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

When a curved plate is submerged, the pressure acting normal to the plate changes continually both in magnitude and direction.
One method to determine the resultant force and its location involves calculating the horizontal and vertical components of the force.
For this, represent the distributed loading acting on the plate using the equivalent loading in two dimensions.
The magnitude of the force due to the weight of the water contained within the block acts through the centroid of the block.
There are also pressure distributions caused by the water along the vertical and horizontal sides of the block.
Along the vertical side, the force has a magnitude equal to the trapezoid&#39;s area, and this force acts through the centroid of the trapezoid.
The force distributed along the horizontal side is constant, and its magnitude is equal to the area of the rectangle. This force acts through the centroid of the rectangle.
Summing these three forces yields the resultant force. The location of the center of pressure is determined by applying the principle of moments.

fluid pressure over curved plate of constant width

Fluid Pressure over Curved Plate of Constant Width

When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the distributed loading acting on the plate by the equivalent loading in two dimensions.
The first step in this method is accounting for the weight of the liquid contained within the block. The magnitude of force due to the weight of the water is given by the product of specific weight, plate thickness and the block area. This force acts through the centroid of the block. In addition, there are pressure distributions caused by the water along the vertical and horizontal sides of the block. The pressure distribution along the vertical side is trapezoidal, while the distribution along the horizontal side is rectangular.
The force acting along the vertical side of the block has a magnitude equal to the area of the trapezoid and acts through its centroid. Meanwhile, the force acting along the horizontal side of the block is constant, with the force&#39;s magnitude being equal to the area of the rectangle, which can act through the centroid or midpoint of the rectangle&#39;s horizontal side.
Once calculations for all three forces on the block are summed, it gives the net resultant force acting on the curved plate. Also, the location of the center of pressure of the liquid acting on the curved plate is determined by applying the principle of moments. While this method may seem complex, it is necessary to ensure that the force acting on the plate is calculated accurately for various engineering applications.

When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and ...

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

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Center of Gravity and Centroid

KEY TERMS AND CONCEPTS

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

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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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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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