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

Wasser fließt durch einen horizontalen, U-förmigen Rohrbogen. Die Querschnittsfläche der Strömung beträgt 0,01 Quadratmeter, und die Größe der Strömungsgeschwindigkeit beträgt 15 Meter pro Sekunde in der gesamten Kurve.
Der Druck am Eingang beträgt 0,2 Megapascal und der Druck am Ausgang 0,16 Megapascal.
Ziel ist es, die Komponenten der Verankerungskraft entlang der x- und y-Richtung zu finden, die zur Sicherung der Biegung erforderlich sind.
Hier, am Ein- und Ausgang, verläuft die Strömung nur in y-Richtung, was darauf hindeutet, dass sich die Größe entlang der x-Richtung auf Null reduziert.
Die Größe der Komponentenkraft in y-Richtung kann durch Vereinfachung des Ausdrucks des Kontrollvolumens ermittelt werden.
Die y-Komponente der Geschwindigkeit ist am Zufluss positiv und am Ausfluss negativ, während der Massenstrom am Zufluss negativ und am Ausfluss positiv ist. Nach der Durchgangsgleichung kann der Massenstrom als konstant angesehen werden.
Mit der Angabe des Massenstroms kann die Kraftkomponente in y-Richtung erhalten werden.

anwendung der linearen impulsgleichung

Mithilfe der linearen Impulsgleichung lassen sich die Kräfte analysieren, die erforderlich sind, um einen 180-Grad-Rohrbogen mit fließendem Wasser an Ort und Stelle zu halten. In diesem Fall fließt Wasser mit einem konstanten Querschnitt von 0,01 Quadratmetern und einer Fließgeschwindigkeit von 15 Metern pro Sekunde durch den Bogen. Der Druck am Eingang beträgt 0,2 Megapascal und der Druck am Ausgang 0,16 Megapascal.

Ziel ist es, die Kraftkomponenten in x- und y-Richtung zu bestimmen, um das Rohr an Ort und Stelle zu halten. Da der Fluss sowohl am Eingang als auch am Ausgang nur in y-Richtung erfolgt, ist die Kraft in x-Richtung null. Die Kraftkomponente in y-Richtung kann berechnet werden, indem das Fließverhalten über das Kontrollvolumen berücksichtigt wird. Die Geschwindigkeit in y-Richtung ist beim Zufluss positiv und beim Abfluss negativ, während die Massendurchflussrate gemäß der Kontinuitätsgleichung im gesamten Bogen konstant bleibt.

Mithilfe des Massenstroms und der Anwendung der linearen Impulsgleichung kann die y-Komponente der Verankerungskraft ermittelt werden. Dieses Verfahren ermöglicht eine klare Analyse der durch den Wasserfluss auf den Rohrbogen wirkenden Kräfte.

Anwendung der linearen Impulsgleichung

Wasser fließt durch einen horizontalen, U-förmigen Rohrbogen. Die Querschnittsfläche der Strömung beträgt 0,01 Quadratmeter, und die Größe der Strömung ...

application-of-the-linear-momentum-equation

Education

Lehre

JoVE Core

Civil Engineering

Bauingenieurwesen

Unit 1

Einheit 1

Finite Control Volume Analysis

Finite-Kontrollvolumen-Analyse

KEY TERMS AND CONCEPTS

WICHTIGE BEGRIFFE UND KONZEPTE

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

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conservation of mass in fixed, nondeforming control volume

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

Continuity and Velocity in Pipe Flow

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conservation of mass in moving, nondeforming control volume

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

Stormwater Detention Basin Mass Balance

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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

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