Name: pressure changes across curved streamlines
Uploaded: 2025-02-13T15:43:14.000Z
Duration: 1 min 16 s
Channel: JoVE

유선에 수직인 흐름에 대한 베르누이의 방정식은 바깥쪽을 향하는 원심력으로 인해 곡선 유선에서 압력이 어떻게 변하는지 설명합니다.
압력은 곡률 중심 근처의 곡선 안쪽에서 더 높으며 이러한 원심력의 균형을 맞추기 위해 바깥쪽으로 감소합니다.
압력 차이는 유체의 속도와 곡선의 선명도에 따라 다릅니다.
압력 차이는 거의 직선에 가까운 유선의 경우 작지만 소용돌이 또는 파이프 굴곡과 같이 급격히 구부러진 흐름에서 더 두드러집니다.
실제 응용 분야에서 이 개념은 유압 구조, 곡선 채널 및 파이프 시스템을 설계하는 데 도움이 되며, 잘못된 압력 계산으로 인해 구조적 결함이 발생할 수 있습니다.
또한 건물 및 교량과 같은 토목 구조물 주변의 바람 흐름에도 적용되며, 곡선 유선으로 인한 압력 차이는 안정성을 보장하기 위해 고려해야 합니다.
물이 곡면을 따라 흐르는 곡선형 댐 및 저수지 설계에서 유선형 전체의 압력 차이는 구조물이 특히 고속 흐름에서 물이 가하는 힘을 견딜 수 있도록 합니다.

유선에 수직인 흐름에 대한 베르누이 방정식

유선에 수직인 흐름에 대한 베르누이 방정식은 유체의 곡률에 의해 유도된 외향 원심력으로 인해 곡선 유선에서 압력이 어떻게 달라지는지 설명합니다. 압력은 곡선의 안쪽, 곡률 중심 근처에서 더 높고, 이러한 원심력을 균형 잡기 위해 바깥쪽으로 감소합니다.

압력 차이는 유체의 속도와 곡률 반경에 따라 달라집니다. 압력 변화는 거의 직선 유선이 있는 흐름에서는 최소입니다. 그러나 압력 차이는 소용돌이, 파이프 굽힘 또는 날카로운 구조물 주변과 같이 급격하게 구부러진 흐름에서 상당해집니다. 이 효과는 다음과 같이 표현됩니다.

<img alt="Equation 1" src="/files/ftp_upload/18034/18034_Equation_1.svg" style="text-align: center; height: 30px;">

이 관계를 통합하고 흐름이 안정적이고, 점성이 없으며, 압축 불가능하다고 가정하면 유선에 수직인 베르누이 방정식이 도출됩니다.

<img alt="Equation 2" src="/files/ftp_upload/18034/18034_Equation_2.svg" style="text-align: center; height: 30px;">

방류로 및 곡선 채널과 같은 수력 구조물은 고속 흐름에서 구조적 무결성을 보장하기 위해 정확한 압력 예측에 의존합니다. 마찬가지로 압력 계산은 과도한 힘으로 인한 고장을 방지하기 위해 굽은 부분이 있는 파이프 시스템의 설계를 안내합니다. 이 개념은 건물 및 교량과 같은 토목 구조물 주변의 바람 흐름에도 적용되며, 강풍 시 불안정성이나 손상을 방지하기 위해 곡선 유선으로 인한 압력 차이를 고려해야 합니다.

유선에 수직인 흐름에 대한 베르누이의 방정식은 바깥쪽을 향하는 원심력으로 인해 곡선 유선에서 압력이 어떻게 변하는지 설명합니다.
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bernoulli-s-equation-for-flow-normal-to-a-streamline

Education

교육

JoVE Core

Civil Engineering

토목공학

Unit 1

제1단원

Fluid Dynamics

유체역학

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 variation is very small. In sharply curved flows, the difference becomes much larger. Vortices, pipe bends, and flow around sharp structures are common examples.

This pressure relationship can be written as an equation and then integrated. Under the assumptions of steady, inviscid, and incompressible flow, it leads to Bernoulli's equation normal to the streamline. The result helps predict pressure in systems where flow bends strongly.

Engineers use these pressure calculations in many settings. They help design spillways and curved channels so high-velocity water does not damage hydraulic structures. They also guide pipe system design at bends to reduce failure from large forces. The same ideas apply to wind flow around buildings and bridges, where curved streamlines can create pressure differences that affect stability.

Pressure Changes Across Curved Streamlines

pressure-changes-across-curved-streamlines

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 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 curved streamlines change pressure in fluids, from pipe bends and vortices to spillways, buildings, and bridges in high-velocity flow.

Pressure Changes Across Curved Streamlines | 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 Changes Across Curved Streamlines

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