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Related Concept Videos

Resultant Moment: Scalar Formulation01:31

Resultant Moment: Scalar Formulation

When multiple forces act on an object in two-dimensional space, the concept of the net moment can be used to understand the tendency of these forces to induce rotational motion about a fixed point. The scalar formulation of the resultant moment is a helpful tool in analyzing the equilibrium of structures subjected to multiple forces.
To determine the resultant moment, the moments caused by all the forces in a system in the x-y plane are considered. Positive moments are typically...
Moment of a Force: Scalar Formulation01:18

Moment of a Force: Scalar Formulation

The moment of a force, also known as torque, measures the ability of the force to create rotational motion in a body about an axis. It is a vector quantity, meaning it has both magnitude and direction. This concept is used extensively in engineering, physics, and mechanics.
Consider a simple example of a flywheel being rotated about a point, O, by applying a force to it. In this case, the moment arm is the perpendicular distance between the point O and the line of action of the force. The...
Moment of a Force About an Axis: Scalar01:28

Moment of a Force About an Axis: Scalar

The moment of a force about an axis is a crucial concept in mechanics that helps determine an object's rotational motion around a specific point or axis. The moment of force can be calculated using scalar analysis, which involves considering the perpendicular distance between the axis of rotation and the line of action of the force or simply the moment arm.
To better understand the concept of moment of force, consider the example of a cyclist riding a bicycle. When the cyclist applies force on...
Couples: Scalar and Vector Formulation01:21

Couples: Scalar and Vector Formulation

One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel's rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment. To...
Moment-of-Momentum Equation01:09

Moment-of-Momentum Equation

The moment-of-momentum equation is a critical tool for analyzing the torque produced by the rotating blades of a wind turbine. This equation is derived by applying Newton's second law to a fluid particle, which states that the rate of change of linear momentum is equal to the external force acting on the particle.
Resultant Moment: Vector Formulation01:30

Resultant Moment: Vector Formulation

When a force is applied to an object, the tendency of the object to rotate about a point is known as its moment. If multiple forces are acting on an object, the sum of moments of all the forces acting on a body can be expressed as the resultant moment of the system. The resultant moment can be considered a vector quantity that can be added and subtracted like any other vector.
The resultant moment of a system of forces can be calculated through vector formulation. For example, if we consider...

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Related Experiment Video

Updated: Jun 26, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Revised moment propagation method for scalar transport.

D Yu1, S S Girimaji, A J C Ladd

  • 1Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611-6005, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2008
PubMed
Summary
This summary is machine-generated.

The moment propagation (MP) method struggles with turbulent scalar transport. An improved MP2 model enhances accuracy, especially in high-velocity flows, by removing velocity-dependent diffusion.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Last Updated: Jun 26, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Area of Science:

  • Fluid Dynamics
  • Computational Physics
  • Turbulence Modeling

Background:

  • The moment propagation (MP) method is used to model passive scalar transport in turbulent fluids.
  • Existing MP models show inaccuracies in capturing scalar field evolution at moderate Reynolds numbers.

Purpose of the Study:

  • To investigate the limitations of the standard MP method for scalar transport.
  • To develop and validate an improved MP model (MP2) for more accurate scalar transport predictions.

Main Methods:

  • Numerical simulations using the moment propagation (MP) method.
  • Theoretical analysis of diffusivity in MP models.
  • Development and testing of the improved MP2 model across various flow conditions.

Main Results:

  • The standard MP method exhibits velocity-dependent diffusion, limiting its applicability.
  • The MP2 model successfully eliminates velocity-dependent diffusion.
  • Accurate scalar transport predictions were achieved with MP2 at grid Péclet numbers over 10, particularly in high-velocity flows.

Conclusions:

  • The MP2 model offers a significant improvement over the standard MP method for turbulent scalar transport.
  • MP2 provides accurate predictions across a wider range of flow velocities and Péclet numbers.
  • The improved model is suitable for simulating scalar transport in complex turbulent environments.