Name: forces in a 180° pipe bend
Uploaded: 2025-02-13T15:43:22.000Z
Duration: 1 min 15 s
Channel: JoVE

물은 수평의 U자형 파이프 굴곡을 통해 흐르고 있습니다. 흐름의 단면적은 0.01 평방 미터이고 유속의 크기는 굽힘 전체에 걸쳐 초당 15 미터입니다.
입구의 압력은 0.2 메가파스칼이고 출구의 압력은 0.16 메가파스칼입니다.
목표는 굽힘을 제자리에 고정하는 데 필요한 x 및 y 방향을 따라 앵커링력의 구성 요소를 찾는 것입니다.
여기서 입구와 출구에서 흐름은 y 방향으로만 흐르며 x 방향의 크기가 0으로 감소함을 나타냅니다.
y 방향의 성분 힘의 크기는 제어 볼륨의 표현을 단순화하여 얻을 수 있습니다.
속도의 y 성분은 유입 시 양수이고 유출 시 음수인 반면, 질량 유량은 유입 시 음수이고 유출 시 양수입니다. 연속성 방정식에 따르면 질량 흐름은 일정한 것으로 간주될 수 있습니다.
질량 흐름의 표현으로, y 방향의 힘의 성분을 얻을 수 있습니다.

선형 운동량 방정식의 적용

선형 운동량 방정식의 적용은 흐르는 물로 180도 파이프 굽힘을 제자리에 고정하는 데 필요한 힘을 분석하는 데 사용할 수 있습니다. 이 경우, 물은 0.01제곱미터의 일정한 단면적과 초당 15미터의 흐름 속도로 굽힘을 통해 흐릅니다. 입구의 압력은 0.2메가파스칼이고 출구의 압력은 0.16메가파스칼입니다.

목표는 파이프를 제자리에 고정하기 위한 x 및 y 방향의 힘 성분을 결정하는 것입니다. 흐름은 입구와 출구 모두에서 y 방향으로만 흐르기 때문에 x 방향의 힘은 0입니다. y 방향의 힘 성분은 제어 볼륨을 가로지르는 흐름 거동을 고려하여 계산할 수 있습니다. y 방향의 속도는 유입에서 양수이고 유출에서 음수이며, 질량 유량은 연속성 방정식에 따라 굽힘 전체에서 일정하게 유지됩니다.

질량 유량을 사용하고 선형 운동량 방정식을 적용하면 앵커링 힘의 y-성분을 찾을 수 있습니다. 이 과정을 통해 물의 흐름으로 인해 파이프 굽힘에 작용하는 힘을 명확하게 분석할 수 있습니다.

물은 수평의 U자형 파이프 굴곡을 통해 흐르고 있습니다. 흐름의 단면적은 0.01 평방 미터이고 흐름의 크기는 ...

application-of-the-linear-momentum-equation

Education

교육

JoVE Core

Civil Engineering

토목공학

Unit 1

제1단원

Finite Control Volume Analysis

유한 제어 체적 해석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Application of the Linear Momentum Equation

forces in a 180° pipe bend

Forces in a 180-degree pipe bend can be found by applying the linear momentum equation to flowing water. The pipe has a constant cross-sectional area of 0.01 square meters, and the water moves at 15 meters per second. The pressure at the inlet is 0.2 megapascals, and the pressure at the outlet is 0.16 megapascals.

The goal is to find the force components in the x and y directions that hold the bend in place. In this case, the flow is only in the y direction at both the entrance and the exit. That means the x-direction force is zero. The y-direction force is found by looking at the flow across the control volume, which is the region being analyzed.

The velocity in the y direction is positive at the inflow and negative at the outflow. The mass flow rate stays constant through the bend according to the continuity equation, which means mass entering equals mass leaving. Using the mass flow rate and the linear momentum equation makes it possible to calculate the anchoring force in the y direction. This gives a clear way to analyze the forces on the pipe bend caused by the water flow.

