2.1. Horizontal Surface Forces

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.

In this section, the topic of fluid statics is introduced, particularly focusing on the study of surface forces and body forces. The reference to 'fluid statics 2' indicates a continuation or deeper dive into previously covered topics.

Think of fluid statics like understanding how water behaves in different situations, like a bathtub versus an ocean. Both have forces at play, and knowing how to measure them is crucial to ensure safety and functionality.

In statics 2, its static surface forces, we are going to see force on plane areas... So, we have to see what are the forces on plane areas, that is horizontal surface.

This chunk discusses the focus on forces acting upon plane surfaces within fluids, specifically horizontal surfaces. Understanding these forces is vital as they play an essential role in many applications, such as designing tanks and dams.

Imagine a flat swimming pool surface. The water pressure pushes down on the surface equally, and illustrations like these help us understand how much force is acting on a horizontal area.

If you see, this is a figure that shows a horizontal surface at a depth h... and we also will see the buoyant force, a very small detail of it, but I think this is very necessary.

Here, the relationship between pressure and depth is described. Pressure increases with depth, represented by the equation P = ρgh, where ρ is density, g is gravity, and h is the depth. Buoyant forces due to various depths are also highlighted.

Think of diving into a pool. As you go deeper, you feel more pressure on your ears. This is similar to how pressure increases in fluids with depth.

The resultant force is going to be the integration of pressure into area... So, F = ∫pdA = pA.

This section covers how to calculate the resultant force acting on a submerged surface. By integrating the pressure over the area, you arrive at the overall force acting on that area, which is critical in engineering applications.

Imagine pouring water into a rectangular tank. The weight of that water exerts force down on the bottom of the tank; calculating this helps in determining how strong the tank needs to be.

Another important thing is...the direction of the force? Always perpendicular, normal to the plane.

It is emphasized that forces acting on surfaces are normal to the plane of the surface. This principle is foundational in understanding how structures hold up against fluid forces.

If you push on a door, you apply force directly towards it. Water pushes on a surface in a similar way; understanding this force is key to ensuring structures do not collapse.

Here, the pressure is no longer constant, because it is not at one elevation it is varying... we have to do the moment balance to find the line of action.

Pressure varies with depth due to the weight of the fluid above any given point. This chunk introduces the concept of finding the line of action through moment balance, as the resultant force's application point is not straightforward in cases of variable pressure.

Imagine holding a balloon underwater. The deeper you go, the more the balloon compresses, illustrating changing pressure. Calculating the moment of each tiny force helps determine where the overall force will act.

The point through which the resultant force acts is called the center of pressure... The center of pressure is not at the centroid.

The center of pressure is identified as the point where the resultant force can be assumed to act. It’s important to note that this is not the same as the centroid due to increasing pressure at greater depths.

Imagine a seesaw; the balance point (center of pressure) might not be at its middle (centroid) due to uneven weights on either side. This is similar with how fluids behave.

We must also be able to find out what corresponding yR and xR is... the moment equilibrium should be done around x axis.

To find the coordinates of the center of pressure (yR and xR), equations involving moments around axes are used. This process is crucial for accurately predicting how forces will act on submerged surfaces.

Think of balancing a long stick at its center. If weights are added unevenly, you must calculate the shifts in balance (yR and xR) to prevent it from tipping over.

So, this is just explaining you that... I will just erase because this was just to you know.

The final insights reinforce understanding about the determination of resultant forces and their locations in relation to submerged areas, emphasizing the applications in real-world design and engineering.

When designing a bridge over water, engineers must know where these forces act to ensure stability, similar to knowing how to distribute weight on a tightrope.

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