However, their disadvantage is that this potential difference is not linear, and their accuracy is not very good. RTDs: They work through a thermoresistive effect, it is an electrical resistance that increases its value in ohms (Ω) as its temperature increases. They exist in various materials, the most common is platinum (PT100), which indicates that it has a resistance of 100 Ω at 0 ° C, but it can also be PT1000, which has 1000 Ω at 0 ° C. This value can be measured and is known as R₀. They exist in different classes and different sensitivities. They can be very precise if they are calibrated through characterization by the Callendar Van Dusen method or the ITS-90 method, in which the behavior of the resistance vs. temperature is obtained through coefficients that are entered into some industrial and scientific readers. Their disadvantages are that they have limited ranges at high temperatures, normally and commercially they only measure up to 660 ° C, they are slow to take the measurement (stabilize), and they are very prone to corrosion. They can crack and stop measuring due to thermal stress (going from low to high temperatures in a short period of time). Even in recent years, infrared thermography (pyrometers and thermal cameras) has gained significant importance due to its ability to measure in hostile or high-temperature environments, thus avoiding contact temperature measurements and preventing damage or accidents. This technology measures the temperature of an object by detecting the infrared radiation it emits, based on the Stefan-Boltzmann law. This technology has advanced significantly since the invention of the bolometer around 1880 by Samuel Pierpont Langley, and with thermal cameras, predictive maintenance can be performed and failures can be anticipated. In measuring thermal thermography, two terms normally arise: heat and temperature, which we explain: Heat is a form of energy in transit that flows spontaneously from warmer to colder bodies. Its study revolutionized science in the 19th century with the development of thermodynamics: Molecular kinetic energy: Heat manifests as the disordered motion of atoms and molecules (kinetic theory) First Law of Thermodynamics: ΔU = Q - W, where heat (Q) contributes to the internal energy (U) and W represents the thermodynamic work performed by the system on its environment. Transmission methods: Conduction (solids), convection (fluids), and radiation (vacuum) Temperature is a measure of the average kinetic energy of particles. Understanding it took centuries of development: • Historical scales: From the arbitrary degrees of Fahrenheit (1724) to the absolute Kelvin scale (1854) • Absolute zero (-273.15°C): Thermodynamic limit where molecular motion ceases • Instrumentation: Evolution from Galileo's thermoscopes to modern optical pyrometers. To measure temperature, we use different reference scales, each with its own characteristics and applications. For example: Celsius (°C) Definition: Based on the melting (0°C) and boiling (100°C) points of water at 1 atm. Usage: Metric system, science, and everyday life in most of the world. Incidentally, in some places, the scale is still called degrees Celsius. However, metrologically, this term has been obsolete since 1948, when the General Conference on Weights and Measures (CGPM) changed it to avoid confusion with the term angular unit (1/100 of a degree). Conversion formula: Kelvin (K) Definition: Absolute scale where 0 K = -273.15°C (absolute zero, absence of molecular motion). Use: Thermodynamics, quantum physics, and astronomy. Conversion formula: Fahrenheit (°F) Definition: Originally based on a mixture of ice, water, and sal ammoniac (0°F) and human body temperature (~96°F, later adjusted to 98.6°F). Use: Primarily in the U.S. and some English-speaking countries. Conversion formula: Rankine (°R) Definition: Absolute scale based on Fahrenheit (0°R = -459.67°F = absolute zero). Use: Thermal engineering in English systems. Conversion formula: Temperature scales are tools for translating human experience into the laws of physics. Their diversity reflects both historical and technical needs, but they all converge on one principle: quantifying thermal energy, from the most extreme cold in the universe to the intense heat of stars. GO TO CONVERTERS...