The magnitude of total pressure and centre of pressure is independent on the shape of the submerged plane surface

The given statement is False. The magnitude of total pressure and the position of the center of pressure are indeed dependent on the shape of the submerged plane surface. Let's understand why this is the case.

Magnitude of Total Pressure
The magnitude of total pressure on a submerged plane surface is influenced by several factors, including:
1. Depth of the fluid: The deeper the fluid, the greater the pressure exerted on the surface.
2. Density of the fluid: The denser the fluid, the greater the pressure exerted on the surface.
3. Acceleration due to gravity: The greater the acceleration due to gravity, the greater the pressure exerted on the surface.

Therefore, the magnitude of total pressure is not solely determined by the shape of the submerged plane surface. It is influenced by the depth, density, and acceleration due to gravity.

Center of Pressure
The center of pressure is the point through which the resultant force of the fluid pressure acts on the submerged surface. It is determined by the shape of the surface and the distribution of pressure on it.

The center of pressure is not necessarily located at the centroid of the surface. It depends on the shape of the surface and the distribution of pressure. For example, if the pressure distribution on the surface is non-uniform, the center of pressure will not coincide with the centroid.

Examples
To illustrate the dependence of total pressure and center of pressure on the shape of the submerged plane surface, consider the following examples:

1. Flat Surface vs. Curved Surface: For a flat surface, the total pressure is evenly distributed. In contrast, for a curved surface, the total pressure varies along the surface due to the curvature. Therefore, the magnitude of total pressure differs between these two shapes.

2. Symmetrical vs. Asymmetrical Shape: In a symmetrical shape, the center of pressure coincides with the centroid. However, in an asymmetrical shape, the center of pressure may be offset from the centroid depending on the pressure distribution.

In conclusion, the magnitude of total pressure and the position of the center of pressure are indeed dependent on the shape of the submerged plane surface. Therefore, the given statement that the magnitude of total pressure and center of pressure are independent of the shape of the submerged plane surface is false.