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Free Jet

Free Jet

Free jets describe the flow of liquid exiting a reservoir through an opening into the atmosphere without resistance. The velocity (v) of the liquid jet is derived using Bernoulli's principle and expressed as:

Steady, Laminar Flow in Circular Tubes

Steady, Laminar Flow in Circular Tubes

Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is...

Steady, Laminar Flow Between Parallel Plates

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.

Bernoulli's Equation for Flow Normal to a Streamline

Bernoulli's Equation for Flow Normal to a Streamline

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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Bernoulli's Equation for Flow Along a Streamline

Bernoulli's Equation for Flow Along a Streamline

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:

Laminar Flow

Laminar Flow

Laminar flow represents a smooth, orderly fluid motion where particles move along parallel paths, resulting in minimal mixing between layers. Streamlined particle paths characterize this flow regime and occur under conditions where viscous forces dominate over inertial forces. The distinction between laminar, transitional, and turbulent flow is primarily determined by the Reynolds number, a dimensionless quantity calculated as:

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Related Experiment Video

Updated: Jun 3, 2025

Microfluidic Chips Controlled with Elastomeric Microvalve Arrays

Microfluidic Chips Controlled with Elastomeric Microvalve Arrays

Published on: October 1, 2007

Control of flow deflection angle around the corner using microjet array.

Yuto Nakadori¹, Satoshi Yuura¹, Takahiro Kagawa¹

¹Department of Advanced Science and Technology, Toyota Technological Institute, 2-12-1 Hisakata, Tempaku-Ku, Nagoya, Aichi, 468-8511, Japan.

Scientific Reports

|January 6, 2025

Summary

A novel microjet array technique actively controls airflow around corners. This method precisely adjusts flow deflection by manipulating vortex dynamics, offering precise control over aerodynamic behavior.

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Last Updated: Jun 3, 2025

Microfluidic Chips Controlled with Elastomeric Microvalve Arrays

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Published on: April 12, 2018

Area of Science:

Fluid dynamics
Aerodynamics
Flow control

Background:

Controlling airflow around corners is crucial in various engineering applications.
Traditional methods often lack precision and efficiency.

Purpose of the Study:

To introduce a new active flow control technique using a microjet array.
To identify key parameters influencing flow deflection angle around a corner.

Main Methods:

Utilized a microjet array to inject jets from a downstream-facing step.
Employed Particle Image Velocimetry (PIV) to measure flow velocities.
Introduced a momentum coefficient for data reduction.

Main Results:

Microjet injection generates a vortex, pulling the flow downwards.
Flow deflection angle increases with supply pressure (jet Mach number).
A linear relationship was found between momentum coefficient and streamline slope.

Conclusions:

The microjet array provides effective active control of flow deflection.
The momentum coefficient parameter enables precise, speed-independent control of flow deflection.
This technique offers precise aerodynamic control for corner flows.