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

湾曲したプレートが水没すると、プレートに垂直に作用する圧力は、大きさと方向の両方で絶えず変化します。
合力とその位置を決定する方法の 1 つは、力の水平成分と垂直成分を計算することです。
このためには、プレートに作用する分布荷重を、2次元の等価荷重を使用して表します。
ブロック内に含まれる水の重量による力の大きさは、ブロックの重心を通じて作用します。
また、ブロックの垂直面と水平面に沿った水による圧力分布もあります。
垂直方向の辺に沿って、力は台形の面積に等しい大きさを持ち、この力は台形の重心を介して作用します。
水平辺に沿って分布する力は一定であり、その大きさは長方形の面積に等しくなります。この力は、四角形の重心を介して作用します。
これら 3 つの力を合計すると、合力が得られます。圧力の中心の位置は、モーメントの原理を適用することによって決定されます。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス:静力学。第14版、ニュージャージー州:ピアソン。セクション9.5、513ページ。</li>
</ol>

一定幅の曲面板にかかる流体圧力

Fluid Pressure over Curved Plate of Constant Width

曲面板の幅が一定の場合、液体中に浸されているとき、板に対して垂直方向にかかる圧力は、強度と方向の両方にわたって連続的に変化します。点における結果力の大きさと位置を計算することは、このような場合にはしばしば難しい課題となります。結果力とその位置を決定するための方法の一つは、結果力の水平成分と垂直成分を別々に計算することです。この複雑な計算は、板にかかる分布荷重を2次元の等価荷重によって表現することによって簡略化することができます。

この方法の最初のステップは、ブロック内に含まれる液体の重さを考慮することです。水の重さによる力の大きさは、比重、板の厚さ、およびブロックの面積の積で与えられます。この力は、ブロックの重心を通って作用します。さらに、ブロックによって引き起こされる垂直および水平側面に沿った圧力分布があります。垂直側面に沿った圧力分布は台形状であり、水平側面に沿った圧力分布は長方形状です。

ブロックに沿って働く力は、台形の面積と同じ大きさで、その重心を通って作用します。一方で、ブロックに沿って働く力は一定であり、その大きさは長方形の面積と同じであり、長方形の水平側面の重心または中点を通って作用することができます。

ブロックにかかるこれら３つの力を合計することで、曲面板に対して作用するネット結果力が得られます。また、曲面板にかかる液体の圧力の中央位置は、モーメントの原理を適用することによって決定されます。この方法は複雑に見えるかもしれませんが、さまざまな機械工学の応用において正確に板にかかる力を計算するためには必要です。

一定の幅の湾曲したプレートを液体に沈めると、プレートに垂直に作用する圧力は、大きさと...

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

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Center of Gravity and Centroid

重心と図心

KEY TERMS AND CONCEPTS

主要用語と概念

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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Centroid and Uses of a Paraboloid Shape

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theorems of pappus and guldinus

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theorems of pappus and guldinus: problem solving

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Pappus and Guldinus Theorems for Surface Area

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Finding the Resultant of Distributed Loads

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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...

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

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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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