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

Quando uma placa curva é submersa, a pressão que age normal à placa muda continuamente tanto em magnitude quanto em direção.
Um método para determinar a força resultante e sua localização envolve o cálculo dos componentes horizontal e vertical da força.
Para isso, represente a carga distribuída atuando na placa utilizando a carga equivalente em duas dimensões.
A magnitude da força devido ao peso da água contida no bloco atua através do centróide do bloco.
Existem também distribuições de pressão causadas pela água ao longo dos lados vertical e horizontal do bloco.
Ao longo do lado vertical, a força tem uma magnitude igual à área do trapézio, e essa força atua através do centróide do trapézio.
A força distribuída ao longo do lado horizontal é constante e sua magnitude é igual à área do retângulo. Essa força atua através do centróide do retângulo.
A soma dessas três forças produz a força resultante. A localização do centro de pressão é determinada pela aplicação do princípio dos momentos.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica: Estática. Décima quarta edição, Nova Jersey: Pearson. Seção 9.5, pp. 513.</li>
</ol>

pressão fluida sobre uma placa curva de largura constante

Fluid Pressure over Curved Plate of Constant Width

Quando uma placa curva de largura constante é submersa em um líquido, a pressão atuando normal à placa varia continuamente tanto em magnitude quanto em direção. Calcular a magnitude e a localização da força resultante em um ponto é frequentemente desafiador para tais casos. Um dos métodos para determinar a força resultante e sua localização envolve calcular separadamente as componentes horizontal e vertical da força resultante. Esse cálculo complexo pode ser simplificado representando o carregamento distribuído atuando na placa pelo carregamento equivalente em duas dimensões.

O primeiro passo nesse método é levar em conta o peso do líquido contido dentro do bloco. A magnitude da força devido ao peso da água é dada pelo produto da densidade, espessura da placa e área do bloco. Essa força atua através do centróide do bloco. Além disso, existem distribuições de pressão causadas pela água ao longo dos lados vertical e horizontal do bloco. A distribuição de pressão ao longo do lado vertical é trapezoidal, enquanto a distribuição ao longo do lado horizontal é retangular.

A força atuando ao longo do lado vertical do bloco tem uma magnitude igual à área do trapézio e atua através de seu centróide. Enquanto isso, a força atuando ao longo do lado horizontal do bloco é constante, com a magnitude da força sendo igual à área do retângulo, que pode atuar através do centróide ou ponto médio do lado horizontal do retângulo.

Uma vez que os cálculos para todas as três forças sobre o bloco são somados, isso dá a força resultante líquida atuando na placa curva. Além disso, a localização do centro de pressão do líquido atuando na placa curva é determinada aplicando o princípio dos momentos. Embora esse método possa parecer complexo, é necessário garantir que a força atuando na placa seja calculada com precisão para várias aplicações em engenharia.

Pressão fluida sobre uma placa curva de largura constante

Quando uma placa curva de largura constante é submersa em um líquido, a pressão que atua normal à placa varia continuamente em magnitude e ...

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

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Center of Gravity and Centroid

Centro de Gravidade e Centroide

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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...

centroid of a body: problem solving

Centroid of a Quarter Circle Wire

The centroid of a quarter circle wire shows how balance points can be found for curved shapes. In physics and engineering, the centroid helps describe stability, balance, and design. For a thin wire bent into a quarter circular arc, the goal is to find the centroid coordinates of the arc itself. Polar coordinates are used to solve this centroid problem. The wire is divided into small differential elements, and each element has a length equal to the radius times the differential angle. The x-...

centroid for the paraboloid of revolution

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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

theorems-of-pappus-and-guldinus-problem-solving

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...

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Fluid pressure changes with depth in liquids used in engineering systems. It matters in hydraulic systems, pumps, and valves, where the forces from moving and resting fluid must be considered to prevent damage or failure. For a fluid at rest, Pascal’s law says the pressure is equal in all directions. Pressure is force per unit area. Its size depends on the fluid’s specific weight, or mass density, and on how deep the measurement point is below the fluid surface. This relationship can be...

fluid pressure over flat plate of constant width

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

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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mechanical engineering

Finding Force on a Curved Plate in Water

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