Name: center of pressure on a submerged plate
Uploaded: 2023-09-22T11:49:33.000Z
Duration: 1 min 2 s
Channel: JoVE

When a flat plate of varying width is submerged in a fluid, the fluid exerts pressure on the plate.
The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate.
The magnitude of the force is equal to the product of the pressure and the differential area, where pressure is proportional to the depth of the strip in the fluid.
Substituting the pressure in the force equation and integrating it gives the resultant force.
Expressing the area integral in terms of the depth of the centroid of the plate gives the resultant force as the product of plate area and the pressure at its centroid. This is equivalent to the volume under the pressure distribution.
The line of action of the resultant force passes through the centroid of this volume and intersects the plate at the center of pressure.
In such cases, the centroid of the plate does not always coincide with the center of pressure of the plate.

fluid pressure over flat plate of variable width

Fluid Pressure over Flat Plate of Variable Width

When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate. Thus, the magnitude of the force is equal to the product of the pressure and the differential area. The pressure can also be expressed in terms of the specific weight of the fluid and the depth of the strip into the fluid.
<img alt="Equilibrium equation p=γz, formula for static physics, mathematical concept illustration." src="/files/ftp_upload/14342/14342_Equation_1.svg" style="text-align: center; height: 11px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
To derive the resultant force acting on the plate, the force acting on each strip of the plate is integrated over the entire plate area.
<img alt="Hydrostatics equation \( F_R = \gamma \int z \, dA \), illustrating force in fluid mechanics." src="/files/ftp_upload/14342/14342_Equations_2.svg" style="text-align: center; height: 15px;" data-altupdatedat="1761830439000" data-alt="Equation 2">
The weighted average of the depths of all points on the plate is used to determine the centroid of the plate. The resultant force acting on the plate is equal to the area of the plate multiplied by the pressure at a depth of its centroid.
<img alt="Shear force equation, \( F_R = \gamma \bar{z} A \), mechanics diagram, physics calculation." src="/files/ftp_upload/14342/14342_Equations_3.svg" style="text-align: center; height: 15px;" data-altupdatedat="1761830439000" data-alt="Equation 3">
The line of action of the resultant force passes through the centroid of the volume under the pressure distribution and intersects the plate at the center of pressure. It is important to note that the centroid of the plate and the center of pressure do not always coincide. The centroid of the plate represents the geometric center of the plate, while the center of pressure represents the point on the plate where the resultant force acts.
The resultant force acting on the plate is equivalent to the weight of the volume of fluid displaced by the plate. This means that the resultant force can also be calculated as the volume under the pressure distribution.

When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and ...

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

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Mechanical Engineering

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Center of Gravity and Centroid

KEY TERMS AND CONCEPTS

center of pressure on a submerged plate

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 resultant, force on the plate, the forces on all strips are integrated over the full area.

The centroid of the plate is the weighted average depth of its points. The resultant force equals the plate area times the pressure at the centroid depth. The line of action of this force passes through the centroid of the pressure volume and meets the plate at the center of pressure.

The centroid of the plate and the center of pressure do not always match. The centroid is the geometric center of the plate, while the center of pressure is the point where the resultant force acts. The resultant force is also equivalent to the weight of the fluid volume displaced by the plate. It can therefore be found from the volume under the pressure distribution.

Center of Pressure on a Submerged Plate

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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 fluid pressure on a submerged flat plate creates a resultant force, and how centroid depth and center of pressure are used to locate it.

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Center of Pressure on a Submerged Plate

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