Hydrostatics - Why is the pressure force the same?

In summary, the pressure at the bottom of a container is equal to the weight of the liquid divided by the area. In the case of a cone and a cylinder with the same depth of water, the pressure at the bottom is the same. However, the weight of the liquid may not be the same in both containers, leading to a difference in weight when placed on scales. This is due to the fact that pressure acts in all directions and there may be additional forces at play, such as the force exerted by the conical surface of the cone.
  • #1
theBEAST
364
0

Homework Statement


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The Attempt at a Solution


So for the cone there is the weight of the liquid (W), the upward force (F_y), and the pressure force acting on the bottom (F_v):
F_v = W - F_y

For the cylinder there is only the weight of the liquid and the pressure force acting on the bottom:
F_v = W

So how are they the same?
 
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  • #2
Pressure = force/area
so
force = pressure * area

At the bottom of each container the depth of water is the same so the pressure must be the same. The area is the same so the force must be the same.

If they were placed on scales they would obviously weigh differently yet the force on the bottom is the same, hence the paradox.

To resolve it remember that pressure acts in all directions.
 
  • #3
sorry,but a doubt of my own from here.

i know that these 2 containers should weigh different.but shouldn't the contact force be equal to the weight of the body and since the force at the bottom is the same ,shouldn't the weight be same?
i think that i might be wrong somewhere but can't figure out what.
 
  • #4
In the case of the cone, is there a force acting on the conical surface? What is the direction of this force? Is the conical surface of the cone exerting a force on the water? What is the direction of this force?
 
  • #5


The reason why the pressure force is the same in both cases is because it is determined by the weight of the liquid above it. In both the cone and the cylinder, the pressure at the bottom is equal to the weight of the liquid above it divided by the area of the bottom surface. This means that as long as the weight of the liquid and the area of the bottom surface are the same, the pressure force will also be the same. This is known as Pascal's principle, which states that the pressure at any point in a confined fluid is transmitted equally in all directions. Therefore, the pressure force at the bottom of both the cone and the cylinder will be the same, regardless of their different shapes or volumes. This principle is important in understanding the behavior of fluids and is utilized in various applications, such as hydraulic systems and water pressure calculations.
 

1. What is hydrostatics?

Hydrostatics is the study of fluids at rest and the forces at work within them. It is a branch of fluid mechanics that focuses on the pressure, density, and motion of liquids and gases that are not in motion.

2. Why is the pressure force the same in hydrostatics?

In hydrostatics, pressure is the force per unit area exerted by a fluid on its surroundings. This force is the same at all points within a fluid at rest because the fluid is in equilibrium, meaning there is no net force acting on it. Therefore, the pressure force must be balanced and equal at all points.

3. How is pressure force related to depth in hydrostatics?

According to Pascal's principle, the pressure of a fluid at any depth is directly proportional to the density of the fluid and the depth. This means that as depth increases, so does pressure force. This relationship is important in understanding the behavior of fluids in different environments, such as in deep sea or high altitude conditions.

4. How does hydrostatic pressure differ from atmospheric pressure?

Hydrostatic pressure is the pressure exerted by a fluid at rest, while atmospheric pressure is the pressure exerted by the weight of the Earth's atmosphere. The main difference is that hydrostatic pressure is caused by the weight of a fluid, while atmospheric pressure is caused by the weight of the gases in the atmosphere.

5. What are some real-world applications of hydrostatics?

Hydrostatics has many practical applications in everyday life, such as in hydraulic systems, scuba diving, and weather forecasting. It is also essential in engineering and construction, as it helps to understand the behavior of fluids in pipes, dams, and other structures. Additionally, hydrostatic principles are used in medical devices, such as blood pressure monitors, and in the design of ships and submarines.

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