7. Average Pressure Calculation Example

So, this is a fluid statics 2, I mean, I call it 2, because we are going to do the surface forces and body forces therefore we need to know, what are we going to study in fluid statics 2.

This section introduces fluid statics, specifically focusing on surface forces and body forces. It highlights the importance of understanding how these forces interact with fluids at rest.

Imagine a swimming pool. The water stays at rest, yet it exerts pressure on the walls and the bottom of the pool. Understanding the forces acting in such a scenario is crucial for designing safe and efficient structures.

The force resultant force is going to be the integration of pressure into area, So, p is constant so it comes out and that becomes pressure into area pA, where p is rho gh, okay, this is the gauge pressure.

In fluid statics, the resultant force on a surface due to a fluid is found by integrating the pressure over the area of that surface. Here, pressure (p) is described using the formula p = ρgh, where ρ is the fluid density, g is the acceleration due to gravity, and h is the depth of the fluid above the area. This equation shows that as depth increases, pressure also increases.

Think of how a deep-sea diver feels more pressure the deeper they go into the ocean. This is similar to pressure acting on a submerged surface, where the pressure increases with depth.

So, we have to see what are the forces on the plane areas, that is horizontal surface. ... Therefore, the change in pressure can be equated to rho into a.

This portion emphasizes the calculation of forces on horizontal surfaces submerged in a fluid. It indicates that the overall effect of pressure on a surface is influenced by the shape and orientation of the area relative to the fluid. The change in pressure is explicitly linked to the fluid density and gravitational acceleration.

Imagine a flat soda can placed on a table and how the weight of the liquid inside exerts force downward on the base of the can. The total force across the can's base is determined by the height of the soda and the area of the base.

Another important thing is, we have to learn and revise again, what are the forces on the plane areas or the inclined surface. ... The pressure is no longer constant, because it is not it is not at one elevation it is varying.

When dealing with inclined surfaces, pressures vary with depth, meaning calculations must account for changing pressure across the surface. The force exerted can be found by integrating the varying pressure across the area.

This is similar to the way snow accumulates unevenly on a slanted roof. As snow builds up, the pressure at the base of the snow pile changes based on how deep the snow is at each point, requiring more careful calculations to avoid roof collapse.

The point through which the resultant force acts is called the center of pressure. This is you might have heard in your fluid mechanics class what calculate the center of pressure.

The center of pressure is defined as the point where the total resultant force acts on a submerged surface. It is crucial because it is not the same as the centroid of the area; often, it can be lower due to increasing pressure with depth.

Consider a door submerged underwater. The door's center of pressure plays a vital role in how the door behaves under the water's force, determining how easy or difficult it is to open.

To find out Y R, the moment equilibrium should be done around x axis. ... This is actually the second moment of inertia with respect to the x axis.

To determine the coordinates of the center of pressure, we perform a moment balance around specific axes. This approach involves calculating the moments created by the resultant forces and how they relate to pressures acting across the surface area.

Picture balancing a seesaw. The forces (weights) on either side affect where the pivot point should be. Similarly, determining the coordinates for resultant forces is about finding balance among various pressures.

--