Forces in a 180° Pipe Bend

conservation of mass in finite cotrol volume

conservation-of-mass-in-finite-cotrol-volume

Continuity Equation for a Fixed Control Volume

The continuity equation describes conservation of mass for a fixed control volume. In fluid mechanics, a system is a collection of the same contents over time, and its mass stays constant. That idea is the starting point for deriving the equation. To analyze flow, a fixed, non-deforming control volume is chosen so it matches the system at one instant. The Reynolds transport theorem then links the system to the control volume. It shows that the rate of change of system mass has two parts: mass...

conservation of mass in fixed, nondeforming control volume

conservation-of-mass-in-fixed-nondeforming-control-volume

Continuity and Velocity in Pipe Flow

Conservation of mass explains how fluid moves through a fixed control volume such as a pipe or duct. In a fixed, nondeforming control volume, the total mass stays constant unless mass enters or leaves through the control surfaces. For steady, incompressible flow, the mass entering the system equals the mass leaving it. A sewer pipe is a useful example of this idea. It can be treated as a fixed control volume with inlet and outlet control surfaces around the flow region. Because the fluid is...

conservation of mass in moving, nondeforming control volume

conservation-of-mass-in-moving-nondeforming-control-volume

Stormwater Detention Basin Mass Balance

Stormwater detention basins use mass balance to manage runoff during heavy rainfall. These basins are especially important in urban areas, where impervious surfaces can increase flooding risk. Engineers use the conservation of mass to track how water enters, is stored in, and leaves the basin. In a detention basin, the control volume is the water inside the basin. Its boundaries are the basin walls, the inflow pipes, and the outflow structures. During a rain event, water comes in through the...

linear momentum in control volume

Momentum Balance for Fluid Control Volumes

Linear momentum balance for a fluid control volume links Newton’s second law to moving fluid. The law says that the rate of change of linear momentum equals the sum of the external forces acting on the system. In a fluid system, this idea helps explain how motion and force are related. A control volume can match the fluid system at a specific moment. When that happens, the forces on the control volume and the system are the same. Reynolds transport theorem explains this connection by splitting...

application of the linear momentum equation

Forces in a 180-degree pipe bend can be found by applying the linear momentum equation to flowing water. The pipe has a constant cross-sectional area of 0.01 square meters, and the water moves at 15 meters per second. The pressure at the inlet is 0.2 megapascals, and the pressure at the outlet is 0.16 megapascals. The goal is to find the force components in the x and y directions that hold the bend in place. In this case, the flow is only in the y direction at both the entrance and the exit.

moment-of-momentum equation

Wind Turbine Torque and Angular Momentum

The moment-of-momentum equation helps explain how wind turbine blades create torque. Torque is the turning effect of a force around an axis. In rotating systems, this equation links the motion of the wind with the force acting on it. The equation begins with Newton's second law for a fluid particle. That law says the rate of change of linear momentum equals the external force on the particle. To find torque, the position of the particle relative to the rotation axis is combined with that force.

conservation of energy in control volume

Turbine Work from Energy Changes

A turbine can turn fluid energy into shaft work when flow passes through a control volume. The fluid enters the turbine at one point and leaves at another. Under steady-flow conditions, there is no energy buildup inside the control volume, so the stored energy does not change with time. This steady-flow setup makes the energy equation simpler. The turbine is treated as doing mechanical work, and heat transfer is taken as negligible, so Q̇ is approximately zero. The flow at the inlet and outlet...

application of the energy equation

Centrifugal Pump Flow Rate Calculation

Centrifugal pump flow rate can be calculated with the energy equation. In this problem, water moves between two reservoirs at different elevations, and the pump provides the energy needed for the transfer. The pump input is 7500 joules per second, the elevation difference is 10 meters, and the head loss from friction and other resistances is 5 meters. Both reservoirs are open to the atmosphere, so the pressure at the inlet and outlet is the same. That means the pressure terms in the energy...

design example: forces in sluice gate

Sluice Gate Water Pressure and Reaction Force

Sluice gates control water flow in channels, reservoirs, and irrigation systems. They work as vertical barriers with an opening that can be raised or lowered. Changing the opening height changes the water velocity and pressure below the gate. The forces on a sluice gate depend on the water depths upstream and downstream, written as z1 and z2. When the gate is closed, the upstream water depth is greater. That creates a strong pressure difference across the gate and a net force toward the...

key terms and concepts

Use the linear momentum equation to find the x and y force components that hold a 180-degree pipe bend in place as water flows through it.

Forces in a 180° Pipe Bend | 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

Forces in a 180° Pipe Bend

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