Name: finding force on a curved plate in water
Uploaded: 2023-09-22T11:49:33.000Z
Duration: 1 min 12 s
Channel: JoVE

Wenn eine gekrümmte Platte untergetaucht wird, ändert sich der Druck, der senkrecht zur Platte wirkt, kontinuierlich sowohl in der Größe als auch in der Richtung.
Eine Methode, um die resultierende Kraft und ihre Position zu bestimmen, besteht darin, die horizontalen und vertikalen Komponenten der Kraft zu berechnen.
Stellen Sie dazu die verteilte Last, die auf die Platte wirkt, unter Verwendung der äquivalenten Belastung in zwei Dimensionen dar.
Die Größe der Kraft aufgrund des Gewichts des im Block enthaltenen Wassers wirkt durch den Schwerpunkt des Blocks.
Es gibt auch Druckverteilungen, die durch das Wasser entlang der vertikalen und horizontalen Seiten des Blocks verursacht werden.
Entlang der vertikalen Seite hat die Kraft eine Größe, die der Fläche des Trapezes entspricht, und diese Kraft wirkt durch den Schwerpunkt des Trapezes.
Die Kraft, die entlang der horizontalen Seite verteilt ist, ist konstant und ihre Größe entspricht der Fläche des Rechtecks. Diese Kraft wirkt durch den Schwerpunkt des Rechtecks.
Die Summierung dieser drei Kräfte ergibt die resultierende Kraft. Die Lage des Druckschwerpunkts wird durch Anwendung des Momentenprinzips bestimmt.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik: Statik. Vierzehnte Auflage, New Jersey: Pearson. Abschnitt 9.5, S. 513.</li>
</ol>

flüssigkeitsdruck über einer gekrümmten platte konstanter breite

Fluid Pressure over Curved Plate of Constant Width

Wenn eine gekrümmte Platte konstanter Breite in einem Flüssigkeitsmedium eingetaucht wird, variiert der Druck, der senkrecht zur Platte wirkt, sowohl in Stärke als auch in Richtung kontinuierlich. Die Berechnung der Stärke und Position der resultierenden Kraft an einem Punkt ist oft eine Herausforderung für solche Fälle. Eine Methode zur Bestimmung der resultierenden Kraft und ihrer Position besteht darin, die horizontalen und vertikalen Komponenten der resultierenden Kraft separat zu berechnen. Diese komplexe Berechnung kann vereinfacht werden, indem die auf die Platte wirkende verteilte Belastung durch eine äquivalente Belastung in zwei Dimensionen dargestellt wird. Der erste Schritt dieser Methode besteht darin, das Gewicht der in dem Block enthaltenen Flüssigkeit zu berücksichtigen. Die Größe der Kraft aufgrund des Gewichts des Wassers wird durch das Produkt aus spezifischem Gewicht, Plattendicke und der Fläche des Blocks gegeben. Diese Kraft wirkt durch das Zentroid des Blocks. Zusätzlich gibt es Druckverteilungen entlang der vertikalen und horizontalen Seiten des Blocks. Die Druckverteilung entlang der vertikalen Seite ist trapezförmig, während die Verteilung entlang der horizontalen Seite rechteckig ist. Die auf der vertikalen Seite des Blocks wirkende Kraft hat eine Stärke, die der Fläche des Trapezes entspricht, und wirkt durch dessen Zentroid. Die auf der horizontalen Seite des Blocks wirkende Kraft ist konstant und ihre Stärke entspricht der Fläche des Rechtecks, das durch das Zentroid oder den Mittelpunkt der horizontalen Seite des Rechtecks wirken kann. Wenn die Berechnungen für alle drei Kräfte auf den Block summiert werden, ergibt sich die resultierende Nettokraft auf die gekrümmte Platte. Auch der Standort des Druckmittelpunkts der Flüssigkeit auf der gekrümmten Platte wird durch Anwendung des Momentsprinzips bestimmt. Obwohl diese Methode komplex erscheinen mag, ist es notwendig, sicherzustellen, dass die auf die Platte wirkende Kraft für verschiedene technische Anwendungen genau berechnet wird.

Flüssigkeitsdruck über einer gekrümmten Platte konstanter Breite

Wenn eine gekrümmte Platte konstanter Breite in eine Flüssigkeit getaucht wird, ändert sich der senkrecht zur Platte wirkende Druck kontinuierlich sowohl in der Größe als auch in der ...

fluid-pressure-over-curved-plate-of-constant-width

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Center of Gravity and Centroid

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finding force on a curved plate in water

Fluid pressure on a curved plate of constant width changes in both size and direction. That makes the total force hard to find directly. A common method is to split the force into horizontal and vertical parts and then combine them.

The calculation becomes simpler by replacing the distributed load with an equivalent two-dimensional loading. The first step is to include the weight of the liquid inside the block. That force equals the specific weight of the liquid times the plate thickness and the block area. It acts through the centroid of the block.

Next, the water pressure on the block sides is found. The pressure on the vertical side forms a trapezoidal distribution. Its force equals the area of the trapezoid and acts through the trapezoid centroid. The pressure on the horizontal side is rectangular and constant. Its force equals the area of the rectangle and can act through the rectangle centroid or midpoint of its horizontal side.

