Name: pressure and speed in bernoulli's equation
Uploaded: 2025-02-13T15:43:14.000Z
Duration: 1 min 30 s
Channel: JoVE

베르누이 방정식은 유선을 따라 압력, 속도 및 고도를 관련시켜 움직이는 유체의 거동을 설명합니다.
이는 에너지 보존의 원리에 의존하며, 일정한 흐름, 비압축성 유체, 점도가 없다고 가정하여 마찰력이 존재하지 않음을 의미합니다.
압력 항은 유체가 특정 지점에서 가하는 힘을 나타냅니다.
속도 항은 유체의 운동 에너지를 나타내며, 이는 유체 속도가 증가함에 따라 압력이 감소함을 나타냅니다.
고도 항은 기준점에 상대적인 수직 위치를 기준으로 유체의 위치 에너지를 반영합니다.
이 원칙은 물 분배 시스템, 댐 배수로 및 벤투리 계량기와 같은 실제 상황에 적용됩니다.
물 분배 시스템에서 베르누이 방정식은 물이 다양한 직경의 파이프를 통해 흐를 때 압력이 어떻게 떨어지는지 예측하여 도시 네트워크 전체에 효율적인 공급을 보장합니다.
베르누이 방정식은 댐 배수로에서 아래로 흐를 때 물의 속도가 어떻게 증가하고 압력이 감소하는지 설명하여 엔지니어가 다양한 유속을 안전하게 관리할 수 있는 구조를 설계하는 데 도움이 됩니다.
하수 시스템에 일반적으로 사용되는 벤츄리 계량기는 파이프 섹션 간의 압력 차이를 감지하여 유량을 측정하여 효과적인 폐수 관리를 보장합니다.

유선을 따라 흐르는 베르누이 방정식

Bernoulli's Equation for Flow Along a Streamline

베르누이 방정식은 유선을 따라 움직이는 유체의 에너지 보존과 관련이 있습니다. 이 방정식은 정상 흐름 하에서 비압축성 및 비점성 유체에 적용됩니다. 이러한 흐름의 경우, 뉴턴의 제2법칙이 압력 차이, 중력 및 속도 변화로 인한 힘을 경험하는 작은 유체 요소에 적용됩니다. 힘의 균형은 다음과 같은 베르누이 방정식 형태로 이어집니다.

<img alt="Equation 1" src="/files/ftp_upload/18033/18033_Equation_1.svg" style="text-align: center; height: 26px;">

여기서 P는 압력, ρ는 유체의 밀도, v는 속도, g는 중력으로 인한 가속도를 나타내며 고도는 h로 표시됩니다. 이 방정식의 각 항은 유체의 단위 부피당 에너지를 나타냅니다.

두 개의 직경이 다른 수평 파이프를 흐르는 물을 생각해 보세요. 지점 1에서 파이프의 직경이 크고 지점 2에서 파이프가 좁아집니다. 베르누이 방정식은 물의 속도가 좁은 구간(지점 2)에서 증가하면 유선을 따라 에너지를 보존하기 위해 압력이 감소해야 한다는 것을 알려줍니다. 베르누이 방정식을 파이프 구간에 적용하면 다음과 같습니다.

<img alt="Equation 2" src="/files/ftp_upload/18033/18033_Equation_2.svg" style="text-align: center; height: 26px;">

베르누이 원리는 유체 흐름 시스템을 이해하고 설계하는 데 중요합니다. 예를 들어, 물 분배망에서 파이프 직경의 변화는 흐름 효율에 영향을 미치는 압력 변화를 일으킵니다. 방정식에서 알 수 있듯이, 파이프가 좁을수록 속도는 증가하고 압력은 감소하여 도시 시스템 전체에 일관된 공급이 보장됩니다. 댐 방류로에서 고도로 인한 유체의 잠재 에너지는 물이 내려갈 때 운동 에너지로 변환됩니다. 이로 인해 속도가 증가하고 그에 따라 압력이 감소하는데, 이는 다양한 방류율을 안전하게 관리할 수 있는 방류로를 설계하는 데 사용되는 현상입니다.

베르누이 방정식은 유선을 따라 압력, 속도 및 고도를 관련시켜 움직이는 유체의 거동을 설명합니다.
그것은 의존합니다 ...

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

Education

교육

JoVE Core

Civil Engineering

토목공학

Unit 1

제1단원

Fluid Dynamics

유체역학

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 elevation. Each term represents energy per unit volume of the fluid. This makes Bernoulli's equation a useful way to track how energy changes as fluid moves.

A simple pipe example shows the main effect. Water flows through a horizontal pipe with two sections. Point 1 has a large diameter, and point 2 has a narrower diameter. When the water speeds up at the narrow section, the pressure must drop to keep energy conserved along the streamline.

Bernoulli's principle also helps explain real flow systems. In water distribution networks, changes in pipe diameter create pressure changes that affect flow efficiency. A narrower pipe raises velocity and lowers pressure, which helps support a steady supply across urban systems. In dam spillways, water loses potential energy as it falls. That energy turns into kinetic energy, so velocity increases and pressure decreases. Engineers use this effect to design spillways that can handle changing discharge rates safely.

Pressure and Speed in Bernoulli's Equation

pressure-and-speed-in-bernoullis-equation

bernoulli's equation for flow along a streamline

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

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...

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 Bernoulli's equation links pressure, speed, and height in flowing fluids, with pipe and dam spillway examples for high school science.

Pressure and Speed in Bernoulli's Equation | 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

Pressure and Speed in Bernoulli's Equation

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