Name: liquid speed from reservoir outlets
Uploaded: 2026-01-30T03:08:28.000Z
Duration: 1 min 14 s
Channel: JoVE

자유 제트는 유체가 노즐에서 나와 공기 중으로 자유롭게 흐를 때 Bernoulli의 방정식으로 설명되는 유체 거동을 보여줍니다.
노즐의 유속은 그 위에 있는 유체 기둥의 높이에 의해 결정되며, 이는 위치 에너지를 운동 에너지로 변환합니다.
제트의 출구 압력은 대기압과 일치하며 유체가 큰 저장소에서 흐를 때 속도가 증가합니다.
유체 관성으로 인해 제트는 노즐 바로 바깥쪽에서 좁아져 가장 작은 단면적을 형성합니다. 이러한 현상을 대정맥 계약(vena contracta)이라고 합니다.
수축대정맥에서 분사의 면적과 노즐의 면적의 비율은 수축 계수를 제공합니다.
나이프 에지(knife-edge), 잘 다듬어진 노즐, 날카로운 가장자리 및 재진입 설계와 같은 다양한 노즐 모양은 흐름 패턴과 수축 계수에 영향을 미칩니다.
배수로 및 둑과 같은 시스템을 설계할 때 대정맥 수축 효과는 정확한 유량 측정을 위해 고려됩니다.
프리 제트는 유체 흐름을 제어하고 구조적 충격을 최소화하기 위해 토목 공학 응용 분야에서 매우 중요합니다.

자유 제트

자유 제트는 저항 없이 개구부를 통해 대기로 저장소에서 빠져나가는 액체의 흐름을 설명합니다. 액체 제트의 속도(V)는 베르누이의 원리를 사용하여 도출되며 다음과 같이 표현됩니다.

<img alt="Equation 1" src="/files/ftp_upload/18037/18037_Equation_1.svg" style="text-align: center; height: 15px;">

여기서 h는 개구부 위의 액체 높이입니다. 이 관계는 저장소 표면과 제트 출구 모두에서 대기압을 가정합니다. 유체 기둥의 높이는 저장소의 노즐에서 유체의 속도를 제어하며, 여기서 유체의 위치 에너지는 흐름 중에 운동 에너지로 변환됩니다.

베나 수축 현상은 액체가 날카로운 모서리의 구멍을 통해 빠져나갈 때 발생하여 제트 직경 d_j가 노즐 직경 d_o보다 작아집니다. 이는 유체 유선이 급격한 모서리를 따라갈 수 없어 수축된 흐름 영역이 생성되기 때문에 발생합니다. 수축 계수는 베나 수축에서 제트의 단면적과 노즐의 단면적의 비율로 제트 수축 정도를 정량화합니다. 이 매개변수는 노즐의 지오메트리에 영향을 받으며, 나이프 에지, 샤프 에지, 웰 라운드, 재진입 노즐과 같은 다양한 설계가 뚜렷한 흐름 패턴과 수축 특성을 생성합니다. 웰 라운드 노즐의 경우 C_c = 1.0인 반면, 샤프 또는 나이프 에지 오리피스는 C_c를 약 0.61로 줄입니다. 재진입 노즐은 더 낮은 값을 나타냅니다.

이러한 흐름 특성과 수축 효과는 저수조에서 산업용 노즐에 이르기까지 액체 배출과 관련된 엔지니어링 응용 분야에서 중요합니다.

자유 제트는 유체가 노즐에서 나와 공기 중으로 자유롭게 흐를 때 Bernoulli의 방정식으로 설명되는 유체 거동을 보여줍니다.
유속 ...

Education

교육

JoVE Core

Civil Engineering

토목공학

Unit 1

제1단원

Fluid Dynamics

유체역학

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Free Jet

liquid speed from reservoir outlets

Free jets show how liquid moves after leaving a reservoir through an opening and flowing into the air without resistance. The jet speed is found with Bernoulli’s principle, and it depends on the height of liquid above the opening. This relationship assumes atmospheric pressure at both the reservoir surface and the jet exit.

The liquid column’s height controls the speed at the nozzle because the fluid’s potential energy changes into kinetic energy during flow. As the liquid leaves the reservoir, its motion reflects this energy conversion. This is why a deeper liquid level can produce a faster jet.

A sharp-edged orifice can also cause vena contracta, which is the narrowed region where the jet becomes smaller than the nozzle opening. This happens because the streamlines cannot follow the abrupt edge smoothly. The contraction coefficient measures this narrowing by comparing the jet area at vena contracta with the nozzle area.

Nozzle shape changes the flow pattern and the amount of contraction. Knife-edge, sharp-edge, well-rounded, and re-entrant nozzles each produce different results. For a well-rounded nozzle, the contraction coefficient is 1.0, while sharp or knife-edged openings reduce it to about 0.61, and re-entrant nozzles produce even lower values. These effects matter in engineering systems that discharge liquid from reservoirs and industrial nozzles.

