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

Вода протекает через горизонтальный-образный изгиб трубы. Площадь поперечного сечения потока составляет 0,01 квадратного метра, а величина скорости потока – 15 метров в секунду по всему изгибу.
Давление на входе составляет 0,2 мегапаскаля, а на выходе – 0,16 мегапаскаля.
Цель состоит в том, чтобы найти составляющие анкерной силы в направлениях x и y, необходимые для фиксации изгиба на месте.
Здесь, на входе и выходе, поток идет только в направлении y, что указывает на то, что величина вдоль направления x уменьшается до нуля.
Величина компонентной силы в направлении y может быть получена путем упрощения выражения контрольного объема.
y-компонента скорости положительна на входе и отрицательна на выходе, в то время как массовая скорость потока отрицательна на входе и положительна на выходе. Согласно уравнению непрерывности, массовый поток можно считать постоянным.
С помощью выражения массового потока можно получить составляющую силы в направлении y.

Применение уравнения линейного импульса

Уравнение линейного импульса можно использовать для анализа сил, необходимых для удержания на месте трубы, изогнутой на 180 градусов, с текущей по ней водой. В этом случае вода течет через изгиб с постоянной площадью поперечного сечения 0,01 квадратного метра и скоростью потока 15 метров в секунду. Давление на входе составляет 0,2 мегапаскаля, а давление на выходе — 0,16 мегапаскаля.

 Цель состоит в том, чтобы определить компоненты силы в направлениях x и y, чтобы удерживать трубу на месте. Поскольку поток идет только в направлении y как на входе, так и на выходе, сила в направлении x равна нулю. Компоненту силы в направлении y можно рассчитать, рассмотрев поведение потока в контрольном объеме. Скорость в направлении y положительна на входе и отрицательна на выходе, в то время как массовый расход остается постоянным на протяжении всего изгиба в соответствии с уравнением непрерывности.

 Используя массовый расход и применяя уравнение линейного импульса, можно найти y-компоненту силы крепления. Этот процесс позволяет провести четкий анализ сил, действующих на изгиб трубы из-за протекающего по ней потока воды.

Вода протекает через горизонтальный-образный изгиб трубы. Площадь поперечного сечения потока составляет 0,01 квадратного метра, а величина потока ...

application-of-the-linear-momentum-equation

Education

JoVE Core

Civil Engineering

Unit 1

Раздел 1

Finite Control Volume Analysis

Анализ методом конечных контрольных объемов

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Forces in a 180° Pipe Bend

Description

Transcript