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Related Concept Videos

Drag01:23

Drag

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Drag is a resistive force opposing an object’s motion through a fluid, resulting from surface pressure and shear forces. It comprises two components: a perpendicular one from pressure and a tangential one from shear stress. Accurate drag calculations use pressure and wall shear stress distributions, often determined through Computational Fluid Dynamics (CFD) or wind tunnel testing. The drag coefficient, a dimensionless measure, depends on factors like shape, Reynolds number, Mach number,...
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Drag Force and Terminal Speed01:18

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An interesting force in everyday life is the force of drag on an object when it is moving in a fluid. Like friction, the drag force always opposes the motion of an object. Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid. This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in. For most large objects, such as cyclists, cars, and baseballs, that are not moving too...
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Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

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Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
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The Fluid Mosaic Model01:34

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The fluid mosaic model was first proposed as a visual representation of research observations. The model comprises the composition and dynamics of membranes and serves as a foundation for future membrane-related studies. The model depicts the structure of the plasma membrane with a variety of components, which include phospholipids, proteins, and carbohydrates. These integral molecules are loosely bound, defining the cell’s border and providing fluidity for optimal function.
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Fluid Pressure01:14

Fluid Pressure

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In mechanical engineering, fluid pressure plays a critical role in designing systems that utilize liquid flow, such as hydraulic systems, pumps, and valves. When designing these systems, engineers must ensure they can withstand the forces created by fluid pressure to avoid damage or failure.
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Accelerating Fluids01:17

Accelerating Fluids

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When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:
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Updated: Feb 11, 2026

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
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Universal expression for the drag on a fluid sphere.

D A Barry1, J-Y Parlange2

  • 1Ecological Engineering Laboratory (ECOL), Environmental Engineering Institute (IIE), Faculty of Architecture, Civil and Environmental Engineering (ENAC), Ecole polytechnique fédérale de Lausanne (EPFL), Lausanne, Switzerland.

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Summary
This summary is machine-generated.

A new formula predicts drag coefficients for spherical particles, drops, and bubbles in liquids. This accurate model covers various scenarios and validates against existing data for fluid dynamics research.

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Area of Science:

  • Fluid dynamics
  • Multiphase flow

Background:

  • Accurate prediction of drag forces is crucial for understanding particle, drop, and bubble behavior in liquids.
  • Existing models may have limitations in their range of applicability or accuracy for different flow regimes.

Purpose of the Study:

  • To develop a unified and accurate expression for predicting drag coefficients.
  • To provide a formula valid for spherical particles, drops, and bubbles across a range of Reynolds numbers.

Main Methods:

  • Development of a novel mathematical expression for drag coefficient prediction.
  • Validation against limiting cases (solid spheres, gas bubbles) and the Hadamard-Rybczynski solution.
  • Comparison with published numerical predictions for diverse physical conditions.

Main Results:

  • A new drag coefficient expression was successfully developed.
  • The formula accurately reproduces known limiting cases and theoretical solutions.
  • The expression demonstrates validity for Reynolds numbers up to a few hundred.

Conclusions:

  • The developed expression offers a reliable tool for predicting drag coefficients in multiphase flow systems.
  • This unified formula enhances the understanding of particle, drop, and bubble dynamics in homogeneous liquids.
  • The findings are supported by comparison with extensive numerical data, confirming its predictive power.