Liquid Speed from Reservoir Outlets

bernoulli's equation for flow along a streamline

bernoulli-s-equation-for-flow-along-a-streamline

Pressure and Speed in Bernoulli's Equation

Bernoulli's equation links pressure, speed, and height in a moving fluid along a streamline. It is used for incompressible, inviscid fluids under steady flow. The idea comes from applying Newton's second law to a small fluid element. That element feels forces from pressure differences, gravity, and changes in velocity. The resulting equation shows how fluid energy is shared. In the equation, P is pressure, ρ is fluid density, v is velocity, g is the acceleration due to gravity, and h is...

bernoulli's equation for flow normal to a streamline

bernoulli-s-equation-for-flow-normal-to-a-streamline

Pressure Changes Across Curved Streamlines

Bernoulli's equation for flow normal to a streamline describes how pressure changes across curved streamlines. When a fluid follows a curved path, the outer side of the curve experiences centrifugal force, which pushes the fluid outward. The pressure is therefore higher on the inner side, near the center of curvature, and lower farther out. The size of this pressure difference depends on the fluid's velocity and the radius of curvature. In flows with nearly straight streamlines, the pressure...

bernoulli's equation: problem solving

Venturi Meter Flow Rate from Pressure

A Venturi meter measures fluid flow rate in a pipeline by using pressure changes and Bernoulli's equation. In a sewage system, it can be used to determine wastewater flow rate by reading the pressure difference across the meter. The narrowed throat makes the fluid speed up, and that change in speed is linked to pressure drop. The first step is to find the cross-sectional areas of the pipe and the Venturi throat. These areas are needed to interpret the pressure difference shown on the pressure...

static, stagnation, dynamic and total pressure

static-stagnation-dynamic-and-total-pressure

Pitot-Static Measurement in Bernoulli Flow

Static pressure, dynamic pressure, stagnation pressure, and total pressure are key ideas in fluid dynamics. They are often explained with Bernoulli's equation. In that equation, p is static pressure, 1/2ρV^2 is dynamic pressure, γz is hydrostatic pressure or potential energy pressure, and pT is total pressure. For incompressible flow, the total pressure stays constant along a streamline. Static pressure is the pressure a fluid exerts when it is at rest, or when flowing fluid is brought to rest...

free jet

Free jets show how liquid moves after leaving a reservoir through an opening and flowing into the air without resistance. The jet speed is found with Bernoulli’s principle, and it depends on the height of liquid above the opening. This relationship assumes atmospheric pressure at both the reservoir surface and the jet exit. The liquid column’s height controls the speed at the nozzle because the fluid’s potential energy changes into kinetic energy during flow. As the liquid leaves the...

continuity equation

Fluid Flow and Area Changes

Fluid flow and area changes are linked by the continuity equation. For a steady flow of an incompressible fluid in a confined system, the mass flow rate stays constant. This idea is useful in nozzles, syringes, and pipes where the cross-sectional area changes. The mass flow rate is written as an equation that connects density, area, and velocity. For incompressible flow, the density stays the same, so the equation becomes simpler. When the area gets smaller, the fluid speed must increase. When...

energy line and hydraulic gradient line

Fluid Head Profiles in Pipes and Channels

Fluid head profiles in pipes and channels show how pressure, speed, and height change in a flowing fluid. These profiles come from Bernoulli's equation for steady, incompressible, inviscid flow. In that equation, total head includes pressure head, velocity head, and elevation head. The energy line (EL) shows the total head available in the flow. It sits above the datum and includes all three energy parts. Under ideal conditions, the EL stays horizontal because the total energy does not change...

design example: designing water slide

Water Slide Speed and Bernoulli's Principle

Water slide speed is controlled by Bernoulli's principle and the height of the slide. Engineers use these ideas to keep the ride exciting while making sure the water stays safe for riders. As water moves downhill, gravity makes it speed up. The water at the bottom depends on the height it starts from. A taller slide gives the water more potential energy at the top. That energy changes into kinetic energy as the water descends, so the flow becomes faster. Bernoulli's principle helps describe...

key terms and concepts

Learn how liquid speed from a reservoir depends on height, Bernoulli’s principle, and nozzle shape, including vena contracta and contraction coefficient.

Liquid Speed from Reservoir Outlets | JoVE K12

JoVE Core Civil Engineering offers a foundational exploration of essential construction materials such as bricks, stones, steel, wood, and concrete, along with fluid mechanics topics like flow over immersed bodies, open channel flow, and dimensional modeling. It also covers key surveying concepts, including leveling, traverse adjustments, curve design, topographic mapping, and geospatial technologies (GPS & GIS). Science-in-action videos showcase laboratory research on materials, fluids, and surveying practices in real-world engineering systems.

civil engineering

Liquid Speed from Reservoir Outlets

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