2.2. Forces on Inclined Surfaces

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. So, in statics 2 its static surface forces, we are going to see force on plane areas, okay. We are going to see force on curved surfaces, like this. So, this is plane areas, this is plane, this is curved surface and we also will see the buoyant force, a very small detail of it, but I think this is very necessary. So, I mean, if we are teaching basics of fluid mechanics in this course in the beginning, so, buoyancy is an important concept that everybody must be aware of.

In this chunk, we introduce the concept of fluid statics and specify that it involves the study of surface and body forces. It's important to learn about forces acting on both plane and curved surfaces, as well as buoyant forces, which play a significant role in fluid mechanics. Here, we're setting the stage for understanding how fluids behave under static conditions.

Think of fluid statics like a still body of water in a pond. The forces acting on the surface of the water and the forces acting on any submerged object, like a rock, are what we will study. Just as a buoy floats because of buoyant force, understanding these concepts helps us see how fluids interact with different shapes.

So, we have to see what are the forces on plane areas, that is horizontal surface. So, if you see, this is a figure that shows, you know, a horizontal surface a depth h, okay. So, this h is the vertical distance to free surface and this we what is the P here, okay. And what is the resultant force at the bottom, okay, and P we are assuming 500 kilo Pascal's, okay, that we are going to see. So, what is the force on the bottom of this tank of water actually, what is the net force on the bottom of this tank?

This chunk describes how to determine the forces on horizontal plane surfaces submerged in a fluid. The depth, denoted as 'h', influences the pressure at the bottom of the tank. We often assume a constant pressure value for simple calculations, and the resultant force can be calculated using the area of the surface and the fluid pressure. It introduces the fundamental relationship between pressure and force in fluid statics.

Imagine a swimming pool. The deeper you go underwater, the heavier the water above you feels due to pressure. If you think about the bottom of the pool, the pressure from the water creates a force that pushes down on the floor. This is similar to how we calculate the forces on a horizontal surface in fluid statics.

Another important thing is, we have to learn and revise again, what are the forces on the plane areas or the inclined surface. So, this has to be taken in a little bit of more detail. What will be the direction of the force? Always perpendicular, normal to the plane, right.

In this chunk, we emphasize how to evaluate the forces on inclined surfaces. The force acts perpendicular to the surface at all times, which is a key aspect of fluid mechanics. Understanding this concept is vital for calculating how fluids exert pressure on differently oriented surfaces.

Picture a slanted roof during a rainstorm. The rain hitting the roof exerts a force directly downwards, perpendicular to the roof surface. This analogy helps us visualize the concept of how forces act on inclined surfaces in fluid statics.

To find out the resultant force what should we do? We do gamma h dA integrated over the entire area, right. h here, if we start if we try to write down in terms of Y this can be related to theta as h is y sin theta and gamma is gamma and dA is dA.

This section deals with how to calculate the resultant force acting on an inclined plane by integrating pressure over the area. Here, 'gamma' represents the fluid density times gravitational acceleration, 'h' is the depth, and 'dA' is an infinitesimal area. The relationship with the angle theta introduces trigonometric considerations to account for the incline.

Think of a dam wall which is inclined. The water pressure pushing against the wall increases with depth. To find the total force on the wall, you would calculate the pressure at different depths (the pressure depends on how deep the water is) and integrate this over the entire area of the wall. This is similar to how we calculate forces on inclined surfaces in fluid mechanics.

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. So, this is what the center of pressure is a quick revision for you again.

The 'center of pressure' is an important concept in fluid mechanics. It represents the point on the surface of an object at which the total pressure force can be considered to act. This point does not necessarily coincide with the centroid of the surface area due to varying pressure across the area as depth increases.

Imagine a flagpole in the wind. While the pressure from the wind acts on the entire flag, the pole behaves as if this pressure concentrated at a single point—this point is analogous to the center of pressure. The location of this point is crucial for understanding stability and forces acting on structures.

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