After these three forces are added, the net resultant force on the curved plate is known. The center of pressure, which is the point where the liquid force acts, is then found using the principle of moments. This method can seem complex, but it gives an accurate force calculation for many engineering applications.

Finding Force on a Curved Plate in Water

center of gravity

Center of Gravity in Balance and Design

The center of gravity is the point where an object’s weight appears to act. It is the spot used to balance the object most evenly. In mechanics, this point helps explain stability and moments of inertia. The center of gravity does not always sit inside the object’s shape. In some cases, it can lie outside the body. That is why the idea is useful for both simple and more complex shapes. Its location can be found with the principle of moments. The object is divided into very small parts, and...

center of mass

Center of Mass in Motion

The center of mass helps explain how an object moves through space. It is the point where the total mass of an object can be treated as concentrated. This idea applies to objects of different shapes and sizes. The center of mass is related to the center of gravity, but they are not the same. The center of gravity is the point where an object’s weight seems to be concentrated. It can be used to balance an object perfectly. Knowing the center of mass also helps predict motion. When a ball is...

centroid of a body

Finding the Center of a Body

The centroid is the geometric center of a body. It is an important idea in engineering, physics, and mechanics. For many objects, it lies inside the body. A body with holes or cavities can be an exception. For a homogeneous body, the centroid matches the center of mass or the center of gravity. Homogeneous means the material has a uniform density. In that case, the centroid can often be found by balancing the moments of the body’s volume. Symmetry can also help locate the centroid. If a...

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Centroid and Uses of a Paraboloid Shape

The centroid of a paraboloid of revolution is the point where its mass is balanced. A paraboloid of revolution is an axially symmetric surface made by rotating a parabola around its axis. In engineering, this location matters because it helps show how forces spread across the shape. Knowing the centroid can help when building parts that must handle stress and pressure reliably. The paraboloid shape has useful structural properties, including rotational symmetry and strength against stress...

composite bodies

Center of Gravity in Composite Bodies

Composite bodies are made of multiple connected parts that act as one larger object. Each part still has its own weight and center of gravity. To find the center of gravity of the whole body, engineers must account for every part. When the density or specific weight is constant, the center of gravity matches the centroid. The centroid is the geometric center of a shape. This idea is useful when analyzing parts that behave as a single unit. Composite bodies are common in mechanical engineering.

theorems of pappus and guldinus

Surface Area and Volume by Centroid Paths

Pappus and Guldinus theorems help find the surface area and volume of bodies of revolution. A body of revolution is formed when a plane curve or plane area is turned around an axis that does not intersect it. For surface area, a curve is revolved around a non-intersecting axis. A small line element on the curve creates a thin ring as it moves. Adding these ring areas gives the total surface area of the solid. The first theorem says that this surface area equals the length of the generating...

theorems of pappus and guldinus: problem solving

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Pappus and Guldinus Theorems for Surface Area

Pappus and Guldinus's theorems help find the surface area and volume of composite shapes. These rules are useful when a solid is made from simple parts that are hard to measure directly. A cylindrical storage tank with a conical top is one example. The tank can be split into two simple shapes: a cylinder and a cone. To find surface area, the first theorem is used for the solid formed by revolving each generating curve around a non-intersecting axis. The calculation uses the length of the...

resultant of a general distributed loading

resultant-of-a-general-distributed-loading

Finding the Resultant of Distributed Loads

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load. This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel...

fluid pressure

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fluid pressure over flat plate of constant width

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Center of Pressure on a Submerged Plate

Fluid pressure on a submerged flat plate depends on depth and shape. A plate under water experiences pressure acting normal to its surface, and the force is spread across the whole area. For a rectangular plate of constant width, this pressure increases from the top edge to the bottom edge. Because the pressure rises with depth, the loading forms a trapezoidal distribution. The resultant force on the plate comes from the trapezoidal volume of water with a specific weight. The line of action of...

fluid pressure over curved plate of constant width

Fluid pressure on a curved plate of constant width changes in both size and direction. That makes the total force hard to find directly. A common method is to split the force into horizontal and vertical parts and then combine them. The calculation becomes simpler by replacing the distributed load with an equivalent two-dimensional loading. The first step is to include the weight of the liquid inside the block. That force equals the specific weight of the liquid times the plate thickness and...

fluid pressure over flat plate of variable width

fluid-pressure-over-flat-plate-of-variable-width

A submerged flat plate experiences fluid pressure that changes with depth. This pressure can create effects such as drag and buoyancy. To study a flat plate with variable width, the pressure distribution across the plate must be analyzed first. The force on a small strip of the plate is found by multiplying the pressure by the strip’s differential area. The pressure can also be written using the fluid’s specific weight and the depth of that strip below the surface. To find the total, or...

key terms and concepts

Learn how to find the resultant fluid force on a curved plate by splitting it into horizontal and vertical parts, then locating the center of pressure.

Finding Force on a Curved Plate in Water | JoVE K12

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Finding Force on a Curved Plate in Water

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