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Related Concept Videos

Steady Flow of a Fluid Stream01:27

Steady Flow of a Fluid Stream

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Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...
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Conservation of Mass in Finite Cotrol Volume01:16

Conservation of Mass in Finite Cotrol Volume

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The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
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Control Volume and System Representations01:16

Control Volume and System Representations

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Two key frameworks are employed to analyze mass, energy, and momentum transfer: the control volume approach and the system approach. These frameworks offer different perspectives, depending on whether the focus is on a specific region in space (control volume approach) or a defined mass of fluid (system approach).
The control volume approach considers a stationary region in space through which fluid flows. This region is bounded by a control surface.  For instance, in the case of water...
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Conservation of Mass in Fixed, Nondeforming Control Volume01:07

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856
The principle of conservation of mass is fundamental in fluid dynamics and is crucial for analyzing flow within fixed control volumes, such as pipes or ducts. This principle states that the total mass within a control volume remains constant unless altered by the inflow or outflow of mass through the control surfaces. This results in a vital relationship for steady, incompressible flow where the mass entering a system equals the mass leaving it.
In the case of a sewer pipe, which can be modeled...
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Eulerian and Lagrangian Flow Descriptions01:22

Eulerian and Lagrangian Flow Descriptions

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Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
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Introduction to Types of Flows01:23

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Fluid flows are categorized by dimensionality and behavior, with one-dimensional flow being the simplest form, where properties like velocity and pressure change only along a single axis. Water moving through straight pipes exemplifies this flow type, as variations in other directions are minimal. One-dimensional analysis helps simplify understanding such flows, focusing solely on changes along the pipe's length.
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Related Experiment Video

Updated: May 27, 2025

Controlling Flow Speeds of Microtubule-Based 3D Active Fluids Using Temperature
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Control of flow behavior in complex fluids using automatic differentiation.

Mohammed G Alhashim1,2, Kaylie Hausknecht3, Michael P Brenner1,3

  • 1School of Engineering and Applied Physics, Harvard University, Cambridge, MA 02138.

Proceedings of the National Academy of Sciences of the United States of America
|February 18, 2025
PubMed
Summary
This summary is machine-generated.

Automatic differentiation (AD) offers a powerful and efficient method for solving complex fluid dynamics inverse design problems. This approach simplifies high-dimensional optimization, proving effective across various fluid flow scenarios.

Keywords:
automatic differentiationchaotic mixingdispersioninverse designoptimization

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Area of Science:

  • Computational fluid dynamics
  • Optimization
  • Applied mathematics

Background:

  • Inverse design of complex flows is computationally expensive due to high-dimensional optimization.
  • Traditional methods often limit control parameters or use adjoint-based approaches, which can be complex.
  • Existing techniques face challenges in efficiently handling particle-laden flows and complex media.

Purpose of the Study:

  • To demonstrate automatic differentiation (AD) as a versatile platform for solving inverse problems in complex fluid dynamics.
  • To showcase the ease of implementation and computational efficiency of AD for high-dimensional optimization.
  • To apply AD to diverse fluid flow problems, including active matter, porous media, and journal bearings.

Main Methods:

  • Leveraging recent advances in automatic differentiation (AD) for gradient computation.
  • Applying AD to solve optimization problems in Newtonian fluids, structured porous media, and journal bearing flows.
  • Utilizing AD for high-dimensional optimization involving particle-laden flows.

Main Results:

  • AD provides a generic and efficient solution for inverse design problems in complex fluids.
  • Demonstrated successful application of AD across multiple challenging fluid dynamics scenarios.
  • AD significantly enhances computational efficiency and simplifies implementation for high-dimensional optimization.

Conclusions:

  • Automatic differentiation is a powerful tool for tackling complex inverse design problems in fluid dynamics.
  • The AD approach offers a more accessible and efficient alternative to traditional optimization methods.
  • This methodology is broadly applicable to various fluid flow systems, including those with active matter and particle suspensions.