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Related Concept Videos

Free Jet01:14

Free Jet

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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:
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Bernoulli's Principle01:01

Bernoulli's Principle

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Bernoulli's equation incorporates how fluid pressure changes across a static, incompressible fluid by equating the kinetic energy contribution to zero. It is also helpful in analyzing horizontal flows in which the gravitational energy density is constant throughout. The latter equation is so useful that it is called Bernoulli's principle. According to Bernoulli's principle, the fluid pressure drops if the speed increases and vice versa.
Bernoulli's principle has several...
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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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Pascal's Law01:04

Pascal's Law

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In 1653, the French philosopher and scientist Blaise Pascal published "Treatise on the Equilibrium of Liquids," which discussed the principles of static fluids. A static fluid is a fluid that is not in motion. When a fluid is not flowing, we say that the fluid is in static equilibrium. If the fluid is water, we say it is in hydrostatic equilibrium. For a fluid in static equilibrium, the net force on any part of the fluid must be zero; otherwise, the fluid will start to flow. Pascal...
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Energy Conservation and Bernoulli's Equation01:16

Energy Conservation and Bernoulli's Equation

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Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
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Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

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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.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines.
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Related Experiment Video

Updated: Jul 8, 2025

Visualization of High Speed Liquid Jet Impaction on a Moving Surface
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Universal Free-Fall Law for Liquid Jets under Fully Developed Injection Conditions.

M Beneitez1, D Moreno-Boza2, A Sevilla2

  • 1DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

Physical Review Letters
|December 15, 2023
PubMed
Summary
This summary is machine-generated.

We discovered a universal shape for vertical liquid jets in air, where gravity dominates viscosity. This new model accurately predicts jet radius, unlike previous theories.

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Area of Science:

  • Fluid dynamics
  • Physics of liquids
  • Aerodynamics

Background:

  • Understanding liquid jet behavior is crucial in various scientific and engineering fields.
  • Previous models, like Mariotte's law, have limitations in describing jet dynamics under specific conditions.

Purpose of the Study:

  • To derive a universal shape for vertical liquid jets in air.
  • To provide an analytical solution for jet radius based on fluid dynamics principles.
  • To validate the theoretical model against experimental data.

Main Methods:

  • Developed an analytical solution using the theory of ideal flows with vorticity.
  • Assumed viscous forces are much smaller than gravitational forces.
  • Neglected surface-tension forces for simplification.

Main Results:

  • Derived a universal equation for scaled jet radius: Rⱼ = [(1+Z/4)¹/² - (Z/4)¹/²]¹/².
  • The equation relates jet radius (Rⱼ) to vertical distance (Z) scaled by gravitational length (l<0xE1><0xB5><0xA2>).
  • Experimental data from long injectors showed excellent agreement with the new theoretical prediction.

Conclusions:

  • The derived universal shape provides a more accurate description of vertical liquid jets.
  • The new model challenges and improves upon existing laws like Mariotte's law.
  • This finding has implications for understanding and predicting liquid jet behavior in air.