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Related Concept Videos

Uncertainty: Overview00:59

Uncertainty: Overview

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Uncertainty in Measurement: Reading Instruments02:46

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Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
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Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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The Uncertainty Principle04:08

The Uncertainty Principle

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Updated: Jul 15, 2025

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
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Quantifying Numerical Uncertainty in Background-Oriented Schlieren.

Pranjal Anand1, Jiacheng Zhang1, Lalit K Rajendran2

  • 1School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA.

Research Square
|October 4, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method to calculate numerical uncertainty in Background Oriented Schlieren (BOS) imaging. By integrating numerical and random uncertainties, the technique significantly improves the accuracy of density field uncertainty prediction in fluid dynamics research.

Keywords:
Background Oriented Schlieren (BOS)Richardson extrapolationuncertainty estimation

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Area of Science:

  • Fluid Dynamics
  • Optical Measurement Techniques
  • Computational Physics

Background:

  • Background Oriented Schlieren (BOS) is a valuable optical technique for visualizing fluid flow.
  • Accurate uncertainty quantification is crucial for reliable BOS measurements.
  • Existing methods often do not fully account for numerical uncertainties inherent in image processing.

Conclusions:

  • The developed method provides a more accurate estimation of total uncertainty in BOS measurements.
  • Accounting for numerical uncertainty enhances the reliability of density field results.
  • This approach has significant implications for improving the rigor of future experimental fluid dynamics studies using BOS.