In this question,how is the pressure at point A equal to the pressure at point C?Plz explain it clearly
Answers
Why is the pressure in point B equal to the pressure in point A?
The pressure of the liquid will be evenly distributed across the bottom of the container. Pressure is force per unit area, and any liquid will find an equilibrium where pressures are equal, so for a given weight of liquid and containers with equal bottom surface areas, pressure will always be the same. If we assume there is a gallon of water in each of these container, the pressure of that one gallon of water will be evenly distributed across the bottom of each container.
This is easy to see in the simpler case (A). The water in that container will naturally find an equilibrium, so that the water is the same height across the entire breadth of the container. That means that any column of water above any point is the same height, and by Pascal’s law exerts the same downward pressure at that particular point of the base.
In the more complex case (B), however, if the water overfills the lower part and stretches up into the neck of container, it still has the same downward pressure everywhere — same weight of water distributed across the same surface area — but the forces involved have changed. In this container the water is prevented from finding its natural equilibrium by the shape of the container; the upper edge of the non-neck part of the container is exerting a downward force that keeps the water from finding that equilibrium. A column of water on the very left (under the neck) might be taller and thus appear to exert a greater downward force, but a column of water to the right of the container adds the downward force of the non-neck upper edge to the smaller weight of water; in fact, the downward force of the non-neck edge actually supports and lifts the water in the neck, receiving some of the pressure it might exert on the base. When we add all these forces together, we find that the pressure exerted on the base is still the same everywhere; the forces may be distributed differently in B than in A, But the water will always find an equilibrium that distributes its weight evenly across the bottom.
Note, however, that the center of mass of the containers will be different; container B might tip over more easily than container A. But that is a separate issue.
If you don’t believe that this downward force exists, imaging poking a hole in the top of container B somewhere to the right of the neck. Obviously we would see a spout of water shooting up as the water in the neck found an opportunity to equalize with the rest of the water. The top edge of the container is applying the force that keeps that spout and that equalization from happening.
If you want to apply Pascal’s law in strangely shaped containers like B, then keep in mind that Pascal’s law really applies to the average height of the water. If you average out the heights of all the columns of water in container B, they will naturally equal the equilibrium height of water in container A.