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Bernoulli's Equation for Flow Along a Streamline01:30

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Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
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Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
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Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
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Bernoulli's Equation for Flow Normal to a Streamline01:16

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Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
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Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
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Related Experiment Video

Updated: Feb 24, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
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A deterministic model for one-dimensional excluded flow with local interactions.

Yoram Zarai1, Michael Margaliot2, Anatoly B Kolomeisky3

  • 1School of Electrical Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel.

Plos One
|August 11, 2017
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Summary
This summary is machine-generated.

This study models particle flow in confined spaces, like cellular transport. It shows that particle interactions, whether attractive or repulsive, can optimize flow and prevent traffic jams, clarifying complex multi-particle dynamics.

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Area of Science:

  • Physics
  • Biophysics
  • Computational Biology

Background:

  • Many natural processes involve numerous molecules interacting in confined spaces.
  • Cellular transport by motor proteins exemplifies collective molecular behavior.

Purpose of the Study:

  • To develop a deterministic model for unidirectional particle flow on a lattice.
  • To analyze the impact of inter-particle forces on flow dynamics and steady-states.

Main Methods:

  • Derivation of a deterministic compartmental model for particle flow.
  • Application of contraction theory to prove model convergence to a unique steady-state.
  • Analysis and simulation of inter-particle forces' effects.

Main Results:

  • The model admits a unique steady-state to which all trajectories converge.
  • Attractive and repulsive forces significantly influence steady-state flow.
  • Inter-particle forces alleviate traffic jams, thereby increasing overall flow.

Conclusions:

  • Theoretical analysis clarifies microscopic aspects of multi-particle dynamics.
  • Inter-particle forces play a crucial role in optimizing collective particle transport.
  • The model provides insights into phenomena like cellular transport.