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

Quando una piastra curva viene sommersa, la pressione che agisce normale alla piastra cambia continuamente sia in grandezza che in direzione.
Un metodo per determinare la forza risultante e la sua posizione prevede il calcolo delle componenti orizzontali e verticali della forza.
Per questo, rappresentare il carico distribuito che agisce sulla piastra utilizzando il carico equivalente in due dimensioni.
L'entità della forza dovuta al peso dell'acqua contenuta all'interno del blocco agisce attraverso il baricentro del blocco.
Ci sono anche distribuzioni di pressione causate dall'acqua lungo i lati verticali e orizzontali del blocco.
Lungo il lato verticale, la forza ha un'entità pari all'area del trapezio e questa forza agisce attraverso il baricentro del trapezio.
La forza distribuita lungo il lato orizzontale è costante e la sua grandezza è uguale all'area del rettangolo. Questa forza agisce attraverso il baricentro del rettangolo.
Sommando queste tre forze si ottiene la forza risultante. La posizione del centro di pressione è determinata applicando il principio dei momenti.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica: Statica. Quattordicesima edizione, New Jersey: Pearson. Sezione 9.5, pp. 513.</li>
</ol>

pressione del fluido su una lastra curva di larghezza costante

Fluid Pressure over Curved Plate of Constant Width

Quando una lastra curva di larghezza costante è immersa in un liquido, la pressione agente normalmente sulla lastra varia continuamente sia in magnitudine che in direzione. Calcolare la magnitudine e la posizione della forza risultante in un punto è spesso complesso per tali casi. Uno dei metodi per determinare la forza risultante e la sua posizione consiste nel calcolare separatamente le componenti orizzontali e verticali della forza risultante. Questo calcolo complesso può essere semplificato rappresentando il carico distribuito agente sulla lastra, tramite il carico equivalente in due dimensioni.

Il primo passaggio in questo metodo consiste nel considerare il peso del liquido contenuto nel blocco. La magnitudine della forza dovuta al peso dell'acqua è data dal prodotto fra peso specifico, spessore della lastra e area del blocco. Questa forza agisce attraverso il baricentro del blocco. Inoltre, ci sono distribuzioni di pressione causate dall'acqua lungo i lati verticali e orizzontali del blocco. La distribuzione di pressione lungo il lato verticale è trapezoidale, mentre la distribuzione lungo il lato orizzontale è rettangolare.

La forza agente lungo il lato verticale del blocco ha una magnitudine uguale all'area del trapezio e agisce attraverso il suo baricentro. Nel frattempo, la forza agente lungo il lato orizzontale del blocco è costante, con la magnitudine della forza uguale all'area del rettangolo, che può agire attraverso il baricentro o il punto medio del lato orizzontale del rettangolo.

Una volta che i calcoli per tutte e tre le forze sul blocco vengono sommati, si ottiene la forza risultante netta che agisce sulla lastra curva. Inoltre, è determinata la posizione del centro di pressione del liquido che agisce sulla lastra curva, applicando il principio dei momenti. Sebbene questo metodo possa sembrare complesso, è necessario assicurarsi che la forza agente sulla lastra venga calcolata con precisione per varie applicazioni ingegneristiche.

Pressione del fluido su una lastra curva di larghezza costante

Quando una piastra curva di larghezza costante viene immersa in un liquido, la pressione che agisce normale alla piastra varia continuamente sia in grandezza che in ...

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

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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...

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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...

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Center of Pressure on a Submerged Plate

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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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