Name: fluid head profiles in pipes and channels
Uploaded: 2025-02-13T15:43:14.000Z
Duration: 1 min 27 s
Channel: JoVE

파이프를 통해 흐르는 유체에서 에너지 라인은 압력, 속도 및 고도 수두를 결합한 유체의 총 에너지를 나타냅니다.
대조적으로, 유압 구배선은 속도를 제외한 압력과 고도 수두의 합만 표시합니다.
이 선은 유체 흐름 시스템의 에너지와 압력의 분포를 시각적으로 나타냅니다.
이 선들 사이의 차이는 속도정(velocity head)이며, 에너지선은 흐름 동안 항상 수력 구배선(hydraulic gradient line)보다 큽니다.
정지 유체에서는 에너지 선과 수력 구배 선이 일치합니다.
양압은 유압 구배선이 파이프 위에 있을 때 발생하고, 음압은 아래에 있을 때 발생하며, 잠재적으로 캐비테이션과 같은 문제를 일으킬 수 있습니다.
파이프 고도 위로 수리적 구배를 유지하면 공기 유입 및 파이프라인 구조적 결함과 같은 문제를 방지할 수 있습니다.
사이펀 시스템에서 이러한 라인을 이해하면 중단 없는 흐름을 유지할 수 있는 적절한 압력이 보장됩니다.
이러한 라인을 모니터링하면 누수 또는 막힘을 감지하고 수격 현상이나 역류를 방지할 수 있는 시스템을 설계하는 데 도움이 됩니다.
피토 튜브 및 피에조미터와 같은 기기는 이러한 라인을 측정하여 토목 공학에서 유압 시스템의 설계 및 분석을 지원합니다.

에너지 라인과 유압 기울기 라인

Energy Line and Hydraulic Gradient Line

베르누이 방정식에 따르면 에너지 라인(EL)과 유압 기울기 라인(HGL)은 유체 흐름 시스템에서 에너지 분포를 그래픽으로 표현합니다. 정상적이고 비압축성이며 비점성 흐름의 경우 베르누이 방정식은 다음과 같이 표현됩니다.

<img alt="Equation 1" src="/files/ftp_upload/18039/18039_Equation_1.svg" style="text-align: center; height: 34px;">

여기서 H는 총 수두, p/γ​는 압력 수두, V^2/2g​는 속도 수두, z는 고도 수두입니다.

에너지 라인(EL)은 흐름에서 사용 가능한 총 수두를 나타냅니다. 기준선 위에 위치하며 세 가지 에너지 구성 요소를 모두 포함합니다. 이상적인 조건에서는 총 에너지가 유선을 따라 변하지 않으므로 수평을 유지합니다. EL의 고도는 정체 압력을 포착하고 총 에너지 값을 제공하는 피토 관을 사용하여 측정할 수 있습니다.

유압 기울기 라인(HGL)은 속도 수두를 제외한 압전 수두(p/γ+ z)를 나타냅니다. EL보다 수직 거리만큼 아래에 있으며, 이는 속도 수두(V^2/2g​)와 같습니다. HGL은 시스템 내의 압력 변화를 나타냅니다. 가압 파이프라인에서는 파이프 위에 있는 반면, 개방 채널 흐름에서는 수면과 일치합니다.

유체 속도 또는 파이프 직경이 변경되면 HGL 고도가 그에 따라 조정됩니다. 파이프 출구에서 압력 수두는 0이므로 HGL이 고도 수두와 일치합니다. 탱크에서 나오는 안정적이고 점성이 없는 흐름의 경우 EL과 HGL은 수평이며 일정한 수두와 대기 출구 압력을 반영합니다.

실제 적용에는 종종 점성 효과와 손실이 통합되어 EL과 HGL을 왜곡합니다. 이러한 개념은 유체 시스템에서 압력과 에너지 분포를 분석하는 데 중요합니다.

파이프를 통해 흐르는 유체에서 에너지 라인은 압력, 속도 및 고도 수두를 결합한 유체의 총 에너지를 나타냅니다.
안으로...

Education

교육

JoVE Core

Civil Engineering

토목공학

Unit 1

제1단원

Fluid Dynamics

유체역학

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 along a streamline. A Pitot tube can be used to measure the EL by capturing stagnation pressure and giving the total energy value.

The hydraulic grade line (HGL) shows the piezometric head, which is the pressure head plus the elevation head. It does not include the velocity head. The HGL lies below the EL by a vertical distance equal to the velocity head, V²/2g. It helps show pressure changes in the system.

In a pressurized pipeline, the HGL is usually above the pipe. In open-channel flow, it matches the water surface. If fluid velocity changes or the pipe diameter changes, the HGL position changes too. At a pipe outlet, pressure head is zero, so the HGL meets the elevation head.

For steady, inviscid flow from a tank, both the EL and HGL are horizontal. This reflects constant head and atmospheric pressure at the outlet. In real systems, viscous effects and losses can bend these lines. These ideas are important for reading pressure and energy in fluid systems.

Fluid Head Profiles in Pipes and Channels

fluid-head-profiles-in-pipes-and-channels

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

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 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 the energy line and hydraulic grade line show total head, pressure changes, and velocity effects in pipes, tanks, and open channels.

Fluid Head Profiles in Pipes and Channels | 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

Fluid Head Profiles in Pipes and Channels

Description

Transcript