Dimensionless Arguments
Dimensionless Arguments - Related Videos
01:15
Dimensionless Groups in Fluid Mechanics
0 Views •
2025
Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
09:26
Persuasion: Motivational Factors Influencing Attitude Change
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2023
Source: William Brady & Jay Van Bavel—New York University Decades of social psychological research sought to understand a fundamental question that pervades our social life including politics, marketing and public health; namely, how are people persuaded to change their attitudes towards an idea, person, or object? Traditional work found that there are key factors that influence whether persuasion is successful or not including the source of the persuasive message ("source"), and the...
02:20
Routes of Persuasion
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2020
Persuasion is the process of changing our attitude toward something based on some kind of communication. Much of the persuasion we experience comes from outside forces. How do people convince others to change their attitudes, beliefs, and behaviors? What communications do you receive that attempt to persuade you to change your attitudes, beliefs, and behaviors? Yale Attitude Change Approach The topic of persuasion has been one of the most extensively researched areas in social psychology...
05:56
Exploring Caspase Mutations and Post-Translational Modification by Molecular Modeling Approaches
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Cited by 1 •
2022
The present protocol uses a biomolecular simulation package and describes the molecular dynamics (MD) approach for modeling the wild-type caspase and its mutant forms. The MD method allows for assessing the dynamic evolution of the caspase structure and the potential effect of mutations or post-translational modifications.
10:31
Nonconscious Mimicry Occurs when Affiliation Goals are Present
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2023
Source: Diego Reinero & Jay Van Bavel—New York University People are social chameleons and regularly engage in nonconscious behavioral mimicry. This occurs when an individual unwittingly imitates the behaviors of another person, such as crossing one's legs moments after a person sitting adjacent does so, or adjusting one's body posture to match a conversation partner. Rapport between two people increases behavioral mimicry, just as mimicry also increases rapport. Psychologists have posited...
FAQs
The Buckingham Pi theorem organizes a physical problem around independent combinations of variables whose dimensions cancel. Instead of treating every measured quantity separately, it identifies a smaller set of dimensionless groups that can express the governing relationship. This reduction clarifies which combinations control behavior and provides a systematic basis for scaling analysis in physics.
Their values compare the relative influence of physical effects within the same relationship. When a governing equation is written in dimensionless form, the associated groups show how competing processes scale with one another. Large or small values can therefore indicate which effects are important under specified conditions, helping researchers simplify models without changing the relevant physical behavior.
Ordinary quantities retain units and may change numerical value when the measurement system changes. Dimensionless arguments do not have that dependence, so their numerical values can be compared directly across unit systems. This feature also helps expose the structure of equations, because relationships expressed through these groups emphasize physical similarity rather than the choice of meters, seconds, or other units.
Reynolds number and Mach number illustrate how different combinations of physical quantities can summarize system behavior without carrying units. Their inclusion in a model allows conditions from separate experiments, simulations, or natural phenomena to be compared through common dimensionless values. In this way, they support interpretation of flow and wave-related problems without requiring identical physical scales.
First identify the variables relevant to the physical relationship and write their dimensions. Then combine them as products of variables raised to selected powers, choosing the powers so every fundamental dimension cancels. The resulting groups can be checked for independence and used with the Buckingham Pi theorem to rewrite the relationship in a more compact, measurement-system-independent form.
They allow systems with different sizes or operating conditions to be compared when their corresponding dimensionless groups are similar. This provides a way to connect laboratory experiments, simulations, and natural phenomena without matching every dimensional quantity individually. Scaling analysis can therefore help assess whether observed behavior is transferable from one physical setting to another.
They are particularly useful in fluid dynamics, heat transfer, mechanics, and wave propagation. In these areas, many variables can interact across different length, time, and energy scales. Dimensionless formulations reduce that complexity, organize comparisons among systems, and help researchers determine which effects require attention when predicting behavior under changed conditions.
A dimensionless formulation shows how the important variables are coupled and which independent combinations govern the result. It can simplify the equations while preserving the relationships that determine system behavior. Researchers can then compare outcomes across different experiments or simulations, identify relevant scaling regimes, and interpret whether changes arise from altered physics or merely from different measurement units.